text:
\section{Introduction}

During Phase $\mathrm{II}$ of the drug development process it is common to have several competing treatments, these may be different doses of the same drug or entirely different treatment regimes. \cite{jaki2016designing} note that, given the high failure rate and cost of Phase $\mathrm{III}$ trials, it is key to that careful consideration be given to which treatments should be carried forward for further study. Multi-arm multi-stage trials (MAMS) \citep{royston2003novel,jaki2013considerations,wason2012optimal} compare several experimental treatments with a common control allowing for the efficient selection of appropriate treatments \citep{jaki2015multi}.\\

MAMS trials reduce the expected number of patients by dropping treatments that are demonstrated to be ineffective/showing lack of promise or stopping the trial altogether if efficacy has been demonstrated. Given the multiple hypotheses and highly adaptive nature of the design, MAMS studies require specialist testing methodology in order to control the error rate of the trial \citep{stallard2003sequential}. \cite{magirr2012generalized} introduced the generalised Dunnett family of tests, where group sequential testing boundaries are defined to account for the multiple analyses, while accounting for the correlation introduced by the comparison of several experimental arms to a common control \citep{dunnett1955multiple}; \cite{urach2016multi} extend this directly defining all elements of the testing procedure. Alternatively fully flexible testing methods have been proposed (for example, \citep{bretz2006confirmatory,schmidli2006confirmatory,posch2005testing,koenig2008adaptive,bauer1999combining}), allowing decisions about which arms should remain in the study to function separately from the hypothesis testing. Both methods require the pre-definition of all study hypotheses, so that the overall testing procedure may be constructed to give strong control of the Family-Wise Error Rate (FWER) \citep{dmitrienko2009multiple}.\\

It is possible that not all experimental treatments are available at the start of the trial as, for example, see in the STAMPEDE trial \citep{sydes2009issues}. STAMPEDE started with five comparisons and subsequently added several more to the protocol. Including further experimental treatments into the trial in progress maintains the benefits of a MAMS design reducing logistical and administrative effort, speeding up the overall development process \citep{parmar2008speeding}, efficiency in the multiple comparisons and allowing direct comparisons of the treatments within the same trial.\\

Treatments may be added to the trial in progress by adjusting the pre-planned testing structure provided no use has been made of the data observed in the trial (thus requiring no interim analysis has been conducted). \cite{bennett2020designs} demonstrate how to suitably adjust the sample size for each treatment arm for such additions. It is possible that treatments may become available after some interim analysis, our methods allow modification at any stage of the trial with the only restriction being that no conclusion of statistical significance has been made. \\

The conditional error approach \citep{proschan1995designed} allows for design modifications during the course of a trial, where these modifications have not been pre-planned. It has been shown these modifications may be accounted for in the setting of treatment selection \citep{koenig2008adaptive,magirr2014flexible} however, adding hypotheses to a testing framework requires further restrictions on any introduced hypotheses \citep{hommel2001adaptive}. We propose a general framework using these principles for the inclusion of additional hypotheses to a testing procedure that allows the inclusion of existing trial information. We show how to apply this in the setting of MAMS designs, demonstrating how to construct an appropriate hypothesis testing structure for the updated trial such that the FWER is strongly controlled.

\section{Altering a trial in progress}

\subsection{A two arm trial}
\label{sec:twoarm}
Suppose we  plan a two arm trial with a continuous outcome to compare a new treatment, $T_1$, and a control, $T_0$. Let $\mu_1$ and $\mu_0$ be the expected responses for patients on treatments $T_1$ and $T_0$ respectively, and define the treatment effect as $\theta_1 = \mu_1 - \mu_0$. We investigate the one sided null hypothesis $H_{01}:\theta_1 \leq 0$.\\

The trial will recruit a total of $n$ patients randomised equally between treatment and control. Let $X_{i,k} \sim N(\mu_k,\sigma^2)$ for $i=1,...,n/2$ and $k=0,1$ then $\hat{\theta}_1$ is the estimate of the treatment effect. For $\xi_1 = \frac{\theta_1\sqrt{n}}{2\sigma}$ this has corresponding Z-value,
$$Z_1 = \frac{\hat{\theta}_1\sqrt{n}}{2\sigma}\sim N(\xi_1,1).$$
We reject $H_{01}$ at leve $\alpha$ when $Z_1 > \Phi^{-1}(1-\alpha)$, where $\Phi$ is the standard normal cdf.

\subsection{Adding a treatment}
\label{sec:simpadd}

Suppose for $\tau \in (0,1)$ after $\tau n$ observations a new treatment, $T_2$, becomes available. Let $\mu_2$ be the expected response for patients receiving this new treatment and define the corresponding treatment effect by $\theta_2 = \mu_2 - \mu_0$ with corresponding null hypothesis $H_{02}:\theta_2 \leq 0$. \\

Suppose, we maintain the pre-planned elements of the trial concerning treatments $T_1$ and $T_0$, such as the same sample size per treatment. Notationally it is convenient to define stage 1 and stage 2 consisting of the patients recruited before and after the treatment is added. From the stage 1 data we find
$$Z_1^{(1)} \sim N(\xi_1\sqrt{\tau},1)$$
and from the stage 2 data we find
$$Z_1^{(2)} \sim N(\xi_1\sqrt{1-\tau},1).$$
The overall Z-value may be reconstructed from the stagewise Z-values
$$Z_1 = \sqrt{\tau}Z_1^{(1)} + \sqrt{1-\tau}Z_1^{(2)}.$$\\

We recruit a further $(1-\tau)n/2$ patients to $T_2$ in stage 2, maintaining equal randomisation to all treatments. Since $T_2$ is added to the trial for stage 2 for $\xi_2 = \frac{\theta_2\sqrt{n}}{2\sigma}$
$$Z_2 \sim N(\xi_2\sqrt{1-\tau},1),$$
is based only on the data available from the second stage of the trial from which we construct the Z-value. Due to the common control and equal randomisation $Z_1^{(2)}$ and $Z_2$ have correlation $1/2$.

\subsection{Hypothesis testing}
\label{sec:addtwo}

For the two arm trial we constructed our hypothesis test in order to control the type $\mathrm{I}$ error rate at some pre-defined level $\alpha$. A natural extension in the case of multiple hypotheses is the Family-Wise Error rate (FWER), for the event $R$ that we reject one or more true null hypothesis the FWER is defined as $P_{\boldsymbol{\theta}}(R)$.\\

Suppose, when adding $T_2$ we test each null hypotheses at a nominal level $\alpha = 0.05$, Figure~\ref{fig:FWERplot} shows the impact on the FWER as we vary $\tau$. Under extremes of $\tau=0$ and $\tau=1$ the trial is not altered and should be designed accordingly to achieve a FWER of $\alpha$. For all values in between we see that the FWER is inflated when compared to the nominal $\alpha$.\\

\begin{figure}[ht]
\makebox[\linewidth]{
\includegraphics[scale=0.5]{005FWER.pdf}}
\label{fig:FWERplot}
\caption{Inflation in the FWER when an additional hypothesis is added to an ongoing two arm trial. The red line is the nominal FWER $\alpha = 0.05$ as per the design and the black line is the actual FWER for the given $\tau$.}
\end{figure}

As is typical in a confirmatory setting \citep{dmitrienko2009multiple} we require strong control of the FWER, that is
\begin{equation}
P_{\boldsymbol{\theta}}(R) \leq \alpha \text{ for all }\boldsymbol{\theta}=(\theta_1,\theta_2).
\label{eq:FWER}
\end{equation}
\cite{sugitani2018flexible} propose methods that account for the introduction of the additional hypothesis, testing any introduced hypothesis based strictly on the data collected after their introduction at level $\alpha$ \citep{hommel2001adaptive}. We build on this approach, incorporating existing information where possible.\\

We construct an overall closed testing procedure \citep{marcus1976closed} that accounts for the adaptive nature of the trial within each test \citep{koenig2008adaptive}. This requires tests of $H_{01}$, $H_{02}$ and $H_{0,12} = H_{01} \cap H_{02}: \theta_1 \leq 0 \text{ } \& \text{ } \theta_2 \leq 0$. Rejecting $H_{01}$ globally when the local level $\alpha$ tests of $H_{01}$ and $H_{0,12}$ are rejected and $H_{02}$ globally when the local level $\alpha$ tests of $H_{01}$ and $H_{0,12}$ are rejected.\\

No changes have been made to the recruitment or analysis concerning $H_{01}$, so as before we reject $H_{01}$ when $Z_1 > \Phi^{-1}(1-\alpha)$ at the end of the trial. It is useful to discuss constructing this test using the conditional error principle \citep{proschan1995designed}.  Given $z_1^{(1)}$ we define the conditional error rate
$$A(z_1^{(1)}) = \mathbbm{P}_{\theta_1 = 0}(\text{Reject }H_{01}|Z_1^{(1)}=z_1^{(1)}).$$
The probability of rejecting the null hypothesis for the remainder of the trial must not exceed $A(z_1^{(1)})$. Writing the test in terms of the stage 2 observations while incorporating the stage 1 data, we reject $H_{01}$ when $Z_1^{(2)} > \Phi^{-1}(1-A(z_1^{(1)}))$. Let $f(z_1^{(1)})$ be the probability density function of $z_1^{(1)}$, under $H_{01}$
\begin{equation}
\int_{z_1^{(1)}}f(z_1^{(1)})A(z_1^{(1)})\mathrm{d}z_1^{(1)} = \alpha,
\label{eq:con}
\end{equation}
which in turn guarantees control of the error rate at the pre-specified level $\alpha$, that is
$$\mathbbm{P}_{\theta_1 = 0}(\text{Reject }H_{01}) = \alpha.$$\\

There is no existing for $H_{02}$ and thus the test must be constructed purely based only on the stage 2 trial data used to construct $Z_2$. We reject the test for $H_{02}$ when $Z_2 > \Phi^{-1}(1-\alpha)$.\\

There is no pre-planned test for  $H_{0,12}$, however there is pre-existing information for $H_{01}$ in the form of $Z_1^{(1)}$. \cite{hommel2001adaptive} show how to use such first stage information in the test of an intersection hypothesis, when adding some initially excluded hypotheses after an interim analysis which we apply to the added hypothesis. Clearly if $H_{0,12}$ is true this implies that $H_{01}$ is also true. Since $H_{01}$ is true we compute the conditional error rate $A(z_1^{(1)})$ as described previously, furthermore under $H_{01}$, $z_1^{(1)}$ is distributed such that equation~\ref{eq:con} holds as before. Thus we may construct the test of $H_{0,12}$ at the end of the trial at level $A(z_1^{(1)})$ allowing for the incorporation of the stage one data given by $Z_1^{(1)}$.\\

For example, consider a Dunnett test \citep{dunnett1955multiple} for $H_{0,12}$. Let
$$Z_D = max(Z_1^{(2)},Z_2)$$
and define the distribution
$$\
\begin{pmatrix}
X \\ Y
\end{pmatrix}
 \sim N\left(
\begin{pmatrix}
0 \\ 0
\end{pmatrix}
,
\begin{pmatrix}
1 & 1/2\\1/2 & 1
\end{pmatrix}\right).$$
We construct the Dunnett p-value,
$$P_D = \mathbbm{P}(X>Z_D \cup Y>Z_D)$$
and may reject $H_{0,12}$ when $P_D < A(Z_1^{(1)})$.\\

The choice to recruit a further $(1-\tau)n/2$ patients to each treatment after the interim analysis is not required. The total number of patients recruited in stage 2 is free to vary however, changes to the ratio of patients on treatment and control requires slight further modification (although the ratio remains fixed after the modification is made). If the ratio of patients between the existing treatment and control differ before and after the design modification it is no longer possible to weight the Z-values in order to recover the pooled test statistic, in which case $Z_1$ would need to be constructed by using the weighted inverse normal \citep{bauer1994evaluation, lehmacher1999adaptive, hartung1999note} with weights defined at the time the modification is made.

\subsection{Simulation study}
\label{sec:sim}

For combincations $(\xi_1,\xi_2)$, with $\sigma/n =1$, $\delta = \Phi^{-1}(0.95)+\Phi^{-1}(0.9)$ and $\tau =0.5$ we simulate 1,000,000 realisations of $Z_1$ and $Z_2$ assuming equal sample size in each treatment at each stage in R \citep{R}. Table~\ref{tab:tests} shows estimates of the probabilities of an error for the local hypothesis tests, as required this is $\alpha$ whichever combination of null hypotheses are true.\\

\begin{table}[ht]
\makebox[\linewidth]{
\begin{tabular}{c c|c c c c}
$\xi_1$ & $\xi_2$ & $P(\text{Reject test of }H_{01})$ & $P(\text{Reject test of }H_{02})$ & $P(\text{Reject test of }H_{0,12})$ & FWER\\\hline
0 & 0 & \textbf{0.05} & \textbf{0.05} & \textbf{0.05} & 0.05\\
$\delta$ & 0 & 0.90 & \textbf{0.05} & 0.86 & 0.05\\
0 & $\delta$ & \textbf{0.05} & 0.66 & 0.36 & 0.05
\end{tabular}}
\caption{Probabilities of rejecting components of the closed testing procedure under proposed testing procedure, type $I$ errors highlighted in bold, $\delta = \Phi^{-1}(0.95)+\Phi^{-1}(0.9)$ such that we have power of $0.9$ when testing $H_{01}$ in the original trial.}
\label{tab:tests}
\end{table}

We compare the overall trial performance of the method proposed above with basing the test for the intersection hypothesis only on evidence for $H_{01}$, that is we reject $H_{0,12}$ when $Z_1 > \Phi^{-1}(1-\alpha)$ (treating the first null hypothesis as a gate keeping procedure \citep{dmitrienko2007gatekeeping}). In both procedures $Z_1^{(1)}$ is used in the test of $H_{0,12}$ by the argument that $H_{0,12} \implies H_{01}$. Table~\ref{tab:probs} shows the global rejection probabilities for the null hypotheses for each testing method. Both testing procedures gives strong control of the FWER. The probabilities of rejecting false $H_{01}$ do not differ largely, with an increase of at most 0.04 for the gate keeping procedure.  When both null hypotheses are false, there is a small decrease of 0.03 in the probability of rejecting $H_{02}$ for the gate keeping procedure. When $H_{01}$ is true and $H_{02}$ is false the gate keeping procedure cannot reject $H_{02}$ without making an error in rejecting $H_{01}$ and thus our proposed procedure increases the probability of rejecting the $H_{02}$ by 0.29. The small advantage for testing $H_{01}$ for the gate keeping procedure is outweighed by the ability to reject $H_{02}$ when there is a low probability of rejecting $H_{01}$ when taking an integrated approach to the test of the intersection hypothesis.

\begin{table}[ht]
\makebox[\linewidth]{
\begin{tabular}{c c|c c c c}
\multicolumn{6}{c}{Dunnett procedure for testing the intersection hypothesis}\\
$\xi_1$ & $\xi_2$ & $P(\text{Globally reject }H_{01}\text{ only})$ & $P(\text{Globally reject }H_{02}\text{ only})$ & $P(\text{Globally reject both})$ & $P(\text{Globally reject any})$ \\\hline
0 & 0 & \textbf{0.03} & \textbf{0.01} & \textbf{0.01} & \textbf{0.05}\\
$\delta$ & 0 & 0.81 & \textbf{0.00} & \textbf{0.05} & 0.86\\
0 & $\delta$ & \textbf{0.00} & 0.29 & \textbf{0.04} & 0.33\\
$\delta$ & $\delta$ & 0.26 & 0.03 & 0.62 & 0.91\\
\multicolumn{6}{c}{}\\
\multicolumn{6}{c}{Gate keeping procedure for testing the intersection hypothesis}\\
$\xi_1$ & $\xi_2$ & $P(\text{Globally reject }H_{01}\text{ only})$ & $P(\text{Globally reject }H_{02}\text{ only})$ & $P(\text{Globally reject both})$ & $P(\text{Globally reject any})$ \\\hline
0 & 0 & \textbf{0.04} & NA & \textbf{0.01} & \textbf{0.05} \\
$\delta$ & 0  & 0.85 & NA & \textbf{0.05} & 0.90\\
0 & $\delta$ & \textbf{0.01} & NA & \textbf{0.04} & 0.05\\
$\delta$ & $\delta$ & 0.28 & NA & 0.62 & 0.90
\end{tabular}}
\caption{Probabilities of global rejection of null hypothesis using the conditional error approach, type $I$ errors highlighted in bold, $\delta = \Phi^{-1}(0.95)+\Phi^{-1}(0.9)$ such that we have power of $0.9$ when testing $H_{01}$ in the original trial.}
\label{tab:probs}
\end{table}

\begin{figure}[ht]
\makebox[\linewidth]{
\includegraphics[scale=0.65]{condpow.pdf}}
\caption{Conditional error rate, $A(z_1{(1)})$, against probability of rejecting the intersection hypothesis $P(\text{Reject }H_{0,12}|z_1^{(1)})$ and corresponding density of conditional error $f(z_1^{(1)}$, $\delta = \Phi^{-1}(0.95)+\Phi^{-1}(0.9)$ such that we have power of $0.9$ when testing $H_{01}$ in the original trial.}
\label{fig:condpow}
\end{figure}

In Figure~\ref{fig:condpow} we examine the probabilities of rejecting the intersection hypothesis $H_{0,12}$ for all combinations of $H_{01}$ and $H_{02}$ true and false. When $H_{01}$ is false the conditional error is likely to be higher than the pre-planned $\alpha$, giving a high chance of rejecting $H_{0,12}$; when $H_{01}$ is true and $H_{02}$ is false there is a small reduction in the probability of rejecting $H_{0,12}$, this explains the deficit of our proposed procedure when $\xi_1 = \delta$ and $\xi_2 = 0$. Conversely when $H_{01}$ is true the conditional error is likely to be quite low: when both null hypotheses are true this corresponds to a low probability of rejecting $H_{0,12}$ however, when $H_{02}$ is false we recover some possibility of rejecting $H_{0,12}$ allowing us to reject $H_{02}$ globally.

\section{General rule for adding hypotheses}
\label{sec:gen}

Suppose there is a set of existing null hypotheses $E$ with a pre-planned closed testing procedure, and we wish to add a set of new null hypotheses $N$. Let $H_e$ be the intersection of some subset of the existing null hypotheses $e \subseteq E$ and $H_n$ be the intersection of some subset of the new hypotheses $n \subseteq N$. To construct an updated closed testing procedure there are three forms of null hypoothesis to consider.\\

\textbf{$H_e$:} Let $\alpha'_e$ be the conditional error rate for the test of $H_e$ at the time the $N$ hypotheses are added, the test of $H_e$ requires the probability of falsely rejecting $H_e$ does not exceed $\alpha'_e$.\\

\textbf{$H_n$:} With no existing test for $H_n$ it must be tested at level $\alpha$.\\

\textbf{$H_e \cap H_n$:} $H_e \cap H_n \implies H_e$ and hence the data already available for $H_e$ is distributed such that computing the corresponding conditional error $\alpha'_e$ will ensure that an equation of the form~\ref{eq:con} holds. Thus we incorporate the existing information into the test of $H_e \cap H_n$ by constructing it such that the probability of falsely rejecting $H_e \cap H_n$ does not exceed $\alpha'_e$.\\

Any intersection of the form $H_e \cap H_n$ must be constructed in this way. While proposing changes to the trial one may or may not add a new hypotheses $H_n$: in the case where $H_n$ added then $H_e \cap H_n$ may be based on the data relating to both $H_e$ and $H_n$ and is tested at $\alpha'_e$; while if $H_n$ is not added the test for $H_e \cap H_n$ is implicitly that of $H_e$ also tested at $\alpha'_e$. In either case the test of $H_e \cap H_n$ is tested at $\alpha'_e$ ensuring that an equation of the form~\ref{eq:con} holds whatever decision is made while proposing changes to the trial design. Noting that any procedure that gives strong control of the FWER is a closed testing procedure \cite{burnett2021adaptive}. So we may add hypotheses to any procedure that ensures strong control of the FWER while maintaining the statistical integrity of the trial. The penalty for doing so compared is the test of hypotheses of the form $H_e \cap H_n$.

\section{Alteration of a Multi-Arm Multi Stage trial in progress}

\subsection{Multi-arm multi-stage trials}
\label{sec:mamsrec}

With multiple experimental treatments to compare with the control, we should consider a MAMS design \citep{jaki2015multi,wason2016some}. This allows us to compare the treatments in the same trial, while incorporating pre-planned interim analyses to facilitate early stopping. This ensures: poorly performing treatments may be dropped for futility; alternatively the trial may be stopped early to declare efficacy, reducing the overall development time and number of patients. This early stopping can be done while formally testing null hypotheses and controlling the FWER (Equation~\ref{eq:FWER}), through the use of generalised Dunnett testing procedures \citep{magirr2012generalized}. We use the extension of this proposed by \cite{urach2016multi}. This directly defines all elements of the closed test allowing us to directly apply our rule for adding hypotheses from Section~\ref{sec:gen}.

Suppose we have $K$ novel treatments, $T_1,...,T_K$ to compare against a common control. We define the null hypotheses $H_{0i}:\theta_i \leq 0$ and corresponding alternatives $H_{1i}:\theta_i > 0$ for all $i=1,...,K$. A MAMS designs will simultaneously test these $K$ hypotheses over $J$ analyses.\\

Let $n$ be the number of patients to be recruited to the control arm in the first stage of the trial. We assume patients are randomised at the desired rate in each stage of the trial. At analysis $j=1,...,J$ the trial will have recruited $r_{k}^{(j)}n$ patients to treatment $k=0,1,...,K$ ($r_0^{(1)}=1$ by construction). Treatments may be dropped futility at each analysis (and removed from any further consideration), suppose treatment $k*$ is stopped at analysis $j*$ we have $r_{k*}^{(j)}=r_{k*}^{(j*)}$ for all $j \geq j*$. If all $T_1,...,T_K$ are dropped for futility the trial stops recruiting. Alternatively the trial may stop early if a treatment or treatments have been selected for further study, such as when the trial is stopped due to a treatment-control comparison yielding statistical significance \citep{urach2016multi}.\\

From the observations at each stage $j=1,...,J$ and treatment $k=1,...,K$ we construct estimates $\hat{\theta}_{k}^{(j)}$. Then defining
\begin{equation*}
\mathcal{I}_{k}^{(j)} = \frac{r_{k}^{(j)}r_{0}^{(j)}n}{\sigma^2(r_{k}^{(j)}+r_{0}^{(j)})},
\end{equation*}
we find the corresponding Z-values
\begin{equation*}
Z_{k}^{(j)} = \hat{\theta}_{k}^{(j)}\sqrt{\mathcal{I}_{k}^{(j)}}.
\end{equation*}\\

In the testing procedures that follow we require that the ratio of patients assigned to each treatment remains consistent through each stage of the trial, that is
\begin{equation*}
\frac{r_0^{(j)}}{r_k^{(j)}} = \frac{r_0^{(l)}}{r_k^{(l)}}
\end{equation*}
for all $k = 1,...,K$ and $j,l = 1,...,J$ \citep{koenig2008adaptive}

\subsection{The Generalised Dunnett procedure}
\label{sec:genDun}

Recall that $R$ is the event that we reject one or more true null hypothesis then extending Equation~\ref{eq:FWER} to $K$ null hypothesis strong control requires that
\begin{equation*}
\mathbb{P}_{\boldsymbol{\theta}}(R) \leq \alpha \text{ for all } \boldsymbol{\theta}=(\theta_1,...,\theta_K).
\label{eq:FWER2}
\end{equation*}
The generalised Dunnett method \citep{magirr2012generalized} simultaneously tests the null hypotheses, defining group sequential testing boundaries that account for the correlation structure of comparing multiple treatments to control to achieve the desired FWER.\\

We define efficacy boundaries $\boldsymbol{u} = (u_1,...,u_J)$ where the null hypothesis in treatment group $k=1,...,K$, $H_{0k}$, is rejected at analysis $j$ if $Z_{k}^{(j)} > u_j$ (and the trial is stopped). We define futility stopping boundaries $\boldsymbol{l} = (l_1,...,l_J)$ where if $Z_{k}^{(j)} < l_j$ the corresponding treatment is dropped for futility.\\

To achieve strong control of the FWER it is sufficient to choose $\boldsymbol{u}$ and $\boldsymbol{l}$ such that under the global null, $\theta_1=...=\theta_K=0$ which we denote by $\boldsymbol{0}$,
\begin{equation*}
\mathbbm{P}_{\boldsymbol{0}}(R) \leq \alpha
\label{eq:gFWER}
\end{equation*}
\citep{magirr2012generalized}. Such testing boundaries may be computed using familiar group sequential theory testing.

\subsection{Group sequential closed testing}
\label{sec:gsc}

Let $\mathcal{K}$ be the set such for any $I \subseteq (1,...,K)$ we have that $\cap_{i\in I} H_{0i} \in \mathcal{K}$. Constructing tests for each $H_{0m} \in \mathcal{K}$ at level $\alpha$. We reject $H_{0k}$ globally when all tests including $H_{0k}$ are rejected at level $\alpha$ for $k=1,...,K$.\\

The generalised Dunnett defines the test for the intersection of all null hypotheses $H_{01}\cap ...\cap H_{0K}$ and implicitly tests all $H_{0m} \in \mathcal{K}$ using the same $\boldsymbol{u}$ and $\boldsymbol{l}$. \cite{urach2016multi} extend this by directly defining all tests required for the closed testing procedure; for each $H_{0m} \in \mathcal{K}$ testing boundaries $\boldsymbol{u}_m = (u_{1,m},...,u_{J,m})$ are in Section~\ref{sec:genDun}, $H_{0m}$ is rejected at stage $j$ if $Z_{k}^{(j)} > u_{j,m}$. The futility boundaries $\boldsymbol{l} = (l_1,...,l_J)$ must be the same for all hypotheses.\\

\subsection{Adding experimental treatment arms}

Suppose at the $J'^{th}$ ($J' \in (1,...,J)$) interim analysis of a MAMS trial in progress we wish to add $T \geq 1$ new treatments. We now have up to $K'= K+1+T$ treatments in total (in the case that all $K+1$ original treatment arms are all still in the trial). We have planned recruitment $r_{k}^{(j)}n$ for treatment $k=1,...,K+T$ at stage $j=1,...,J$ where $r_k^{(j)}=0$ for all $k > K$. When modifying the trial we define a modified recruitment plan, recruiting $r_{k}^{\prime(j)}n$ patients for each treatment $k = 1,...,K+T$ at each remaining stage of the trial  $j=J',...,J$ (we could also use this opportunity to modify the number of stages); for $j \leq J'$ we know that $r_{k}^{\prime(j)}n = r_{k}^{(j)}n$ while for $j > J'$ we fix the planned recruitment for the remainder of the trial at this point. As in Section~\ref{sec:simpadd} we use the independent increments of the Z-values splitting the trial according to patients recruited before and after the $J'^{th}$ analysis. For $j = J'+1 ,..., J$ and $k = 0,1,...,K$ the sample that would have been recruited is given by $r_{k}^{\star(j)} = r_{k}^{(j)} - r_{k}^{(J')}$, from which we compute Z-values $Z_{k}^{\star(j)}$. For each $k=1,...,K$ and $j=J'+1,...,J$ we define weights,
$$w_{1,k}^{(j)} = \sqrt{\frac{r_{k}^{(J')} + r_{0}^{(J')}}{r_{k}^{(j)} + r_{0}^{(j)}}},$$
$$w_{2,k}^{(j)} = \sqrt{1- w_{1,k}^{(j)}w_{1,k}^{(j)}}$$
and re-construct the Z-values for the remainder of the trial as
$$Z_{k}^{(j)} = w_{1,k}^{(j)} Z_{k}^{(J')} + w_{2,k}^{(j)}  Z_{k}^{\star(j)}.$$
Weighting together the Z-values in this way will allow us to modify the ratio of patients recruited to each treatment at the time of the design modification. As in Section~\ref{sec:mamsrec} these ratios must remain fixed for all stages of the trial after the modification has been made.

\subsection{Incorporating additional hypotheses}
\label{sec:tests}

We now have null hypotheses $H_{0i}:\theta_i \leq 0$ and alternatives $H_{1i}:\theta_i > 0$ for all $i=1,...,K+T$, and require strong control of the FWER across all $K+T$ tests. We construct a closed testing procedure following the rule introduced in Section~\ref{sec:gen}.  We define three sets: the set of existing null hypotheses $H_{01},...,H_{0K}$ and all intersections, $\mathcal{K}$; the set of added null hypotheses $H_{0K+1},...,H_{0K+T}$  and all intersections, $\mathcal{T}$; and the set of all intersections between existing and added null hypotheses, $\mathcal{KT}$.\\

The conditional error rate of each test for $H_{0m} \in \mathcal{K}$ is maximised under the global null \citep{stallard2015flexible}. Given the existing estimates, $\hat{\boldsymbol{\theta}}^{(J')} = (\hat{\theta}_{1}^{(J')},...,\hat{\theta}_{k}^{(J')})$ and under the originally planned trial described in Sections~\ref{sec:mamsrec}, \ref{sec:genDun} and \ref{sec:gsc} we write the conditional error for each $H_{0m} \in \mathcal{K}$ under the global null as
\begin{equation*}
B_{m}(\hat{\boldsymbol{\theta}}^{(J')}) = \mathbb{P}_{\boldsymbol{0}}(\text{Reject }H_{0m}|\hat{\boldsymbol{\theta}}^{(J')}) \leq \alpha.
\end{equation*}
As in Equation~\ref{eq:con} we have that under the global null
\begin{equation*}
\int_{\hat{\boldsymbol{\theta}}^{(J')}}f(\hat{\boldsymbol{\theta}}^{(J')})B_{m}(\hat{\boldsymbol{\theta}}^{(J')}) \mathrm{d}\hat{\boldsymbol{\theta}}^{(J')} = \alpha
\label{eq:condint}
\end{equation*}
as required. It is useful to re-write the testing boundaries for each $H_{0m} \in \mathcal{K}$ in terms of only the data collected after stage $J'$, that is for $j=J'+1,...,J$ and $k=1,...,K$
$$u_{j,k,m} = \frac{u_{j,m} -w_{1,k}^{(j)} Z_{k}^{(J')}}{w_{2,k}^{(j)}}$$
for $k=1,...,K$, $H_{0k}$ is rejected at stage $j$ of the trial if $Z_{k}^{\star(j)} > u_{j,k,m}$ and
$$l_{k,j,m} = \frac{l_{j,m} -w_{1,k}^{(j)} Z_{k}^{(J')}}{w_{2,k}^{(j)}}$$
where if $Z_{k}^{\star(j)} < l_{k,j,m}$ $T_k$ is dropped for futility. This allows computation of the conditional error rate based $Z_{k}^{\star(j)}$ for $j = J'+1 ,..., J$ and $k = 0,1,...,K$.\\

For  each $H_{0m} \in \mathcal{K}$ the hypothesis test must be constructed at level $B_{m}(\hat{\boldsymbol{\theta}}^{(J')})$. For each $H_{0m} \in \mathcal{T}$ the hypothesis test must be constructed at level $\alpha$. For each $H_{0m} \in \mathcal{KT}$ the hypothesis test must be constructed at level $B_{m}(\hat{\boldsymbol{\theta}}^{(J')})$. This ensures each test for the trail as a whole is constructed at level $\alpha$ as required, while including any existing trial data and allowing for any changes to recruitment for $T_0,T_1,...,T_K$, and the FWER is strongly controlled.\\

For each hypothesis $H_{0m} \in K \cup T \cup KT$ we define the testing boundaries for the modified trial at the required error rate $\boldsymbol{u}'_m = (u'_{J'+1,m},...,u'_{J,m})$ and  $\boldsymbol{l}'_m = (l'_{J'+1,m},...,l'_{J,m})$. At stage $j = J'+1 ,..., J$ for treatment $k = 0,1,...,K$ the recruitment is governed by $r_{k}^{\star\prime(j)} = r_{k}^{\prime(j)} - r_{k}^{(J')}$, with corresponding Z-values $Z_{k}^{\star\prime(j)}$. For each experimental treatment from the first stage of the trial $k=1,...,K$ we define weights for data before and after stage $J'$, for $j=J'+1,...,J$ and $k=1,...,K$
$$w_{1,k}^{\prime(j)} = \sqrt{\frac{r_{k}^{(J')} + r_{0}^{(J')}}{r_{k}^{\prime(j)} + r_{0}^{\prime(j)}}},$$
$$w_{2,k}^{\prime(j)} = \sqrt{1- w_{1,k}^{\prime(j)}w_{1,k}^{\prime(j)}}$$
and construct the Z-values for for the hypothesis tests as
$$Z_{k}^{\prime(j)} = w_{1,k}^{\prime(j)} Z_{k}^{(J')} + w_{2,k}^{\prime(j)}  Z_{k}^{\star\prime(j)}$$
allowing us to write the testing boundaries for each $H_{0m} \in \mathcal{K}$ in terms of only the data collected after stage $J'$, that is for $j=J'+1,...,J$ and $k=1,...,K$
$$u'_{j,k,m} = \frac{u'_{j,m} -w_{1,k}^{\prime(j)} Z_{k}^{(J')}}{w_{2,k}^{\prime(j)}}$$
rejecting $H_{0m} \in \mathcal{K}$ at analysis $j=J'+1,...,J$ if $Z_{k}^{\star\prime(j)} > u_{j,k,m}$ and
$$l'_{k,j} = \frac{l'_{j} -w_{1,k}^{\prime(j)} Z_{k}^{(J')}}{w_{2,k}^{\prime(j)}}$$
where if $Z_{k}^{\star\prime(j)} < l_{k,j}$ $T_k$ dropped for futility (note for $k>K$ $u'_{j,m}$ and $l'_{j}$). With this in place $\boldsymbol{u}'_m $ and $\boldsymbol{l}'_m$ may be computed as per the generalised Dunnett test.

\section{Example}
\label{sec:exam}
\subsection{An illustrative example}

For the initial design consider a three stage trial to compare two treatments with a control, recruiting $n=10$ patients to each treatment at each stage of the trial; that is $J=3$, $K=2$ and $\boldsymbol{r}_k=(1,2,3)$ for $k=0,1,2$. Under this design we test the null hypotheses $H_{01}:\theta_1 \leq 0$ and $H_{02}:\theta_2 \leq 0$. The testing boundaries are constructed for a FWER of $\alpha = 0.05$, let $\delta = \Phi^{-1}(0.75)\sqrt{2}$  and $\sigma = 1$. At a configuration of $\boldsymbol{\theta} = (\delta,0)$ we have a target power of $1-\beta = 0.9$. Defining the triangular testing boundaries \citep{whitehead1997design} we first compute the testing boundary for $H_{01}\cap H_{02}$ using the \texttt{mams()} function of the MAMS package in R \citep{jaki2019r}. This sets futility boundary for all tests with the upper boundaries computed for testing both $H_{01}$ and $H_{02}$ separately.\\

Suppose after the first analysis $J'=1$ we add two further treatments $T=2$, adding the null hypotheses $H_{03}:\theta_3 \leq 0$ and $H_{04}:\theta_4 \leq 0$. Given $\boldsymbol{Z}^{(1)} = (2,1.5)$, the trial would continue in all arms at the interim analysis. Computing the conditional error rate for each existing test we construct all required tests as described in Section~\ref{sec:tests}. Using triangular testing boundaries ensuring all lower boundaries correspond to those of $H_{01}\cap H_{02}\cap H_{03}\cap H_{04}$. We continue recruiting 10 patients per treatment per stage, allowing for a maximum total sample size of 130 patients.\\

Table~\ref{tab:condsim} shows the operating characteristics of the updated trial based on 1,000,000 simulations of the remainder of the trial. Due to the tests being conditional on the first stage observations the probabilities of rejecting the null hypotheses under the global null are not 0.05. Since $Z_1^{(1)} > Z_2^{(1)}$ we observe higher probabilities of rejecting $H_{01}$ than $H_{02}$ for equivalent values of $\theta_1$ and $\theta_2$, for example when $\theta_1 = \theta_2 = \delta$ the probability of rejecting $H_{01}$ is 0.13 higher. Similarly since $Z_1^{(1)} >0$ and $Z_2^{(1)} >0$ the probability of rejecting $H_{01}$ or $H_{02}$ is higher than the probability of rejecting $H_{03}$ or $H_{04}$, for example when $\theta_1 = \theta_2 =\theta_3 = \theta_4 = \delta$ we have probabilities of 0.94, 0.81, 0.59 and 0.59 of rejecting $H_{01}$,$H_{02}$, $H_{03}$ and  $H_{04}$ respectively. We also see the benefit of incorporating all treatments in the same trial, with a reduction in the expected sample size and a chance to reject multiple null hypotheses, when there are more beneficial treatments overall.

\begin{table}
\makebox[\linewidth]{
\begin{tabular}{c | c c c c c}
$\boldsymbol{\theta}$ & $\mathbb{P}_{\boldsymbol{\theta}}(R_1)$ & $\mathbb{P}_{\boldsymbol{\theta}}(R_2)$ & $\mathbb{P}_{\boldsymbol{\theta}}(R_3)$ & $\mathbb{P}_{\boldsymbol{\theta}}(R_4)$ & $\mathbb{E}_{\boldsymbol{\theta}}(N)$\\\hline
$( 0 , 0 , 0 , 0 )$  										 &  0.19  &  0.09  &  0.02  &  0.02  &  72 \\
$( \delta , 0 , 0 , 0 )$  							 &  0.97  &  0.08  &  0.02  &  0.02  &  54 \\
$( 0 , \delta , 0 , 0 )$  							 &  0.23  &  0.94  &  0.02  &  0.02  &  59 \\
$( \delta , \delta , 0 , 0 )$  					 &  0.96  &  0.83  &  0.02  &  0.02  &  53 \\
$( 0 , 0 , \delta , 0 )$  							 &  0.16  &  0.07  &  0.79  &  0.02  &  66 \\
$( \delta , 0 , \delta , 0 )$  					 &  0.95  &  0.08  &  0.57  &  0.02  &  54 \\
$( 0 , \delta , \delta , 0 )$  					 &  0.22  &  0.88  &  0.63  &  0.03  &  58 \\
$( \delta , \delta , \delta , 0 )$  		 &  0.95  &  0.82  &  0.55  &  0.03  &  53 \\
$( 0 , 0 , \delta , \delta )$  					 &  0.15  &  0.07  &  0.69  &  0.68  &  63 \\
$( \delta , 0 , \delta , \delta )$  		 &  0.93  &  0.08  &  0.57  &  0.58  &  54 \\
$( 0 , \delta , \delta , \delta )$  		 &  0.21  &  0.84  &  0.63  &  0.63  &  58 \\
$( \delta , \delta , \delta , \delta )$  &  0.94  &  0.81  &  0.59  &  0.59  &  53 \\
\multicolumn{6}{c}{}\\
\end{tabular}}
\makebox[\linewidth]{
\begin{tabular}{c | c c c c c}
$\boldsymbol{\theta}$  & Fail to reject  & Reject one & Reject two & Reject three & Reject four\\\hline
$( 0 , 0 , 0 , 0 )$  										 &  0.76  &  0.17  &  0.06  &  0.01  &  0.00 \\
$( \delta , 0 , 0 , 0 )$  							 &  0.03  &  0.87  &  0.09  &  0.01  &  0.00 \\
$( 0 , \delta , 0 , 0 )$  							 &  0.06  &  0.71  &  0.21  &  0.02  &  0.00 \\
$( \delta , \delta , 0 , 0 )$  					 &  0.01  &  0.19  &  0.77  &  0.03  &  0.01 \\
$( 0 , 0 , \delta , 0 )$  							 &  0.18  &  0.65  &  0.11  &  0.04  &  0.01 \\
$( \delta , 0 , \delta , 0 )$  					 &  0.02  &  0.44  &  0.47  &  0.07  &  0.01 \\
$( 0 , \delta , \delta , 0 )$  					 &  0.03  &  0.38  &  0.41  &  0.16  &  0.02 \\
$( \delta , \delta , \delta , 0 )$  		 &  0.01  &  0.15  &  0.37  &  0.45  &  0.03 \\
$( 0 , 0 , \delta , \delta )$  					 &  0.08  &  0.43  &  0.36  &  0.09  &  0.04 \\
$( \delta , 0 , \delta , \delta )$ 		   &  0.01  &  0.28  &  0.30  &  0.33  &  0.07 \\
$( 0 , \delta , \delta , \delta )$  		 &  0.02  &  0.26  &  0.25  &  0.30  &  0.16 \\
$( \delta , \delta , \delta , \delta )$  &  0.01  &  0.12  &  0.24  &  0.22  &  0.42
\end{tabular}}

\caption{Operating characteristics for the remainder of the trial given $\boldsymbol{Z}_1 = (2,1.5)$ under corresponding configuration $\boldsymbol{\theta}$. Where $R_i$ is the event that $H_{0i}$ is rejected and $N$ is the total sample size (note 30 participants already recruited).}
\label{tab:condsim}
\end{table}

\subsection{Comparison of performance}

We compare our proposed method with two options that maintain the integrity of the results given that observations are already available from the trial: option one is to conduct a separate MAMS trial comparing the new treatments with the control in addition to the trial already in progress; option two is to conclude the current trial and start a new trial incorporating all four experimental treatments. In examining these unmodified designs we make no use of the previous trial data, meaning these trials do not benefit from the patients already recruited.\\

As before we add two treatments, $T=2$, at the first analysis, $J'=1$. We keep all other parameters as before, keeping them consistent for each design. We estimate the operating characteristics of our proposed method based on 10,000 simulations. This is a lower number of simulations than would be ideal, due to the computationally intensive nature of the simulation. In practice we do not expect this to be used as a pre-planned scheme and hence only one set of updated testing boundaries need computing, making longer simulations more viable as seen in Section~\ref{sec:exam}. For the unmodified option one, we use the original trial for $H_{01}$ and $H_{02}$ and compute boundaries for a two stage trial for $H_{03}$ and $H_{04}$. For the unmodified option two, we compute boundaries for a two stage trial for $H_{01}$, $H_{02}$, $H_{03}$ and $H_{04}$. We use 1,000,000 simulations to estimate the operating characteristics for each unmodified design. \\

We break the operating characteristics of our proposed method down, with Table~\ref{tab:stop} showing the behaviour of the first stage of the trial and Table~\ref{tab:prop1} showing trial that continues beyond the first interim analysis. We see a relatively high probability of the trial concluding at the first analysis, before the treatments are added; this shows the first stage data should not be disregarded. If the trial continues beyond the first stage we observe a similar pattern to that shown in Table~\ref{tab:condsim}. With lower probabilities of rejecting $H_{03}$ or $H_{04}$ than rejecting $H_{01}$ or $H_{02}$. The probabilities of rejection are lower than Table~\ref{tab:condsim} since $l^{(1)} = 0$ allows for less promising stage-1 Z-values to progress the trial beyond the first analysis.\\

\begin{table}[ht]
\makebox[\linewidth]{
\begin{tabular}{c | c  c c}
$\boldsymbol{\theta}$ & $\mathbb{P}_{\boldsymbol{\theta}}(\text{Continue beyond stage 1})$ & $\mathbb{P}_{\boldsymbol{\theta}}(\text{Stop for efficacy at first analysis})$ & $\mathbb{P}_{\boldsymbol{\theta}}(\text{Stop for futility at first analysis})$ \\\hline
$( 0 , 0 )$  					 &  0.64 & 0.02 & 0.34 \\
$( \delta , 0 )$  		 &  0.64 & 0.35 & 0.01 \\
$( \delta , \delta )$  &  0.46 & 0.53 & 0.00 \\
\end{tabular}}
\caption{Performance of the original trial at the first interim analysis.}
\label{tab:stop}
\end{table}

\begin{table}
\makebox[\linewidth]{
\begin{tabular}{c | c c c c c}
$\boldsymbol{\theta}$ & $\mathbb{P}_{\boldsymbol{\theta}}(R_1)$ & $\mathbb{P}_{\boldsymbol{\theta}}(R_2)$ & $\mathbb{P}_{\boldsymbol{\theta}}(R_3)$ & $\mathbb{P}_{\boldsymbol{\theta}}(R_4)$ & $\mathbb{E}_{\boldsymbol{\theta}}(N)$\\\hline
$(0,0,0,0)$  										&  0.03  &  0.02  &  0.01  &  0.01  &  78  \\
$(\delta,0,0,0)$  							&  0.91  &  0.00  &  0.01  &  0.01  &  71  \\
$(\delta,\delta,0,0)$  					&  0.79  &  0.84  &  0.02  &  0.02  &  77  \\
$(0,0,\delta,0)$  							&  0.01  &  0.02  &  0.71  &  0.01  &  78  \\
$(\delta,0,\delta,0)$  					&  0.86  &  0.01  &  0.64  &  0.03  &  71  \\
$(\delta,\delta,\delta,0)$  		&  0.82  &  0.82  &  0.61  &  0.01  &  75  \\
$(0,0,\delta,\delta)$  					&  0.02  &  0.02  &  0.63  &  0.63  &  79  \\
$(\delta,0,\delta,\delta)$  		&  0.82  &  0.01  &  0.60  &  0.60  &  70  \\
$(\delta,\delta,\delta,\delta)$ &  0.77  &  0.77  &  0.61  &  0.61  &  76  \\
\multicolumn{6}{c}{ }
\end{tabular}}
\makebox[\linewidth]{
\begin{tabular}{c | c c c c c}
$\boldsymbol{\theta}$  & Fail to reject  & Reject one & Reject two & Reject three & Reject four\\\hline
$(0,0,0,0)$  										&  0.94  &  0.05  &  0.01  &  0.00  &  0.00  \\
$(\delta,0,0,0)$  							&  0.08  &  0.89  &  0.02  &  0.00  &  0.00  \\
$(\delta,\delta,0,0)$  					&  0.04  &  0.30  &  0.62  &  0.04  &  0.00  \\
$(0,0,\delta,0)$  							&  0.29  &  0.68  &  0.03  &  0.00  &  0.00  \\
$(\delta,0,\delta,0)$  					&  0.05  &  0.40  &  0.52  &  0.03  &  0.00  \\
$(\delta,\delta,\delta,0)$  		&  0.01  &  0.19  &  0.35  &  0.44  &  0.01  \\
$(0,0,\delta,\delta)$  					&  0.12  &  0.48  &  0.37  &  0.02  &  0.00  \\
$(\delta,0,\delta,\delta)$  		&  0.03  &  0.27  &  0.35  &  0.33  &  0.01  \\
$(\delta,\delta,\delta,\delta)$ &  0.02  &  0.15  &  0.21  &  0.30  &  0.32
\end{tabular}
}
\caption{Under our proposed update procedure, probabilities of rejecting null hypotheses and expected sample size under the corresponding configuration of $\boldsymbol{\theta}$ for our proposed update procedure when the trial continues beyond the first stage. Where $R_i$ is the event that we reject $H_{oi}$ and $N$ is the total sample size (including the 30 patients  included in stage one).}
\label{tab:prop1}
\end{table}

Comparing our proposed procedure with option one shown in Table~\ref{tab:opt1}, conducting two separate trials produces similar probabilities for rejecting $H_{01}$ or $H_{02}$. Our method is sensitive to $\theta_3$ and $\theta_4$ due to their ability to also conclude the trial early. Two separate trials increase the probabilities of rejecting $H_{03}$ or $H_{04}$; this is partially due to the disconnect between trials, if one concludes early the other may continue and reject and null hypothesis. Given this and that patients are recruited to the control in both trials we see that our proposed method significantly reduces the expected sample size, with 70--80 patients including the first stage of the trial for trials that continue beyond the first stage (for the trial as a whole this expected sample size drops to 50--60 over the scenarios we have examined)  whereas option one requires 90--95 patients. There are two key flaws in option one: while this method incorporates all existing data for $H_{01}$ and $H_{02}$ there is no multiplicity adjustment between the existing and added hypotheses, as we have two separate trials of two null hypotheses each with a FWER of $\alpha$; if we wish to select some subset of treatments for further study, there is no guarantee of direct comparability between each trial.\\

\begin{table}
\makebox[\linewidth]{
\begin{tabular}{c | c c c c c c}
$\boldsymbol{\theta}$ & $\mathbb{P}_{\boldsymbol{\theta}}(R_1)$ & $\mathbb{P}_{\boldsymbol{\theta}}(R_2)$ & $\mathbb{E}_{\boldsymbol{\theta}}(N_1)$ & $\mathbb{P}_{\boldsymbol{\theta}}(R_3)$ & $\mathbb{P}_{\boldsymbol{\theta}}(R_4)$ & $\mathbb{E}_{\boldsymbol{\theta}}(N_2)$\\\hline
$( 0 , 0 , 0 , 0  )$  									 &  0.03  &  0.03  &  49  &  0.03  &  0.03  &  38 \\
$( \delta , 0 , \delta , 0 )$  					 &  0.93  &  0.02  &  47  &  0.82  &  0.04  &  39 \\
$( \delta , \delta , \delta , \delta )$  &  0.81  &  0.81  &  45  &  0.77  &  0.77  &  39 \\
\multicolumn{7}{c}{ }
\end{tabular}}
\makebox[\linewidth]{
\begin{tabular}{c | c c c c c c}
 & \multicolumn{3}{c}{Original trial} & \multicolumn{3}{c}{Additional trial}\\
$\boldsymbol{\theta}$  & Fail to reject  & Reject one & Reject two &  Fail to reject  & Reject one & Reject two\\\hline
$( 0 , 0 , 0 , 0  )$  									 &  0.95 & 0.04 & 0.01  & 0.95 & 0.04 & 0.01 \\
$( \delta , 0 , \delta , 0 )$  					 &  0.07 & 0.90 & 0.02  & 0.18 & 0.78 & 0.04 \\
$( \delta , \delta , \delta , \delta )$  &  0.02 & 0.34 & 0.64  & 0.07 & 0.31 & 0.62
\end{tabular}
}
\caption{Under two separate trials, probabilities of rejecting null hypotheses and expected sample size under the corresponding configuration of $\boldsymbol{\theta}$ for our option one assuming the trial continues beyond the interim analysis. Where $R_i$ is the event that we reject $H_{oi}$, $N_1$ is the total sample size in the original trial and $N_2$ is the total sample size in the additional trial.}
\label{tab:opt1}
\end{table}

Comparing the operating characteristics of option two in Table~\ref{tab:opt2} with our method in Table~\ref{tab:prop1}, we see that the probabilities of rejecting $H_{01}$ or $H_{02}$ are lower while the probabilities of rejecting $H_{03}$ or $H_{04}$ are similar, this  leads to a reduction in the probabilities of rejecting multiple hypotheses. For example, when $\theta_1 = \theta_2 =\theta_3 = \theta_4 = \delta$ the probabilities of rejecting $H_{01}$,$H_{02}$, $H_{03}$ and $H_{04}$ are 0.77, 0.77,  0.61  and  0.61 respectively, while they are all 0.64 under option two and the probability of rejecting two or more hypotheses falls by 0.12 compared to our proposed method. The expected sample size of the trial conducted under option two is reduced by 8--15 patients this does not account for the fact that 30 patients have been recruited who do not contribute to the result.

\begin{table}
\makebox[\linewidth]{
\begin{tabular}{c | c c c c c}
$\boldsymbol{\theta}$ & $\mathbb{P}_{\boldsymbol{\theta}}(R_1)$ & $\mathbb{P}_{\boldsymbol{\theta}}(R_2)$ & $\mathbb{P}_{\boldsymbol{\theta}}(R_3)$ & $\mathbb{P}_{\boldsymbol{\theta}}(R_4)$ & $\mathbb{E}_{\boldsymbol{\theta}}(N)$\\\hline
$(0,0,0,0)$  										&  0.02  &  0.02  &  0.02  &  0.02  &  62 (+30)\\
$(\delta,0,0,0)$  							&  0.75  &  0.01  &  0.01  &  0.01  &  63 (+30)\\
$(\delta,\delta,0,0)$  					&  0.67  &  0.67  &  0.02  &  0.02  &  62 (+30)\\
$(0,0,\delta,0)$  							&  0.01  &  0.01  &  0.75  &  0.01  &  63 (+30)\\
$(\delta,0,\delta,0)$  					&  0.67  &  0.02  &  0.67  &  0.02  &  62 (+30)\\
$(\delta,\delta,\delta,0)$  		&  0.64  &  0.64  &  0.64  &  0.03  &  62 (+30)\\
$(0,0,\delta,\delta)$  					&  0.02  &  0.02  &  0.67  &  0.67  &  62 (+30)\\
$(\delta,0,\delta,\delta)$  		&  0.64  &  0.03  &  0.64  &  0.64  &  62 (+30)\\
$(\delta,\delta,\delta,\delta)$ &  0.64  &  0.64  &  0.64  &  0.64  &  63 (+30)\\
\multicolumn{6}{c}{ }
\end{tabular}}
\makebox[\linewidth]{
\begin{tabular}{c | c c c c c}
$\boldsymbol{\theta}$  & Fail to reject  & Reject one & Reject two & Reject three & Reject four\\\hline
$(0,0,0,0)$  										&  0.95  &  0.04  &  0.01  &  0.00  &  0.00 \\
$(\delta,0,0,0)$  							&  0.24  &  0.73  &  0.02  &  0.00  &  0.00 \\
$(\delta,\delta,0,0)$  					&  0.11  &  0.43  &  0.43  &  0.02  &  0.01 \\
$(0,0,\delta,0)$  							&  0.24  &  0.73  &  0.02  &  0.00  &  0.00 \\
$(\delta,0,\delta,0)$  					&  0.11  &  0.43  &  0.43  &  0.02  &  0.00 \\
$(\delta,\delta,\delta,0)$  		&  0.07  &  0.31  &  0.28  &  0.33  &  0.03 \\
$(0,0,\delta,\delta)$  					&  0.11  &  0.43  &  0.43  &  0.02  &  0.00 \\
$(\delta,0,\delta,\delta)$  		&  0.07  &  0.31  &  0.27  &  0.33  &  0.03 \\
$(\delta,\delta,\delta,\delta)$ &  0.05  &  0.24  &  0.19  &  0.18  &  0.35
\end{tabular}
}
\caption{Under starting a new trial incorporating all treatments, probabilities of rejecting null hypotheses and expected sample size under the corresponding configuration of $\boldsymbol{\theta}$ for option two assuming the trial continues beyond the interim analysis. Where $R_i$ is the event that we reject $H_{oi}$ and $N$ is the total sample size (note 30 additional patients are recruited but not used in the analysis).}
\label{tab:opt2}
\end{table}

\section{Discussion}

The motivation for adding a treatment to a trial in progress is clear. Should a new treatment become available it is desirable incorporate it allowing direct comparisons while preserving integrity and avoiding delays to the overall development process. Our proposed general framework for adding experimental treatments to a trial in progress builds upon the work of \cite{hommel2001adaptive}, allowing any trial with strong control of the FWER to add new hypotheses. This also allows other alterations to the design of the trial while ensuring that all information already collected is utilised in inference and decision making.\\

This framework can be applied in our motivational setting of MAMS platform trials \citep{meyer2021systematic,meyer2020evolution}. The examples in Section~\ref{sec:exam} demonstrate that this does indeed strongly control the FWER as expected.

Our examples in Sections~\ref{sec:sim} and~\ref{sec:exam} show the penalty adding treatments in terms of the probability of rejecting the null hypotheses is marginal and only has a notable impact on the introduced arms, optimising the recruitment proportions across configurations of the true treatment effects may reduce the impact of this further. In addition the combination of utilising the existing data and the efficient use of control patients across the trial yields a reduction in the expected sample size when compared to alternatives that do not make such use of the existing data. The operating characteristics are not the primary motivation to adding treatments to a trial in progress. As for MAMS designs in general this allows for reduction in logistical and administrative effort and speeding up the overall development process as well as allowing direct comparisons of the treatments within the same trial.\\

The general framework for adding hypotheses to a trial in progress has broader application than, being applicable to any testing procedure that gives strong control of the FWER. The addition of hypotheses in this way allows for the incorporation of existing trial data into decisions about how to plan the remainder of the trial.

\section{Software}
Software relating to the examples in this paper is available at \href{https://github.com/Thomas-Burnett/Adding-treatments-to-clinical-trials-in-progress.git}{https://github.com/Thomas-Burnett/Adding-treatments-to-clinical-trials-in-progress.git}.

\section*{Acknowledgements}

This research was supported by the NIHR Cambridge Biomedical Research Centre (BRC-1215-20014). This report is independent research supported by the National Institute for Health Research (Prof Jaki's Senior Research Fellowship, NIHR-SRF-2015-08-001). T Jaki received funding from the UK Medical Research Council (MC\_UU\_00002/14). Franz K{\"o}nig is a member of the EU Patient-Centric Clinical Trial Platform (EU-PEARL) which has received funding from the Innovative Medicines Initiative 2 Joint Undertaking, grant No 853966. This Joint Undertaking receives support from the EU Horizon 2020 Research and Innovation Programme, EFPIA, Children's Tumor Foundation, Global Alliance for TB Drug Development, and SpringWorks Therapeutics. The views expressed in this publication are those of the authors. These views are not necessarily those of the NHS, the National Institute for Health Research or the Department of Health and Social Care (DHSC). The funders and associated partners are not responsible for any use that may be made of the information contained herein.

{
\setlength{\bibsep}{0.0pt}
\baselineskip20pt
\bibliographystyle{biorefs}

redpajama_set_name: RedPajamaArXiv


Congratulations to Wesley Johnson in his outstanding performance at Escape From Alcatraz this past Sunday in California. Wes got first in his division in the swim, averaging 1:06 minutes/hundred! Wes was also able to run and bike after having shin splints and being hit by a motor vehicle this past year. With the help of a fellow athlete, Dr. Tom Fletcher, at Wasatch Health Solutions, in Murray, Utah.


text:
Opinion: McKenzie scandal highlights need for a national integrity commission
AuthorCentre for Public IntegrityPosted on January 21, 2020 CategoriesMediaTagscoverage
By Hannah Aulby, originally published in the Canberra Times on 21st January 2020.
The ability for Nationals deputy leader Bridget McKenzie to use public money for partisan political gains, and face no official retribution, highlights serious flaws in our accountability system.
The response to the findings of the Australian National Audit Office has been pretty standard of recent political scandals. Media reports over two to three days heighten the pressure. The politician in question denies any wrongdoing, the opposition calls for their resignation, the Prime Minister comes out supporting his colleague, the crossbench calls for a national integrity commission, and then there are attempts to set up a Senate inquiry. A Senate inquiry report may be published months afterwards, with recommendations that gather dust along with hundreds of other inquiry reports. The politician in question pushes through the initial media storm, and then continues on their way.
Other politicians see the survival of their colleague and take note – allegations of corruption are not properly investigated and retribution is minimal.
The Australian public see the politician survive relatively unscathed and begin to expect more of the same behaviour from their elected representatives. Public trust in government to act in the public interest suffers.
Each of the accountability institutions listed above – the Audit Office, the media, and the Senate – are doing the best they can with the resources and powers available to them. But none have the necessary jurisdiction, investigative powers or enforcement mechanisms to systematically ensure the government is held to account to act in the public interest. At best, political misconduct is currently met with haphazard responses from unco-ordinated agencies with limited ability to improve political behaviour or punish misconduct.
So what changes do we need to make to lift the integrity of elected representatives in the future?
The Centre for Public Integrity researches integrity reforms necessary to fill the gaps in our accountability system and lift public trust. Our board members are corruption experts and former judges including Tony Fitzgerald, AC QC, David Ipp, AO QC and Stephen Charles, AO QC.
Our research shows that ministerial integrity could be lifted by strengthening codes of conduct and establishing a national integrity commission.
Codes of conduct are designed to ensure elected representatives act in accordance with integrity, fairness and the public interest. Australia currently has no parliamentary code of conduct, meaning that the majority of MPs are not bound by any standard of behaviour. Our ministerial code of conduct is weak and unenforced, with no real retribution for breaking the rules. It sits within the Department of Prime Minister and Cabinet, leaving the PM to monitor and enforce compliance within his own cabinet.
Australia needs a parliamentary code of conduct to ensure all elected representatives uphold a high standard of conduct. Our ministerial code of conduct should be strengthened to include a commitment to spend public money in the public interest and adhere to merit-based procurement and granting processes. Both parliamentary and ministerial codes should include explicit penalties for breaches, to be enforced by an independent and well-resourced parliamentary integrity commissioner.
Integrity commissions are independent statutory agencies established to investigate and expose corruption in government and the public sector. Integrity commissions have the powers of a royal commission to question witnesses, hold public hearings and uncover complex webs of corruption. Each state in Australia has an integrity commission, and these have exposed many cases of serious and systemic corruption including the property and mining deals of Eddie Obeid in NSW, the lobbying efforts of Brian Burke in Western Australia and the undue electoral influence of property developers in Queensland.
There is no such body operating at a federal level. There is no agency with the necessary powers and jurisdiction to investigate corruption allegations involving the federal government and public service. The government announced it would establish a weak and ineffective integrity commission one year ago, and has made little progress since.
Australia urgently needs a national integrity commission with teeth. It requires a broad jurisdiction to investigate any conduct of any person which adversely affects the impartial exercise of public office. It needs to be able to call and question witnesses, publish reports, and hold public hearings. Exposure through public reports and public hearings is necessary to dissuade others from engaging in future corrupt conduct, as those considering engaging in corruption will see that allegations are investigated and offenders held responsible. A national integrity commission with strong powers is crucial to increasing public trust and lifting political culture.
The government's proposed Commonwealth Integrity Commission will not be able to investigate or expose corruption. It will not be able to begin investigations of its own accord, will not be able to accept allegations from the public, and will not be able to pursue referrals unless it can show evidence of a criminal offence being committed. It would not have been able to investigate the Bridget McKenzie affair, as there is little evidence of a criminal offence.
It will also not be able to hold public hearings or make a public report. Members of the public will not hear of any corruption investigations unless the Director of Public Prosecutions decides to pursue a case, and this may be months or years after the initial conduct took place. The proposed commission will do more to hide corruption than expose it.
Systemic reform of our accountability system is needed to improve the integrity of our political culture. Public trust will continue to be eroded if politicians engaging in misconduct are not faced with any real retribution. And those in power will continue to believe that they can act for themselves and their mates. Accountability reform must reinsert public interest to the heart of public decision making, starting with stronger codes of conduct and an effective national integrity commission.
Hannah Aulby is the executive director of The Centre for Public Integrity.
← Opinion: Your government does not want corruption investigated
ABC PM: Federal ICAC would investigate sports grants affair, former NSW auditor-general says →

redpajama_set_name: RedPajamaCommonCrawl


My role as a wedding photographer in Cornwall is one that I simply love. Sharing such an important and happy occasion in a couple's life together is a great honour and one that I don't take lightly. I am unobtrusive in my approach, blending in to the background and capturing those special moments happening all around you, some which you may not notice. My friendly and relaxed personality that puts everyone at ease, combined with the beauty of Cornwall's landscape and rugged coastline enables me to create natural but stunning images that you can treasure for eternity.


Let your business grow on new trajectory. Here are some ways that will ourish your business.
Get your business spread in the existing market Getting new customers is not bad. But better will be to sell more to the existing customers; retain the existing customers. Acquisition of new customers will involve higher promotion out-go. Whereas, selling to existing customers will be cost-effective. Pricing is another aspect which will help your business in penetrating the existing market. Remember that always charging competitive price may not help. Sometimes you need to reduce the weight/quantity of the product (indirect pricing) or offer free gifts. You may even change the packaging.
You may seek referrals During or after every job or sale, ask your satised customers if he knows anyone else who would be interested in your products or services. However, this is possible only if your deliverable can delight the customers.
Innovate or modify your product Every product or service has some life. It is always suggestible to go for product innovation or modication. This will help in adding new customers also. However, research & development wing should be strong enough to perform this. Just think of transformation of ofine business into online business.
You may start locally but increase the market reach. Many businesses have gone this way and grew tremendously. There are many ways to get it- open stores in new locations, go virtual, acquire other companies, make tie-ups, use social media, use website etc.
Trade shows can be a great way to grow too. Because trade shows draw people who are already interested in the type of product or service you offer. They can powerfully improve your bottom line.
Big market customers try to follow the customers of niche market. Once your product or service has got hold in niche market, it will be easy to extend the present big market. Think of branded apparels, use of home appliances, mobile handsets and many more.
Don't forget that reducing cost directly helps in increasing bottom line and thus valuation of business. It is not necessary to cut costs in all the areas. Few areas where it can be done are- reduce wastages, electricity cost admin costs and other indirect costs.
Diversication in products and services is interesting way to empower growth. Package the products. Simply think of a burger or pizza is available with sauce and chilli akes and cold drinks. Or, a restaurant serves meal with pickle and 'papad' and 'chutney'.
Franchising is good way to grow your business. It may not be possible to directly reach the customers to create brand of your product or services and go for franchising model.
To conclude, there is no option to let your business grow. The above ways are not exhaustive but there are ways possible to achieve that depending upon the nature of product/services and business model.


I have recently completed a draft chapter, titled "Human Rights and Chinese Tradition," for the Handbook on human rights in China being edited by Sarah Biddulph and Joshua Rosenzweig. Anyone interested can take a look; I have uploaded it to my personal archive here. Comments are very welcome!
Steve, I suggest making this the Featured Post. Mine has been up for six months, which is surely more than enough!
Hi Bill, well … I don't know that just an announcement of the availability of an essay counts as a "featured post." Manyul and I are more than happy to host substantive "featured" posts of the variety that you have contributed, and maybe I'll come up with one myself, but my instinct is to leave "Roots" there for now. Is that OK?


text:
Rainy pattern to return to Monterey Peninsula…
Rainy pattern to return to Monterey Peninsula over weekend after dry spell
A paraglider takes advantage of gusty winds at Marina State Beach Wednesday. After more dry weather Thursday, the forecast calls for rain to return to the Monterey Peninsula Friday night. (Tom Wright – Monterey Herald)
PUBLISHED: March 3, 2021 at 2:43 p.m. | UPDATED: March 3, 2021 at 2:44 p.m.
MARINA — After a long dry spell, the National Weather Service forecast calls for a rainy pattern to return to the Monterey Peninsula this weekend into next week.
"The next chance of rain for Monterey will be Friday evening," said Matt Mehle, a meteorologist with the National Weather Service. "We have a cold front approaching from the north so we have some rain moving into the North Bay Friday afternoon and then down into San Francisco and eventually down here into Monterey by Friday evening."
The weather service expects between a tenth and a quarter of an inch of rain in Monterey and as much as half an inch in Big Sur. The light rain is expected to let up by late Saturday morning, with the rest of the weekend staying dry with highs in the mid-50s in Monterey before another chance of rain moves in on Monday.
"We have unsettled weather for much of next week with additional rain chances and much colder temperatures," Mehle said.
The rain is much needed as most sites in the Monterey area are about 50% of normal since the start of the rainy season Oct. 1. While February is typically one of the wettest months, the .47 inches of rain recorded at the Monterey Airport last month was only 15% of the normal precipitation amounts. All of Monterey County is in an "abnormally dry" drought status according to the U.S. Drought Monitor.
Mehle said none of the storms next week appear to be major storms like the one that brought flooding and debris flows to Monterey County in January.
"I just looked at some of the tools that we use to see if there's going to be an atmospheric river, anything with a big moisture tap, and it's just not there," he said. "It will be beneficial when you look at the seven-day rainfall totals but nothing that's going to be like our January atmospheric river."
With meteorological winter now over, the chances for local rainfall totals to catch up to normal are dwindling. Mehle said there's no sign of a "miracle March" rain pattern in the forecast to boost those totals.
"The pattern this year just does not look favorable for a 'miracle March' at this point," he said. "Obviously our month just started and there's a lot of ground left in the month, but long-range models at least to the middle of the month just show these smaller systems but nothing overly strong or with lots of moisture. Beyond that, some of the longer-range stuff is showing conditions less likely for rainfall."
More in Weather
Weather |
Capitola Village and wharf: Storm-smashed then, storm-smashed now
Latest Headlines |
Santa Cruz locals weigh in on President's visit
How warming temperatures will make California downpours even wetter


text:
Shelf Awareness for Tuesday, September 26, 2017
#BannedBooksWeek Update: Book Search, Photo Op
Banned Books display at Powell's in Portland, Ore.
Banned Books Week is underway, and we'll be showcasing some of your creative events, displays, social media posts and more. Let us know some of the unusual ways your bookstore or library is celebrating.
An Unlikely Story, Plainville, Mass.: "Happy #BannedBooksWeek, the week customers ask why all of their favorite books are on one table. #wordshavepower."
Galaxy Bookshop, Hardwick, Vt., is launching the "Busy Person's Book Club," for which "participants are invited to take a book related to the month's theme or genre that they can share and discuss with the group." The inaugural theme is "banned or controversial."
The Curious Iguana bookstore and Flying Dog Brewery's 1st Amendment Society in Frederick, Md., have organized a Banned Book Search throughout the city. Anyone who finds a book can keep it and is invited as a VIP guest to the Curious Iguana and Flying Dog's Cheers to Freedom party on October 1.
River Lights Bookstore, Dubuque, Iowa: "Join the fun! Stand up (or better yet, sit in a comfy chair) and read a Banned Book this week. We still have a few openings...."
Eugene Public Library, Eugene, Ore.: On Sunday, people of all ages were "invited to drop in at the Downtown Library to create a green screen photo posing 'with' your favorite controversial author, current or historical."
Garden District Bookshop, New Orleans, La.: "Books allow us to get inside people other than ourselves, they show us the world through other people's eyes. Just one of the reasons during Banned Books Week and throughout the year we stand up for your Right to Read."
San Francisco's Aardvark Books May Close
Aardvark Books in San Francisco "is set to depart its longtime location at 227 Church St. (and Market)," Hoodline reported, adding: "In the neighborhood since 1978, the independently-owned shop sells new and secondhand books, magazines, graphic novels and ephemera." The building that houses Aardvark has been put on the market for $2.8 million, and the listing indicates that it will be delivered vacant once the sale closes.
The bookstore posted a message last night on Facebook: "We know that many of you learned today that our building has been put on the market. We want you all to know that although the building is on the market, it has not yet been sold. It is uncertain what our future will be.
"If the building is sold, we will remain open at least through the winter holidays. If Aardvark closes, we will be sure to let everyone know our plans, but for now we will continue to buy and sell books like normal. We hope to see you in the store soon and that you will continue supporting independent bookstores."
For anyone concerned about the shop's popular resident cat, the message concluded: "And, on a side note, Owen is in no danger of homelessness."
Book World Opening Store in Jefferson City, Mo.
Book World, which operates more than 40 bookstores in Wisconsin, North Dakota, Minnesota, Illinois, Iowa and Michigan will be adding its first Missouri store, at Capital Mall in Jefferson City, the News Tribune reported.
"We expect it to do very well," said Gregg Belonger, Book World's director of store operations. An October 3 opening is planned, as work on the store's interior is nearly done. "We should have it 99% by the end of the day Thursday." He added that for a small company, the new location is "getting to be a stretch. I don't know that we could go much further away from our home office. But from the looks of it, it's certainly worth giving it a chance."
B&N Maintains Dividend Despite Some Doubters
Although some financial observers say they expect Barnes & Noble to cut its relatively high dividend, the company's board voted last week to pay another quarterly dividend of 15 cents next month, maintaining its annual rate of 60 cents. At B&N's current share price of $7.75, the dividend yield is 8.3%.
Bloomberg said earlier this month that the company will likely cut the dividend by half "soon." And over the weekend, Seeking Alpha wrote that "on the surface, [B&N] is a very attractive dividend stock, because of its extremely high yield... however, the company's deteriorating fundamentals have called into question whether the dividend is sustainable."
The article is rather harsh about B&N's business prospects, with some dated observations like "physical bookstores are on the way out." But it points out that B&N's sales have declined steadily over the past five years. Moreover, in fiscal 2017, Seeking Alpha observed, "the company did not fully cover its dividend with earnings--earnings-per-share of $0.30 were half the $0.60 per share annualized dividend." But free cash flow just did cover the dividend, which amounted to $43.8 million.
Earlier this month, in a conference call with analysts, B&N's new CEO Demos Parneros emphasized that trade book sales had their best quarterly performance in two years; B&N sees a strong lineup of titles for the fall; the company is working on a new smaller store prototype; the pilot of a "ship-from-store program" for online sales is expanding; the company continues to review its store leases with an eye to "identifying opportunities to open new stores in new markets as well as opportunities to relocate stores as their leases expire instead of simply vacating markets"; and it continues to refreshen stores, improve merchandising and strengthen customer service. These efforts, Parneros says, will revitalize B&N. And with that, increased sales should help make the dividend sustainable and lift the company's share price.
PubWest GoFundMe Campaign for Conference Scholarships
PubWest has launched a GoFundMe "Next Generation Campaign" to raise funds for the Jack W. Swanson Scholarship, which is designed "to help aspiring publishers thrive in the publishing industry." PubWest aims to raise enough money so that the Jack W. Swanson Scholarship can send five scholarship recipients--publishing interns or first- and second-year publisher employees--to the annual PubWest Conference, which will be held next in Pasadena, Calif., February 15-17, 2018. The scholarships cover conference tuition, travel, lodging, conference intensives, and other optional events. Donations to the GoFundMe campaign, which has a goal of $5,000, can be made here.
"PubWest firmly believes in the future of publishing, and as a long-standing trade association, one of our central roles is to promote publishing as a lifelong profession," said PubWest executive director Kent Watson. "The career trajectory of past scholarship recipients has been incredible, and this year we decided to extend our fundraising outreach to all industry professionals who want to support the next publishing generation."
Image of the Day: Jason Reynolds at BookPeople
Indies First spokesperson Jason Reynolds (c.) and author most recently of Patina (Caitlyn Dlouhy/Atheneum) visited BookPeople, Austin, Tex., earlier this month. Here he posed with BookPeople booksellers (l.-r.) Holly Jerbergs, Shannon Brewer, Eugenia Vela and Tomoko Bason. (To read five things Reynolds loves about indies, click here.)
Book Video of the Day: The Nordstrom Way
The Nordstrom Way to Customer Experience Excellence: Creating a Values-Driven Service Culture by Robert Spector (Wiley), a new, completely revised edition of the business book classic that updates the Nordstrom story. The video features an interview of the author by former Village Books co-owner Chuck Robinson.
Personnel Changes at Diamond
At Diamond Comic Distributors, Josh Hayes has been promoted to head the book market division, Diamond Book Distributors, as executive v-p. He was formerly director of e-commerce business development. He joined Diamond in 2002 as national sales manager, then was promoted to associate director of sales and marketing of the book division and director of sales and marketing before leaving in 2012. For three years, he worked for Lighting Supply Company and Fiat Chrysler Automobiles before returning to Diamond. Earlier he worked at Borders as a senior planner/analyst and buyer for Waldenbooks.
Diamond v-p of sales and marketing Roger Fletcher said, "DBD has grown tremendously over the years, expanding its services and results to the point where we decided the time was right to put Josh in place to propel the business into the future."
At the same time, Kuo-Yu Liang, who has been v-p of sales and marketing, Diamond Book Distributors, and founded the division in 2003, will become v-p of international sales and business development of Diamond Comic Distributors.
Fletcher commented: "We've always been aggressive about finding new international markets for English language comics and graphic novels, and Kuo has been a big part of that success. He has a fantastic ability to prospect for new revenue and has great connections in place to build our sales internationally."
PGW to Distribute Tuttle Publishing
Effective January 2018, Publishers Group West will sell and distribute Tuttle Publishing to the industry. PGW already handles Tuttle's e-books, which will continue. It will also handle the publisher's gift sales.
Founded in 1948 as Charles E. Tuttle Company, Tuttle Publishing, North Clarendon, Vt., includes Periplus Editions and Journey Editions, and has an Asian focus, covering design, cooking, arts and crafts, martial arts, language, travel and spirituality. Tuttle has published more than 6,000 books and has an active backlist of about 1,700 titles. It publishes some 150 new titles a year.
Book Trailer of the Day: A Year in the Wilderness
A Year in the Wilderness: Bearing Witness in the Boundary Waters by Amy and Dave Freeman (Milkweed Editions).
Media Heat: Muhammad Yunus on Marketplace Morning Report
Marketplace Morning Report: Muhammad Yunus, author of A World of Three Zeros: The New Economics of Zero Poverty, Zero Unemployment, and Zero Net Carbon Emissions (PublicAffairs, $28, 9781610397575).
Fresh Air: Candice Millard, author of Hero of the Empire: The Boer War, a Daring Escape, and the Making of Winston Churchill (Anchor, $17, 9780307948786).
Sirius XM's Town Hall: Hillary Clinton, author of What Happened (Simon & Schuster, $30, 9781501175565).
Fox's Making Money with Charles Payne: Jordan Belfort, author of Way of the Wolf: Straight Line Selling: Master the Art of Persuasion, Influence, and Success (North Star Way, $26.99, 9781501164286).
Late Show with Stephen Colbert: Michael Bloomberg, co-author of Climate of Hope: How Cities, Businesses, and Citizens Can Save the Planet (St. Martin's Press, $26.99, 9781250142078).
TV: The President Is Missing
Showtime "has won the latest hotly contentious presidential race" by acquiring the rights to adapt The President is Missing, the upcoming novel from President Bill Clinton and James Patterson, into a TV series. Indiewire reported that the book, which is scheduled for release next June by Knopf and Little, Brown, "tells the story of what happens when a sitting U.S. president suddenly disappears. Clinton, who's long been a fan of Patterson and political thrillers, brought his insider knowledge of what it's like to hold the most powerful office in the land."
"I'm really enjoying writing this book and working with Jim, and I can't wait to see Showtime bring the characters to life," said Clinton.
Indiewire noted that "insiders said Clinton and Patterson met with at least 16 different outlets while pitching the project. Showtime had a bit of an edge, however, thanks to Clinton's long-standing relationship with CBS chairman/CEO Leslie Moonves. (CBS also produces and airs Zoo, which Patterson executive produces.)"
In an unfortunate choice of words, David Nevins, Showtime Networks president/CEO, called landing the book "a coup of the highest order," adding that the "pairing of President Clinton with fiction's most gripping storyteller promises a kinetic experience, one that the book world has salivated over for months and that now will dovetail perfectly into a politically relevant, character-based action series for our network."
Patterson commented: "The White House is such an exciting world to explore and is made even more so with the unique insights of a former President. Rich storytelling opportunities for this series abound."
National Book Foundation: '5 Under 35'
The National Book Foundation has announced the 2017 "5 Under 35" honorees, recognizing debut fiction writers under the age of 35 "whose work promises to leave a lasting impression on the literary landscape." They were selected by National Book Award winners and finalists, or writers previously recognized by the 5 Under 35 program. Each receives $1,000, and will be honored November 13. This year's picks are:
Lesley Nneka Arimah, author of What It Means When a Man Falls from the Sky: Stories (Riverhead), selected by Chris Bachelder, 2016 National Book Award finalist for fiction
Halle Butler, author of Jillian (Curbside Splendor), selected by Lydia Millet, 2016 National Book Award longlist for fiction
Zinzi Clemmons, author of What We Lose (Viking), selected by Angela Flournoy, 2015 National Book Award finalist for fiction and 5 Under 35 honoree
Leopoldine Core, author of When Watched: Stories (Penguin), selected by Karan Mahajan, 2016 National Book Award finalist for fiction
Weike Wang, author of Chemistry (Knopf), selected by Sherman Alexie, 2007 National Book Award winner for young people's literature
Awards: Cundill History; SCBWI MSs
The longlist has been unveiled for the $75,000 Cundill History Prize, administered by McGill University in Montreal. Three finalists will be named October 26 in London, and the winner announced on November 16 in Montreal. The two runners-up each receive a Recognition of Excellence Award worth $10,000. This year's longlisted titles are:
Black Elk by Joe Jackson
Blood in the Water: The Attica Prison Up-rising of 1971 and its Legacy by Heather Thompson
Martin Luther by Lyndal Roper
Meetings with Remarkable Manuscripts by Christopher de Hamel
The Evangelicals: The Struggle to Shape America by Frances FitzGerald
The House of the Dead: Siberian Exile Under the Tsar by Daniel Beer
The Islamic Enlightenment: The Struggle Between Faith and Reason, 1798 to Modern Times by Christopher de Ballaigue
Vietnam: A New History by Christopher Goscha
Russia in Revolution: An Empire in Crisis, 1890 to 1928 by Stephen Smith
The Great Leveler: Violence and the History of Inequality from the Stone Age to the Twenty-First Century by Walter Schneidel
The Society of Children's Book Writers & Illustrators announced this year's winners of the Sue Alexander Award and Most Promising Picture Book Award, which were chosen from manuscripts submitted for individual critiques by editors and agents at the SCBWI Annual Conference in Los Angeles.
Christine DeHerrera's Jeezus Geeks & Rainbow Freaks (YA realistic fiction) won the Sue Alexander Award, which is given to "the manuscript deemed most promising for publication." She will have her synopsis presented to a group of editors and agents.
Meg Lentz's This Door took the Picture Book Award, which recognizes "the picture book manuscript with the most promise." She receives $500 to finish the work-in-progress.
Review: Wild Horse Country: The History, Myth, and Future of the Mustang
Wild Horse Country: The History, Myth, and Future of the Mustang by David Philipps (W.W. Norton, $27.95 hardcover, 368p., 9780393247138, October 10, 2017)
David Philipps (Lethal Warriors), a Pulitzer Prize-winning correspondent for the New York Times, lives on the eastern slope of the Colorado Rockies. On the other side and west, to California's Sierra Nevadas, lies the Great Basin, the thinly populated land that is home to wild horse herds growing so fast that nobody knows quite what to do with them. Wild Horse Country is Philipps's illustrated investigation into the history, politics, legends and management of these storied symbols of America. Descended from strays, the wild horse "is not pedigreed. It has no stature.... It is beholden to no one. It will not be subjugated." No wonder it is the United States' only animal besides the bald eagle to be protected by specific national law--and no wonder this law has created such philosophical, financial and emotional drama.
Like a good reporter, Philipps goes where the story is. This is a place where there are "no fences, no power lines, no road signs, no roads"--a place that one Nevadan describes as "nothing but miles and miles of miles and miles." He interviews paleontologists who verified the presence of early horses in North America 50 million years ago. He describes the Spanish explorers' reintroduction of the horse in about 1500, and its adoption by Native American Indians. His research uncovers the very profitable killing of mustangs in the 1920s for Ken-L Ration dog food (marketing spokesdog: Rin Tin Tin) and perhaps the first animal rights activist, Frank Litts, who bombed the slaughterhouse "because horse slaughter was morally wrong." Similarly impassioned, Velma "Wild Horse Annie" Johnston almost singlehandedly drove the Wild Free-Roaming Horses and Burros Act through Congress in 1971. Since no story of American wild horses can ignore the writers who helped create their mystique, Philipps also explores the backdrop to Zane Grey's 40 pulp novels of the Wild West.
However, Philipps reserves more concern for the current state of these inspirational animals. The Federal Bureau of Land Management (BLM) manages the herds. With little budget and a typical bureaucratic snarl of regulations and acronyms, the BLM is trying to deal with a mustang population growing 15% a year. Philipps watches today's helicopter round-ups and interviews the BLM employees directing them. He visits fourth-generation cattle ranchers who hate both the feral mustangs and the BLM bureaucrats. He follows the post-round-up trail to the "holding" ranches in Kansas and Oklahoma, where the government pays out more than a billion dollars in board fees to their wealthy owners every year "trying to preserve a symbol of freedom... [by keeping] it in captivity."
The colorful, well-researched and well-reasoned Wild Horse Country concludes with an attempted answer to the wild horse dilemma, "something that could limit the herds without poisoning the legend." His solution is a refreshingly low-cost, simple one--cultivate the mustang's natural predator: the mountain lion. That solution, however, will need money and courageous leadership--things that the BLM and Congress seem to be sorely lacking. Without action, the United States may have more real mustangs than mustang school mascots. --Bruce Jacobs, founding partner Watermark Books & Cafe, Wichita, Kan.
Shelf Talker: Pulitzer Prize-winner David Philipps gets to the heart of the wild horse controversy with a little history, a little mystique, a little humor and a lot of solid investigation.
by David Philipps
Top-Selling Self-Published Titles
The bestselling self-published books last week as compiled by IndieReader.com:
1. Misadventures of a City Girl by Meredith Wild and Chelle Bliss
2. Dirty Little Secret by Kendall Ryan
3. Delirious (Quantum Series Book 6) by M.S. Force
4. Drunk on You (Hope Town Book 4) by Harper Sloan
5. Forget Me Not by Willow Winters
6. Fire and Fantasy by Various
7. We Own Tonight by Corinne Michaels
8. Play On by Samantha Young
9. The Broken Duke by Jess Michaels
10. Betrayed & Blessed: The Viscount's Shrewd Wife by Bree Wolf
[Many thanks to IndieReader.com!]


All the same great features of oregular Spark Pucks, but with 3° canting for reduced knee strain. Near infinite adjustability for splitboards with inserts. Quick mounting with super fine foot placement, angle, and toe/heel centering adjustments.
3° Canting: With 3° of canting to reduce strain, your knees will thank you.
Oversize Disk: Center disk overlaps binding channels for maximum strength and rigidity.
Adjustability: near infinite adjustability, for your perfect stance placement.
+/- 3° angle adjustments in 3° increments.
Stance width adjustments: .17 inch (4.2mm) increments.


text:
Safari from Zanzibar to Ruaha National Park
Home/ Safari from Zanzibar to Ruaha National Park
Safari from Zanzibar to Ruaha National Park | 1 Day Safari to Ruaha from Zanzibar | 2 Days Safari to Ruaha from Zanzibar | 4 Days fly in safari to Ruaha from Zanzibar | 3 Days fly in safari to Ruaha from Zanzibar
Ruaha National Park is the largest National Park in Tanzania, covers an area of about 22,000 km². It is one of the few of Tanzania's famous wilderness areas, whereby the experience of game viewing spiced up by the exciting landscape and its Great Ruaha River. The park has a high concentration of elephants, and magnificent mammals like greater and lesser kudus, sable and roan antelopes can easily be spotted in miombo woodland. The park is also a habitat for endangered wild dogs, leopards, cheetahs, giraffes, zebras, elands, impalas, bat-eared foxes and jackals.
When you are visiting Zanzibar and/or Dar Es Salaam, Ruaha National Park is only a short flight away. From Zanzibar we fly daily to one of the best National pak in Tanzania. In few minutes you will be in the middle of the bush and the amazing wildlife. The possibilities are unlimited… a quick Day Safari, Flying out of Zanzibar early morning, a full day game drive with a bush lunch included, and before the sun sets over Zanzibar, you will be back, or even more perfect, spend a few nights… so you can explore and feel the real African Bush experience.
RUAHA - one of the least busy places to visit in Tanzania
WILDLIFE SPECIES IN RUAHA NATIONAL PARK
The wider Ruaha area hosts 10% of the world's lion population and has been a Lion Conservation Unit since 2005. It's not uncommon to find prides of more than 20 lion in the park. Leopard stalk the thicker woodland areas, while cheetah can be found scanning the plains for prey. The wild dog is endangered, but Ruaha is home to almost 100 of them. There are healthy populations of hyena and black-backed jackal too.
Elephant are seen in high densities during the dry season, when they gather around the dry riverbed to dig for water with their trunks and front feet. The park is also home to plentiful buffalo, zebra, giraffe, greater and lesser kudu, Lichtenstein's hartebeest, waterbuck, bushbuck, and impala.
There are more than 570 species of birds, including the eponymous Ruaha red-billed hornbill. Migrant birds from Europe, Asia, Australia and Madagascar arrive during the rainy season between February and April.
Top Safaris from Zanzibar to Ruaha
TRIP INSIGHT TANZANIA by Air packages are available year-round, subject to availability of accommodation and internal flights. INCLUSIONS: All logistics starting and ending at Dar es Salaam or Zanzibar International Airport, all light-aircraft flights within Tanzania, private road transfers from airport to hotel in Zanzibar, all park fees and taxes, shared safari activities, all meals and house drinks on safari, and half-board basis (breakfast and dinner included) on Zanzibar, and medical evacuation insurance. EXCLUSIONS: International flights to Tanzania, Tanzania entry visa, inoculations, gratuities, additional activities, meals and drinks.
Ask for the Quote
WhatsApp: +255 759 694 668, email: info@tripinsighttanzania.com or FILL the form below:
Trip Insight Tanzania
These tours are arranged by Trip Insight Tanzania which organize tours to all Tanzania National Parks, Mountain Climbing, Cultural activities and Beach Holidays in Zanzibar
Welcome to Trip Insight; For many years we have been planning trips the length and breadth of the Country. The secret to our success? Our commitment to first-hand knowledge of every destination, lodge and activity we recommend. Collectively, we spend more than 365 days a year on safari to ensure you get the best, unbiased advice.
Whether you are dreaming of a first-hand meeting with the Big 5, getting up close and personal to a gorilla, witnessing one of the planet's most spectacular natural events, or simply relaxing on a pristine beach, our experts will tell you how and where to do it.
ZANZIBAR AND RUAHA MAPS
Ruaha & Zanzibar Safari FAQ
What is Ruaha National Park famous for?
Ruaha National Park is renowned for its excellent wildlife-sighting opportunities. Combined with the low numbers of visitors, this makes it a spectacular destination. The wider Ruaha area hosts 10% of the world's lion population and has been a Lion Conservation Unit since 2005.
When to visit Ruaha National park?
The middle and end of the Dry season (June to October) is the prime time for watching wildlife in Ruaha National Park. Animals are easier to spot because the bush thins out and wildlife concentrates around trusted water sources.
In which country is Ruaha National Park?
Tanzania; Ruaha National Park is a national park in Tanzania. The addition of the Usangu Game Reserve and other important wetlands to the park in 2008 increased its size to about 20,226 km2 (7,809 sq mi).
How to visit Ruaha National park by Car?
Ruaha is 625km from Dar es Salaam and 130km from Iringa. Travel time depends on the traffic and state of the roads but is around nine hours from Dar. By air – Daily scheduled flights fly into the park's two airstrips (Msembe and Jongomero) from Arusha, Dodoma, Kigoma and Dar es Salaam.
How many lions are in Ruaha National Park?
The greater Ruaha landscape holds around a tenth of the world's lions: it is the second largest lion population left after Selous, and is one of only six lion populations left in the world that still has over 1000 lions.
Do I need a Covid test to enter Zanzibar?
From May 2021 a negative RT-PCR COVID-19 test certificate with QR code is required for all travellers using a sample collected within 96 hours before arrival to Tanzania. Fully vaccinated travellers are also required for a negative RT-PCR COVID-19 test certificate with no exception.
How many days do you need in Zanzibar?
A minimum of three days should be what you allocate for your Zanzibar holiday. There is so much that you can do and enjoy in Zanzibar, from simply walking on fine white sand beaches to scuba diving in the Indian Ocean as well as the spice tour among so much more.
Can you drink alcohol in Zanzibar?
Yes, you can drink alcohol in Zanzibar, but be discreet. If you drink in the appropriate places and respect the local Muslim culture, having a few drinks is fine.
How expensive is Zanzibar?
The average price of a 7-day trip to Zanzibar is $2,386 for a solo traveler, $4,285 for a couple, and $8,034 for a family of 4. Zanzibar hotels range from $38 to $217 per night with an average of $64, while most vacation rentals will cost $20 to $400 per night for the entire home.
What is the best time to visit Zanzibar?
The best time to visit Zanzibar is during the archipelago's dry season, from July to September, which is a very popular time to travel. However, it's worthwhile travelling at most times of year, with balmy temperatures between 28°C and 34°C and sunshine the norm.


text:
Q: Django and regex not working with primary keys Why this dont work? State.objects.filter(pk__regex=r'^[0-9]')
I get an error:

no operator matches the given name and argument type(s)

A: Regex is for strings, but a pk is an integer.
I'm not exactly sure what you are trying to do, but if you want to just get all States with pk between 0 and 9, you can use range:
State.objects.filter(pk__range=(0, 9))

redpajama_set_name: RedPajamaStackExchange


text:
Q: How to upload a csv to box folder using powershell i'm new to powershell i have a script running on multiple devices to fetch details and i want a single csv to be generated with those details in a box folder . i wanted to know how to upload a csv to box folder using powershell without hard coding any credentials in script.
Any help will be thankfull.

A: Your question seems more authentication-related than PowerShell syntax-related.
I would first check out the documentation below from Box to get started:
Automate Box Integration Tasks from PowerShell
This link describes how to install the module and use it with these examples:
PowerShell
Install the module
Install-Module BoxCmdlets

Connect
$box = Connect-Box  -OAuthClientId "$OAuthClientId" -OAuthClientSecret "$OAuthClientSecret" -CallbackURL "$CallbackURL"

Search for and retrieve data
$id = "123"
$files = Select-Box -Connection $box -Table "Files" -Where "Id = `'$Id`'"
$files

There's a whole getting started guide here Use Box CLI with OAuth 2.0 | developer.box.com and chapter 5 focuses on using Powershell scripts with the CLI


I had every intention of posting the results of my Christmas party tables on Friday.
It really was a nice party, but seemed a bit unimportant as I heard the terrible news of the shootings in Connecticut.
So instead of sharing my party post, I spent the day weekend holding my babies.
I picked up Mini Me for a dentist appointment that morning and kept him beside me all day. I just couldn't bear to let him go. Fortunately, he's a very loving child and loves to give hugs and kisses so didn't mind Mom's clinginess and random hugging.
I am so blessed to know that as bad as the hurt is for those families, I KNOW they will see their loved ones again. I KNOW that families are forever. I hold that knowledge to be one of my greatest and most treasured foundations of my life.
I pray for the peace of the knowledge for the families touched by this terrible tragedy.
And for the rest of us, go and hold your babies and be grateful for every moment of forever with them.


Once again celebrities gave their best at the most important red carpet, Academy Awards. These Oscars 2019 we could see a lot of color among stars, above all pink was the biggest tendency. We could see from pale pink to neon shades. There was also a lot of silver gowns that made an impact.
Karl Lagerfeld, legendary designer for Chanel and Fendi passed away in Paris yesterday ending some fashion era and leaving us with some iconic design and moments we will remember forever. Below you can enjoy 10 my favourite designs and some important fashion moments.
Hoy os quiero compartir street style captado durante evento de moda B Capital por nuestro fotógrafo Lejo Ramirez.
Propuesta de Maestros Ancestrales, proyecto de la revista Fucsia sin ninguna duda fue para mi el mejor desfile en el marco de esta edición de BCapital.
BCapital arranco fuerte este año inaugurando el espacio de moda colombiana en Teatro Faenza con desfile de talentoso diseñador Jorge Duque.
En este video os voy a mostrar un resumen de viaje con mi familia polaca a amazonas, caminatas por selva, isla de los micos y excursion con barco por jungla hundida y mucho más. Viajan conmigo al paraíso !!!
Check out my last video from Colombian fashion week, the best of local fashion, streetstyle, backstage make up trends and more.
And today last part of streets style inspiration, the best looks of Bogota Fashion Week found by our photographers Juan from @walkscapades and Julian @jcarv.
Today I want to share with you my three looks from Bogota Fashion Week, on this ocasion I wanted to show you how you can dress really trendy without spending a lot mixing vintage clothing with high street fashion.
Otro edición de Bogota Fashion Week se terminó, mostrando varios talentos colombianos que conquistaron su audiencia.


Get onto the current neon trend with this loungewear set. Featuring a neon yellow knitted fabric, off shoulder cable stitch detail jumper and shorts, what's not to love? Team with chunky trainers and cute sports socks to complete the look.