text:
\section{Introduction}
\label{sec:introduction}
\input{sections/01_introduction}

\section{Statistical Methods}
\label{sec:statistical_methods}
\input{sections/02_statistical_methods}

\section{Data}
\label{sec:data}
\input{sections/03_data}

\section{Simulation Studies}
\label{sec:simulations}
\input{sections/04_simulation_studies}

\section{Data Application}
\label{sec:data_application}
\input{sections/05_data_application}

\section{Discussion}
\label{sec:discussion}
\input{sections/06_discussion}

\begin{supplement}[id=suppA]
  \sname{Supplement A}
  \stitle{Supplemental figures and tables}
  \slink[doi]{10.1214/00-AOASXXXXSUPP}
  \sdatatype{.pdf}
  \sdescription{Additional figures, tables, and discussion.}
\end{supplement}

\begin{supplement}[id=suppB]
  \sname{Supplement B}
  \stitle{Code to reproduce paper analysis}
  \slink[doi]{10.1214/00-AOASXXXXSUPP}
  \sdatatype{.zip}
  \sdescription{Directory with code to perform analysis and
generate figures in paper, also available at \href{https://github.com/janewliang/PanelRePROducible}{https://github.com/janewliang/PanelRePROducible}}
\end{supplement}

\bibliographystyle{imsart-nameyear}

\subsection{Model Validation}
For model validation, we applied PanelPRO-5BC and PanelPRO-11 to the data from the HCP study (Section \ref{sec:usc}). We also ran the BayesMendel models nested within these models (BRCAPRO for PanelPRO-5BC and BRCAPRO, MMRpro, and Melapro for PanelPRO-11). The code to reproduce the validation results is avalable in \cite{liang2021panelprorepo}. Some of the families in the HCP study report tumor marker testing results, so we ran the models with and without incorporating this extra risk-modifying information. To evaluate the models, we used the performance metrics described in Section \ref{sec:diagnostic_metrics} and obtained percentile confidence intervals from 1000 bootstrap samples.

The metrics and confidence intervals for PanelPRO-5BC are reported in Figure~\ref{fig:usc_pp5} and Supplemental Table~S5; those for for PanelPRO-11 are reported in Figure~\ref{fig:usc_pp11} and Supplemental Table~S6 \citep{liang2021panelprofigs}. Metrics use outcome labels based on carrier status of individual genes as well as groups of genes. Both types remain fairly consistent between the full PanelPRO models and their submodels. The results for models run with risk modifiers are often similar to those without risk modifiers. The MMRpro submodel appears to have better discrimination than PanelPRO-11 for Lynch syndrome genes MLH1, MSH2, and MSH6. The HCP cohort contains a high proportion of ovarian cancer, as well as cases of brain, pancreatic, and small intestine cancers, all of which are also associated with MLH1, MSH2, and MSH6 (Figure~\ref{fig:mutxcanc}). Only PanelPRO-11, which appears to be slightly over-predicting the carrier probabilities for these genes, incorporates these additional associations, suggesting that the ascertainment process of the cohort makes this a difficult discrimination problem.

We acknowledge that the small sample size of the data-processed cohort makes it difficult to detect meaningful differences. The wide bootstrap confidence intervals are likely also attributable to the small number of cases. Similarly, the observation that incorporating risk modifiers into the models makes a limited impact on the results may be due to the relatively low number of families with tumor marker information. Section S6 of the supplementary material \citep{liang2021panelprofigs} contains discussion on how often PanelPRO-5BC and PanelPRO-11 improve over the BayesMendel submodels in the 1000 bootstrap replicates; the full model does not consistently have better metrics across bootstraps. These results are again likely due to limitations in the sample size and ascertainment process for the HCP data that cause it to deviate from the makeup of the general population, for which the model parameters were estimated.

\begin{figure}[!hbtp]
    \centering
    \includegraphics[width=\linewidth]{figs/usc_pp5/diagnostics.png}
    \caption{AUC, calibration, and MSE for the full PanelPRO-5BC model (black) and the BRCAPRO submodel (blue) evaluated on the HCP cohort, with (open points) and without (closed points) risk modifiers. ``BRCAPRO genes'' indicates any of the genes in BRCAPRO (BRCA1, BRCA2), and ``Any'' indicates any of the five genes in PanelPRO-5BC. 95\% bootstrap percentile confidence intervals are also shown.}
    \label{fig:usc_pp5}
\end{figure}

\begin{figure}[!hbtp]
    \centering
    \includegraphics[width=\linewidth]{figs/usc_pp11/diagnostics.png}
    \caption{AUC, calibration, and MSE for the full PanelPRO-11 model (black) and its BayesMendel submodels BRCAPRO, MMRpro, and Melapro (blue) evaluated on the HCP cohort, with (open points) and without (closed points) risk modifiers. ``BRCAPRO genes'', ``MMRpro genes'', and ``Any BM'' indicate any of the genes in BRCAPRO (BRCA1, BRCA2), MMRpro (MLH1, MSH2, MSH6), and any model in the BayesMendel package (BRCA1, BRCA2, MLH1, MSH2, MSH6, CDKN2A), respectively. ``Any'' indicates any of the eleven genes in PanelPRO-11. 95\% bootstrap percentile confidence intervals are also shown.}
    \label{fig:usc_pp11}
\end{figure}

The AUC confidence intervals for some genes, especially low-penetrant genes, overlap with 0.5. However, we note that the lower bound for the ``Any'' AUC is consistently above 0.5 for both PanelPRO-5BC and PanelPRO-11. Moreover, it is still beneficial to include lower-penetrant genes so that PanelPRO can estimate the probabilities of carrying pathogenic variants of these genes.

A key contribution of the multi-syndrome predictions enabled by PanelPRO is the ability to acknowledge syndrome overlap in counseling individuals at risk. To illustrate, Figure~\ref{fig:usc_pp11_thresh} shows the probabilities of carrying a pathogenic variant of any PanelPRO-11 gene against the probabilities for carrying a pathogenic variant of any BRCAPRO gene (BRCA1 or BRCA2, left) and any MMRpro gene (MLH1, MSH2, or MSH6, right) in the HCP cohort. Of the 150 HCP counselees who are carriers of any pathogenic variant in PanelPRO-11, 61 had carrier probabilities above a 2.5\% threshold for PanelPRO but not BRCAPRO and 0 had carrier probabilities above 2.5\% for BRCAPRO but not PanelPRO. Similarly, 89 counselees had carrier probabilities above above 2.5\% for PanelPRO but not MMRpro, and 0 had carrier probabilities above 2.5\% for MMRpro but not PanelPRO. This demonstrates that the potential refinement in counseling practice by jointly considering syndromes whose phenotypes overlap can affect a large proportion of families.

\begin{figure}[!hbtp]
    \centering
    \includegraphics[width=0.49\linewidth]{figs/usc_pp11/thresh_any_brcapro.png} \hfill \includegraphics[width=0.49\linewidth]{figs/usc_pp11/thresh_any_mmrpro.png}
    \caption{Probabilities of carrying a pathogenic variant of any PanelPRO-11 gene plotted against the probabilities for carrying a pathogenic variant of any BRCAPRO gene (BRCA1 or BRCA2, left) and against the probabilities for carrying a pathogenic variant of any \mbox{MMRpro} gene (MLH1, MSH2, or MSH6, right) in the HCP cohort. Counselees who are true pathogenic variant carriers of BRCA1 or BRCA2 are colored blue; those who are true pathogenic variant carriers of MLH1, MSH2, or MSH6 are colored orange; and those who are carriers of pathogenic variants of any of the six other PanelPRO-11 genes are colored black. Reference lines are drawn at 2.5\%.}
    \label{fig:usc_pp11_thresh}
\end{figure}

\subsection{Sensitivity to Family Size}
To examine the performance that can be achieved by PanelPRO-5BC and PanelPRO-11 when very extensive family history is available, we simulated additional families with a large number of relatives. Each simulated counselee has four maternal aunts, maternal uncles, paternal aunts, paternal uncles, sisters, and brothers. The counselee and their siblings each have four daughters and four sons, for a total of 112 simulated relatives in each family. These are unrealistically large for most clinical applications, and serve here to provide a best case scenario.

Performance metrics and bootstrap confidence intervals obtained from evaluating PanelPRO-5BC and PanelPRO-11 on the HCP cohort, simulated families with structures sampled from the HCP cohort, and large simulated families are reported in Supplemental Figures~S8-S9 and Supplemental Tables~S11-S12 \citep{liang2021panelprofigs}. To make the simulation results more comparable to the results from the HCP data, we computed these metrics based on a subset of the simulated families that has the same number of families as the HCP cohort, with the same number of pathogenic variant carriers for each gene. While the metrics usually look best when PanelPRO can take advantage of a detailed family history, the results from the real data and a simulation with fewer relatives often do not lag too far behind. We also note that the results from the HCP cohort are typically better calibrated than those from either set of simulated families, albeit with wide confidence intervals. The process of subsetting the simulated families to have the same number of carriers as the HCP cohort does not match the ascertainment process for the cohort, which is likely the driving force behind this phenomenon.

\subsection{Model Parameters}

In summary, the PanelPRO framework can be used to train a Mendelian model with any $K$ genes and $R$ cancers. The training involves meta-analysis or literature reviews to identify allele frequency inputs for each of the genes and age-dependent penetrance inputs for each of the gene-cancer combinations. PanelPRO converts these into clinically relevant carrier probabilities and absolute risk evaluations.

To illustrate, we present three different examples of PanelPRO models that collectively span 11 genes, plus a hypothetical PANC gene, and 11 cancers. PANC is an unspecified pancreatic cancer susceptibility gene used in the PancPRO \citep{wang2007pancpro} Mendelian model for identifying individuals at high risk for pancreatic cancer. The current PanelPRO package includes all the input estimates discussed here, as well as others, with the exception of PANC, which is only discussed here in the context of back-compatibility with PancPRO. Allele frequencies and penetrances used to construct the models are estimated based on existing literature. For BRCA1 and BRCA2, we used the non-Ashkenazi, Ashkenazi Jewish and Italian allele frequency estimates from BRCAPRO \citep{chen2004bayesmendel, antoniou2002comprehensive}; for MLH1, MSH2, and MSH6, we used the allele frequency estimates from MMRpro \citep{chen2004bayesmendel, chen2006prediction}; for the hypothetical PANC gene, we used the allele frequency estimate from Pancpro \citep{chen2004bayesmendel, wang2007pancpro}; and for CDKN2A, we used the allele frequency estimate from Melapro \citep{chen2004bayesmendel, berwick2006prevalence}. Allele frequency estimates for ATM, CHEK2, and PALB2 were taken from \cite{lee2016incorporating}. Finally, we estimated allele frequencies for EPCAM and PMS2 from a 25-gene panel study of 252,223 individuals \citep{rosenthal2017clinical}.

Racially-informed (All Races, American Indian and Alaska Native, Asian, Black, White, Hispanic, White Hispanic, and White Non-Hispanic) probabilities of developing cancer (unconditional on genotype) were taken from the DevCan database \citep{statistical2020devcan}; penetrances for non-carriers are estimated by PanelPRO based on these values as well as the carrier penetrances and allele frequencies. When available, we took cancer penetrances for carriers from data included in the BayesMendel package: the BRCA1 and BRCA2 estimates for the probability of developing breast or ovarian cancer \citep{chen2020penetrance}; the MLH1, MSH2, and MSH6 estimates for the probability of developing colorectal or endometrial cancer \citep{wang2020penetrance, felton2007constitutive}; the PANC estimates for the probability of developing pancreatic cancer  \citep{wang2007pancpro, klein2002evidence}; and the CDKN2A estimates for the probability of developing melanoma \citep{wang2010estimating, begg2005lifetime, bishop2002geographical}. These gene$\times$cancer combinations are colored orange in Figure~\ref{fig:mutxcanc}. Combinations colored in blue were obtained based on a literature review and are also available in the All Syndromes Known to Man Evaluator (ASK2ME) \citep{braun2018clinical} tool. Combinations in white are not included, as insufficient evidence of association has been accrued.

The sensitivities and specificities for tumor marker testing of ER, CK5/6, CK14, HER, and PR are from \cite{lakhani2002pathology, lakhani2005prediction}; the sensitivity and specificity for MSI testing are from \cite{chu2007random}. While the probability distribution of death from other causes does not come into play for the analysis in this paper, the PanelPRO package takes estimates for these values from DevCan \citep{statistical2020devcan}. The hazard ratios used for incorporating prophylactic mastectomies and oophorectomies into risk assessment are based on \cite{katki2007incorporating}.

\begin{figure}[!hbtp]
    \centering
    \footnotesize
    {\setlength{\tabcolsep}{2.5pt}
    \begin{tabular}{>{\raggedleft}p{3.25cm}|*{11}{p{0.55cm}|}}
        \multicolumn{1}{c}{} & \multicolumn{1}{c}{\rotatebox{90}{Brain}} & \multicolumn{1}{c}{\rotatebox{90}{Breast}} & \multicolumn{1}{c}{\rotatebox{90}{Colorectal}} & \multicolumn{1}{c}{\rotatebox{90}{Endometrial}} & \multicolumn{1}{c}{\rotatebox{90}{Gastric}} & \multicolumn{1}{c}{\rotatebox{90}{Kidney}} & \multicolumn{1}{c}{\rotatebox{90}{Melanoma}} & \multicolumn{1}{c}{\rotatebox{90}{Ovarian}} & \multicolumn{1}{c}{\rotatebox{90}{Pancreatic}} & \multicolumn{1}{c}{\rotatebox{90}{Prostate}} & \multicolumn{1}{c}{\rotatebox{90}{\shortstack{Small \\ Intestine}}} \\
        \cline{2-12} \vspace{0.5mm}
        ATM (0.0019) & & \cellcolor{PPColVar} & \cellcolor{PPColVar} & & \cellcolor{PPColVar} & & & & \cellcolor{PPColVar} & \cellcolor{PPColVar} & \\
        \cline{2-12} \vspace{0.5mm}
        BRCA1 (0.0005829) & & \cellcolor{BMColVar} & & & & & & \cellcolor{BMColVar} & \cellcolor{PPColVar} & & \\
        \cline{2-12} \vspace{0.5mm}
        BRCA2 (0.000676) & & \cellcolor{BMColVar} & & & & & & \cellcolor{BMColVar} & \cellcolor{PPColVar} & \cellcolor{PPColVar} & \\
        \cline{2-12} \vspace{0.5mm}
        CDKN2A (0.00015) & & & & & & & \cellcolor{BMColVar} & & \cellcolor{PPColVar} & & \\
        \cline{2-12} \vspace{0.5mm}
        CHEK2 (0.0026) & & \cellcolor{PPColVar} & \cellcolor{PPColVar} & & & \cellcolor{PPColVar} & & & & \cellcolor{PPColVar} & \\
        \cline{2-12} \vspace{0.5mm}
        EPCAM (0.000011) & & & \cellcolor{PPColVar} & & & & & & & & \\
        \cline{2-12} \vspace{0.5mm}
        MLH1 (0.00045) & \cellcolor{PPColVar} & & \cellcolor{BMColVar} & \cellcolor{BMColVar} & \cellcolor{PPColVar} & & & \cellcolor{PPColVar} & \cellcolor{PPColVar} & & \cellcolor{PPColVar} \\
        \cline{2-12} \vspace{0.5mm}
        MSH2 (0.00050) & \cellcolor{PPColVar} & & \cellcolor{BMColVar} & \cellcolor{BMColVar} & \cellcolor{PPColVar} & & & \cellcolor{PPColVar} & \cellcolor{PPColVar} & & \cellcolor{PPColVar} \\
        \cline{2-12} \vspace{0.5mm}
        MSH6 (0.00018) & \cellcolor{PPColVar} & & \cellcolor{BMColVar} & \cellcolor{BMColVar} & \cellcolor{PPColVar} & & & \cellcolor{PPColVar} & & & \cellcolor{PPColVar} \\
        \cline{2-12} \vspace{0.5mm}
        PALB2 (0.00057) & & \cellcolor{PPColVar} & & & & & & & \cellcolor{PPColVar} & & \\
        \cline{2-12} \vspace{0.5mm}
        PANC (0.0034) & & & & & & & & & \cellcolor{BMColVar} & & \\
        \cline{2-12} \vspace{0.5mm}
        PMS2 (0.00084) & & & \cellcolor{PPColVar} & \cellcolor{PPColVar} & & & & \cellcolor{PPColVar} & & & \\
        \cline{2-12}
    \end{tabular}
    }
    \caption{Associations between the 11 genes, plus a hypothetical PANC gene, (rows) and 11 cancers (columns) collectively incorporated in the PanelPRO models illustrated in this paper. PANC is only listed in order to discuss back-compatibility with PancPRO and is not a gene that can currently be specified in the PanelPRO package. Population-level allele frequencies are given in parentheses (the CHEK2 allele frequency is for the 1100delC only; the allele frequencies for all other genes are for any pathogenic variant). Orange cells correspond to penetrances that are available in the BayesMendel package \citep{chen2004bayesmendel}, and blue cells correspond to penetrances based on a literature review that are also available in ASK2ME \citep{braun2018clinical}.}
    \label{fig:mutxcanc}
\end{figure}

\subsection{USC-Stanford HCP Cohort}
\label{sec:usc}
In Section \ref{sec:data_application}, we validate our method using data from the USC-Stanford Hereditary Cancer Panel (HCP) Testing Study, a prospective, multi-center study on multiplex gene panel testing for cancer susceptibility \citep{idos2019multicenter}. A diverse group of 2000 patients was recruited from three medical centers: 1) USC Norris Comprehensive Cancer Center; 2) Los Angeles County + USC Medical Center; 3) Stanford University Cancer Institute. Eligible patients met clinical guideline criteria for genetic testing or had a $\geq$2.5\% probability of mutation carriage calculated by the following validated models or algorithms: BayesMendel \citep{chen2004bayesmendel}, BOADICEA \citep{antoniou2008boadicea}, IBIS (Tyrer-Cuzick) \citep{tyrer2004breast}, PREMM 1,2,6 \citep{euhus2001understanding, kastrinos2009risk, kote2011brca2}, National Comprehensive Cancer Network (NCCN) Guidelines, or a personal history of $\geq$10 cumulative lifetime tubular adenomas \citep{idos2019multicenter}. Diagnostic yield and off-target mutation detection was evaluated for 25- or 28-gene multi-gene panels \citep{idos2019multicenter} and performed by Myriad Genetic Laboratories (Salt Lake City, UT).

We validate two models, PanelPRO-5BC and PanelPRO-11, using this data. We excluded families if: the counselee is a carrier of one or more variants only in genes not included in the model; the counselee has a variant of uncertain significance (VUS), but not a pathogenic variant for any of the genes in the model; or the models cannot be applied to the pedigree (typically due to ``loops''/inter-marriages or the reporting of cancer affection ages that are greater than the individual's censoring age). We thus consider 1612 families for validating PanelPRO-5BC (average family size of 34.15) and 1468 families for PanelPRO-11 (average family size of 33.78). Tables~\ref{tab:usc_pp5_summary} and \ref{tab:usc_pp11_summary} summarize the number of pathogenic variant carriers and cancer cases among the counselees in the study for PanelPRO-5BC and PanelPRO-11, respectively.

\begin{table}[!hbtp]
    \caption{Number of counselees in the HCP multi-gene panel testing study who are pathogenic variant carriers (Table~\ref{tab:usc_pp5_summary_genes}) and cancer cases (Table~\ref{tab:usc_pp5_summary_cancers}) for genes and cancers modeled by PanelPRO-5BC. These counts are based on the 1612 families left after processing the data for validating PanelPRO-5BC.}
    \label{tab:usc_pp5_summary}
    \centering
    \begin{subtable}{\textwidth}
        \caption{Counselees who are pathogenic variant carriers.}
        \label{tab:usc_pp5_summary_genes}
        \centering
        \begin{tabular}{ccccccc}
            \hline
            ATM & BRCA1 & BRCA2 & CHEK2 & PALB2 & Any Carrier & Non-Carrier \\
            \hline
            23 & 41 & 35 & 22 & 15 & 113 & 1499 \\
            \hline
        \end{tabular}
    \end{subtable}

    \begin{subtable}{\textwidth}
        \caption{Counselees who are cancer cases.}
        \label{tab:usc_pp5_summary_cancers}
        \centering
        \begin{tabular}{ccccc}
            \hline
            Breast & Ovarian & Other Cancer & Any Cancer & No Cancer \\
            \hline
            485 & 106 & 693 & 1161 & 451 \\
            \hline
        \end{tabular}
    \end{subtable}
\end{table}

\begin{table}[!hbtp]
    \caption{Number of counselees in the HCP multi-gene panel testing study who are pathogenic variant carriers (Table~\ref{tab:usc_pp11_summary_genes}) and cancer cases (Table~\ref{tab:usc_pp11_summary_cancers}) for genes and cancers modeled by PanelPRO-11. These counts are based on the 1468 families left after processing the data for validating PanelPRO-11.}
    \label{tab:usc_pp11_summary}
    \centering
    \begin{subtable}{\textwidth}
        \caption{Counselees who are pathogenic variant carriers.}
        \label{tab:usc_pp11_summary_genes}
        \centering
        \begin{tabular}{ccccccc}
            \hline
            ATM & BRCA1 & BRCA2 & CDKN2A & CHEK2 & EPCAM & MLH1 \\
            \hline
            23 & 41 & 35 & 5 & 27 & 1 & 9 \\
            \hline
        \end{tabular}

        \vspace{2mm}

        \begin{tabular}{cccccc}
            \hline
            MSH2 & MSH6 & PALB2 & PMS2 & Any Carrier & Non-Carrier \\
            \hline
            11 & 9 & 14 & 15 & 150 & 1318  \\
            \hline
        \end{tabular}
    \end{subtable}

    \begin{subtable}{\textwidth}
        \caption{Counselees who are cancer cases.}
        \label{tab:usc_pp11_summary_cancers}
        \centering
        \begin{tabular}{cccccccc}
            \hline
            Brain & Breast & Colorectal & Endometrial & Gastric & Kidney &  Melanoma & Ovarian \\
            \hline
            9 & 444 & 218 & 50 & 36 & 15 & 92 & 93 \\
            \hline
        \end{tabular}

        \vspace{2mm}

        \begin{tabular}{cccccc}
            \hline
            Pancreatic & Prostate & Small Intestine & Other Cancer & Any Cancer & No Cancer\\
            \hline
            36 & 26 & 1 & 254 & 1055 & 413  \\
            \hline
        \end{tabular}
    \end{subtable}
\end{table}

Additionally, breast tumor marker and MSI testing results are reported for some of families. In the PanelPRO-5BC validation subset, there are 204 families with at least one relative tested for ER, 167 for PR, and 55 for HER (a total of 226 or 14\% families reported any results). In the PanelPRO-11 validation subset, there are 185 families with at least one relative tested for ER, 153 for PR, 45 for HER, and 3 for MSI (a total of 208 or 14.2\% families reported any results). Information on preventative interventions like mastectomies, oopherectomies, and hysterectomies was not available.

We used racial or ancestry-informed allele frequencies and penetrances when available to match those reported in the data. Missing ages of cancer diagnosis and censoring ages were imputed by PanelPRO \citep{lee2021panelpro}.
\subsection{Data Generation}
For each simulation study, we generated 1,000,000 families with structures sampled from families in the HCP study. Each simulated family includes the counselee and their grandparents, parents, and siblings, as well as any other offspring of the above. Genotypes for the founders of each family were sampled from non-Ashkenazi Jewish population-level allele frequencies. Then, the genotypes of their descendants were assigned based on Mendelian inheritance, with all genes assumed to be independent. The genotypes of non-blood relatives (i.e. spouses of the descendants) were sampled from the non-Ashkenazi Jewish population-level allele frequencies. Cancer status and age of diagnosis were simulated conditional on the individual's genotype, based on the cancer penetrances for ``All Races'' used in the models. Based on the genotype and cancer diagnosis statuses of each individual, we simulated results from biomarker testing for ER, CK5/6, CK14, PR, and HER for those with breast cancer and MSI for those with colorectal cancer. The code to simulate families and reproduce these simulation studies is publicly available \citep{liang2021panelprorepo}.

\subsection{Performance Metrics}
\label{sec:diagnostic_metrics}
To evaluate the carrier probabilities from our models, we consider several performance metrics \citep{steyerberg2010assessing}. We use the area under the curve (AUC) as a measure for discrimination, the expected divided by the observed number of events (E/O) as a measure of calibration, and mean squared error (MSE) as a measure of overall accuracy. When computing these metrics, non-carriers are defined as individuals who are not variant carriers of any gene in the model. Percentile confidence intervals are obtained from 1000 bootstrap samples.

\subsection{Back-Compatibility}
Four Mendelian risk prediction models are currently implemented in the BayesMendel R package (Table \ref{tab:pp7}), each incorporating information from between 1-3 genes and cancers. Altogether, these models span seven genes (including a hypothetical PANC gene) and six cancers.

\begin{table}[!hbtp]
    \centering
    \caption{Genes and cancers incorporated in the four existing BayseMendel Mendelian risk prediction models.}
    \label{tab:pp7}
    \begin{tabular}{rll}
        \hline
        BayesMendel model & Gene(s) & Cancer(s) \\
        \hline
        BRCAPRO & BRCA1, BRCA2 & Breast, Ovarian \\
        MMRpro & MLH1, MSH2, MSH6 & Colorectal, Endometrial \\
        Pancpro & hypothetical PANC & Pancreatic \\
        Melapro & CDKN2A & Melanoma \\
        \hline
    \end{tabular}
\end{table}

To validate the reverse-compatibility of our approach, we fit these existing models using the PanelPRO and BayesMendel packages and evaluated their performance on 1,000,000 simulated families, using the same model parameters and settings. These families were simulated assuming only the presence of the gene-cancer associations incorporated in the four existing models (orange in Figure~\ref{fig:mutxcanc}), and based on family structures sampled from the HCP cohort. Because PanelPRO and BRCAPRO from the BayesMendel package handle contralateral breast cancer using different approaches, we eliminated it from consideration when fitting the models, to obtain a more direct comparison. The resulting metrics and carrier probabilities are virtually identical between the two sets of models, as expected (Supplemental Figure~S1 and Supplemental Table~S1 \citep{liang2021panelprofigs}).

\subsection{PanelPRO-5BC}

We then simulated and evaluated 1,000,000 families under PanelPRO-5BC, a model that obtains carrier probabilities for ATM, BRCA1, BRCA2, CHEK2, and PALB2 based on family history of breast and ovarian cancer. As a point of reference, we also used the PanelPRO package to evaluate the simulated families with the BRCAPRO submodel, which only considers BRCA1 and BRCA2. Figure~\ref{fig:sim_pp5} plots metrics with bootstrap confidence intervals for PanelPRO-5BC; these metrics are also reported in Supplemental Table S2 \citep{liang2021panelprofigs}.

The results for the PanelPRO-5BC model and its BRCAPRO submodel are highly similar.
The metrics for PanelPRO-5BC and BRCAPRO were also  similar to each other across bootstrap replicates, as described in Section S6 of the supplementary material \citep{liang2021panelprofigs}. Incorporating simulated tumor marker testing for ER, PR, and HER in the model led to slightly better discrimination and precision of BRCA1 and BRCA2, as well as differences in calibration.

\begin{figure}[!hbtp]
    \centering
    \includegraphics[width=\linewidth]{figs/sim_pp5/diagnostics.png}
    \caption{AUC, calibration, and MSE for the full PanelPRO-5BC model (black) and the BRCAPRO submodel (blue) evaluated on 1,000,000 families simulated based on PanelPRO-5BC, with (open points) and without (closed points) risk modifiers. ``BRCAPRO genes'' indicates any of the genes in BRCAPRO (BRCA1, BRCA2), and ``Any'' indicates any of the five genes in PanelPRO-5BC. 95\% bootstrap percentile confidence intervals are also shown.}
    \label{fig:sim_pp5}
\end{figure}

\subsection{PanelPRO-11}

As another illustration of the flexibility of our approach, we considered PanelPRO-11, an 11-gene (ATM, BRCA1, BRCA2, CDKN2A, CHEK2, EPCAM, MLH1, MSH2, MSH6, PALB2, and PMS2), 11-cancer (brain, breast, colorectal, endometrial, gastric, kidney, melanoma, ovarian, pancreatic, prostate, and small intestine) model. The performance metrics resulting from evaluating PanelPRO-11 on 1,000,000 simulated families are plotted in Figure~\ref{fig:sim_pp11} and are reported in detail in Supplemental Table S3 \citep{liang2021panelprofigs}. We also evaluated the three BayesMendel submodels (BRCAPRO, MMRpro, Melapro) that are nested within PanelPRO-11. Including biomarker testing results can improve the metrics, particularly discrimination, for related genes such as MLH1, MSH2, MSH6, and PMS2. The very large calibration confidence intervals for EPCAM can be attributed to its low allele frequency, and the therefore low number of cases among the 1,000,000 simulated counselees.

Throughout, the full PanelPRO-11 model's metrics are closely aligned with those of its submodels, with slightly better discrimination in some cases. In nearly all of the bootstrap samples, PanelPRO-11 has a better AUC and MSE. PanelPRO-11's improvement in terms of calibration is less consistent, but the differences in model calibration are typically small (less than 2\%) within bootstrap samples. Furthermore, whether or not PanelPRO improves over the submodel seems to be largely dependent on how well calibrated both models are; when both models are well-calibrated, PanelPRO's calibration will be better about half the time. See Section S6 of the supplementary material for additional details \citep{liang2021panelprofigs}. PanelPRO-11 is thus able to produce the results of the existing BRCAPRO, MMRpro, and Melapro models, while also computing probabilities for being a carrier of ATM, CHEK2, EPCAM, PALB2, and PMS2.

\begin{figure}[!hbtp]
    \centering
    \includegraphics[width=\linewidth]{figs/sim_pp11/diagnostics.png}
    \caption{AUC, calibration, and MSE for the full PanelPRO-11 model (black) and its BayesMendel submodels BRCAPRO, MMRpro, and Melapro (blue) evaluated on 1,000,000 families simulated based on PanelPRO-11, with (open points) and without (closed points) risk modifiers. ``BRCAPRO genes'', ``MMRpro genes'', and ``Any BM'' indicate any of the genes in BRCAPRO (BRCA1, BRCA2), MMRpro (MLH1, MSH2, MSH6), and any model in the BayesMendel package (BRCA1, BRCA2, MLH1, MSH2, MSH6, CDKN2A), respectively. ``Any'' indicates any of the eleven genes in PanelPRO-11. 95\% bootstrap percentile confidence intervals are also shown.}
    \label{fig:sim_pp11}
\end{figure}

The AUC for predicting pathogenic variant carriers of ``Any'' gene is 0.69. This is lower than the discrimination for most of the individual genes, many of which have AUCs above 0.8 or even 0.9. Groupings of genes that have individually high AUCs, like the BRCAPRO genes (BRCA1 and BRCA2) or the MMRpro genes (MLH1, MSH2, and MSH6), tend to retain good discrimination. However, including poorly-discriminating genes, as expected, pulls down the group AUC. This trend is observable for both PanelPRO-11 and the PanelPRO-5BC AUC results in Figure~\ref{fig:sim_pp5}(a).

Figure~\ref{fig:AUC_RR} plots the AUCs from this simulation study against the relative risks of developing each of the 11 cancers in PanelPRO-11 by age 70, for pathogenic variant carriers compared to noncarriers. Both male and female relative risks are shown; see Supplemental Figure~S2 for plots that separate between sexes \citep{liang2021panelprofigs}. Genes with lower AUCs correspond to those that have low relative risks for each of the eleven cancers. It appears that good discrimination for a given gene requires the gene to have a high relative risk for at least one cancer in the model.
This trend is not expected for allele frequency (Supplemental Figure~S3 \citep{liang2021panelprofigs}). Note that ATM and CHECK2 have both low penetrance and high prevalence, but their low AUC is likely attributable to the former.
The AUCs, allele frequencies, and relative risks plotted in Figure~\ref{fig:AUC_RR} and Supplemental Figures~S2-S3 are summarized in Supplemental Table S4 \citep{liang2021panelprofigs}.

\begin{figure}[!hbtp]
    \centering
    \includegraphics[width=0.95\linewidth]{figs/sim_pp11/AUC_RR.png}
    \caption{Area under the curve (AUC) from evaluating PanelPRO-11 on 1,000,000 simulated families plotted against the relative risk of developing each cancer by age 70, for pathogenic variant carriers compared to noncarriers.}
    \label{fig:AUC_RR}
\end{figure}
\subsection{Proposed Model}
Suppose that a given counselee has a family of size $I$, and let $\boldsymbol{G}_i = \left( G_{1i}, \dots, G_{Ki} \right)$ be the genotype vector for the $i$th family member, $i= 1, \dots, I$, where the counselee is indexed by 1. Each element $G_{ki}$ stores individual $i$'s carrier status for a pathogenic variant in the $k$th gene. Let $\mathcal{G}$ denote the set of all $2^K$ possible genotypes. In the simple case where only wild-type and heterozygous carriers need to be considered, $G_{ki}$ is binary. Then, in a two-gene model, $\boldsymbol{G}_i$ has length $K=2$ and there are $2^2 = 4$ possible genotypes (noncarrier for both genes, carrier of only the first pathogenic variant, carrier of only the second pathogenic variant, and carrier of pathogenic variants for both genes). Generally, more than two states can be assumed: for instance, we can differentiate between carriers of variants on one allele vs. both alleles. Then there are three possible states encoded as $0, 1,$ or $2$, and $3^K$ possible genotypes. One can also assume the presence of additional states implied by having multiple variant types for a given gene.

Each individual in the family also has a vector of phenotypes $\boldsymbol{H}_i = \left( \boldsymbol{H}_{1i}, \dots , \boldsymbol{H}_{Ri} \right)$, where $R$ is the arbitrary but fixed number of cancers or other phenotypes in the model. For individual $i$, let $T_{ri}$ be the age of diagnosis for cancer $r$, $C_i$ be their censoring age (current age or age of death), and $\delta_{ri} = \mathbb{I}(T_{ri} \leq C_i)$ be the binary indicator for the occurrence of cancer $r$ before the censoring age. Then the observed history of cancer $r$ is $\boldsymbol{H}_{ri} = (C_i, \delta_{ri})$ when $\delta_{ri} = 0$ and $\boldsymbol{H}_{ri} = (C_i, \delta_{ri}, T_{ri})$ when $\delta_{ri} = 1$.

Denote the binary indicator of the $i$th individual being male as $U_i$. Finally, let  $\boldsymbol{H} = \left( \boldsymbol{H}_1 , \dots, \boldsymbol{H}_I \right)$ and $\boldsymbol{U} = \left( \boldsymbol{U}_1, \dots , \boldsymbol{U}_I \right)$ indicate the phenotypes and sexes of all family members, respectively.

Of interest is the estimation of the counselee's conditional probabilities $\mathbb{P}(\boldsymbol{G}_1 = \boldsymbol{g}_1 | \boldsymbol{H}, \boldsymbol{U})$ for all genotypes $\boldsymbol{g}_1 \in \mathcal{G}$. To obtain the posterior distribution, we apply Bayes' rule as presented by \cite{murphy1969application} and described by \cite{lange2003mathematical}:
\begin{align}
    \label{eq:bayes}
    \mathbb{P}(\boldsymbol{G}_1=\boldsymbol{g}_1 | \boldsymbol{H}, \boldsymbol{U}) \propto \mathbb{P}(\boldsymbol{G}_1=\boldsymbol{g}_1) \mathbb{P}(\boldsymbol{H} | \boldsymbol{G}_1=\boldsymbol{g}_1, \boldsymbol{U}).
\end{align}
After computing the right-hand side, the posterior probabilities must be normalized so that they sum to 1. $\mathbb{P}(\boldsymbol{G}_1=\boldsymbol{g}_1)$ is the population-based frequency of the counselee's observed genotype $\boldsymbol{g}_1$, which we generally estimate from published literature. $\mathbb{P}(\boldsymbol{H} | \boldsymbol{G}_1=\boldsymbol{g}_1, \boldsymbol{U})$ is the conditional probability of the observed cancers for the entire pedigree given that the counselee has genotype $\boldsymbol{g}_1$. It can be computed by integrating over the entire set of possible family genotypes, using the law of total probability:
\begin{align}
    \label{eq:totalprob}
    & \qquad \mathbb{P}(\boldsymbol{H} | \boldsymbol{G}_1=\boldsymbol{g}_1, \mathbf{U}) \nonumber \\
    & = \sum_{\boldsymbol{g}_2, \dots, \boldsymbol{g}_I \in \mathcal{G}} \mathbb{P}(\boldsymbol{H} | \boldsymbol{G}_1 = \boldsymbol{g}_1, \dots, \boldsymbol{G}_I = \boldsymbol{g}_I, \mathbf{U}) \mathbb{P}(\boldsymbol{G}_2=\boldsymbol{g}_2, \dots, \boldsymbol{G}_I=\boldsymbol{g}_I | \boldsymbol{G}_1=\boldsymbol{g}_1) \nonumber \\
    & = \sum_{\boldsymbol{g}_2, \dots, \boldsymbol{g}_I \in \mathcal{G}} \left[ \prod_{i=1}^I \prod_{r=1}^R \mathbb{P}(\boldsymbol{H}_{ri} | \boldsymbol{G}_i=\boldsymbol{g}_i, U_i) \right] \mathbb{P}(\boldsymbol{G}_2=\boldsymbol{g}_2, \dots, \boldsymbol{G}_I=\boldsymbol{g}_I | \boldsymbol{G}_1=\boldsymbol{g}_1).
\end{align}
In Eq.~\ref{eq:totalprob}, the joint genotype distribution conditional on the counselee's genotype $\mathbb{P}(\boldsymbol{G}_2, ..., \boldsymbol{G}_I | \boldsymbol{G}_1)$ is derived using properties of Mendelian inheritance. One must have estimates of the population allele frequency of each variant and know the exact relationship between the counselee and each relative in the pedigree. We assume genotype independence across the founding family members, followed by conditionally independent genotypes in subsequent generations \citep{berry1997probability}. In order to model $\mathbb{P}(\boldsymbol{H} | \boldsymbol{G}_1, ..., \boldsymbol{G}_I, \boldsymbol{U}) = \prod_{i=1}^I \prod_{r=1}^R \mathbb{P}(\boldsymbol{H}_{ri} | \boldsymbol{G}_i, \boldsymbol{U}_i)$ in the integration step, we assumed that the relatives' phenotypes are independent conditional on genotype and sex. $\mathbb{P}(\boldsymbol{H}_{ri} | \boldsymbol{G}_i, \boldsymbol{U}_i)$ is computed from the sex-specific penetrances.

Two types of penetrances can be used. The net penetrance is the genotype-specific probability of developing a phenotype by a given age, \textit{in the absence} of death and other competing risks. The crude penetrance is the genotype-specific probability of developing a phenotype by a given age \textit{prior to} dying or developing other phenotypes. We typically use estimates reported in peer-reviewed literature, which are most often net. In such cases, we convert the estimates to crude when needed. Our implementation uses net penetrances $\mathbb{P} \left(T_{ri} = t \middle| \boldsymbol{G}_i, U_i \right)$ to calculate the carrier probabilities. Explicitly,
\begin{align}
    \mathbb{P} \left(\boldsymbol{H}_{ri} \middle| \boldsymbol{G}_i, U_i \right) =
    \begin{cases}
        1 - \sum_{s=1}^{C_i} \mathbb{P} \left(T_{ri} = s \middle| \boldsymbol{G}_i, U_i \right) & \text{ if } \delta_{ri} = 0 \\
        \mathbb{P} \left(T_{ri} = T_{ri}^{obs} \middle| \boldsymbol{G}_i, U_i \right) & \text{ if } \delta_{ri} = 1,
    \end{cases}
\end{align}
where $T_{ri}$ is the random variable and $T_{ri}^{obs}$ is the observed cancer age. We assume that the censoring process and deaths by causes unrelated to a given cancer are independent of the time to cancer diagnosis. We further assume that censoring and death by other causes are non-informative with respect to carrier status. An in-depth discussion of the trade-offs involved in these modeling choices is provided by \cite{Katki2008}.

Once these carrier probabilities have been obtained, they can be used to calculate the future risk of developing any of the cancers in the model. The future risk that the counselee develops the cancer indexed by $r$ can be computed using either the net or crude penetrances, and has a slightly different interpretation depending on which penetrance estimates are used.

The counselee's $t_0$-year net future risk for a given cancer indexed by $r$ is
\begin{align}
    & \qquad \mathbb{P}(T_{r1} \leq C_1 + t_0 | T_{r1} > C_1, \boldsymbol{H}, \boldsymbol{U}) \nonumber \\
    & = \sum_{\boldsymbol{g}_1} \mathbb{P}(\boldsymbol{G}_1 = \boldsymbol{g}_1 | \boldsymbol{H}, \boldsymbol{U}) \mathbb{P}(T_{r1} \leq C_1 + t_0 | T_{r1} > C_1, \boldsymbol{G}_1 = \boldsymbol{g}_1, U_1) \nonumber \\
    & = \sum_{\boldsymbol{g}_1} \mathbb{P}(\boldsymbol{G}_1 = \boldsymbol{g}_1 | \boldsymbol{H}, \boldsymbol{U}) \cdot \frac{\mathbb{P}( C_1 \leq T_{r1} \leq C_1 + t_0 | \boldsymbol{G}_1 = \boldsymbol{g}_1, U_1)}{\mathbb{P}(T_{r1} > C_1 | \boldsymbol{G}_1 = \boldsymbol{g}_1, U_1)}.
\end{align}
The numerator and denominator of the fractional term in the final expression can be computed from the net genotype-specific penetrances. This $t_0$-year risk prediction can be interpreted as the probability of developing cancer $r$ within $t_0$ years, conditional on being disease-free at the counselee's current age and assuming a hypothetical world where there is no death or other phenotypes.

More realistically, one may consider the crude future risk, which can be interpreted as the probability of developing cancer $r$ within $t_0$ years, conditional on being disease-free and alive at the current age and assuming that the counselee survives all competing risks and death. For individual $i$, let $T_{d,ri}$ be their age of death from causes other than cancer $r$, $T_{ri}^* = \min(T_{ri}, T_{d,ri})$ be their age of first outcome (either cancer $r$ or death from causes other than cancer $r$), and $J_{ri} = \mathbb{I}(T_{ri}^* = T_{ri})$ be the binary indicator for developing the $r$th cancer. The counselee's crude risk can be calculated as
\begin{align}
    & \qquad \mathbb{P}(T_{r1}^* \leq C_1 + t_0, J_{r1} = 1 | T_{r1}^* > C_1, \boldsymbol{H}, \boldsymbol{U}) \nonumber \\
    & = \sum_{\boldsymbol{g}_1} \mathbb{P}(\boldsymbol{G}_1 = \boldsymbol{g}_1 | \boldsymbol{H}, \boldsymbol{U}) \mathbb{P}(T_{r1}^* \leq C_1 + t_0, J_{r1} = 1 | T_{r1}^* > C_1, \boldsymbol{G}_1 = \boldsymbol{g}_1, U_1) \nonumber \\
    & = \sum_{\boldsymbol{g}_1} \mathbb{P}(\boldsymbol{G}_1 = \boldsymbol{g}_1 | \boldsymbol{H}, \boldsymbol{U}) \nonumber \\
    & \qquad\quad \cdot \frac{\mathbb{P}(C_1 \leq T_{r1}^* \leq C_1 + t_0, J_{r1} = 1 | \boldsymbol{G}_1 = \boldsymbol{g}_1, U_1)}{\mathbb{P}(T_{r1}^* > C_1, J_{r1} = 1 | \boldsymbol{G}_1 = \boldsymbol{g}_1, U_1) - \mathbb{P}(T_{r1}^* \leq C_1, J_{r1} = 0 | \boldsymbol{G}_1 = \boldsymbol{g}_1, U_1)},
\end{align}
The fractional term in the final expression is computed directly from the crude penetrances for cancer $r$ and the probability distribution of dying by other causes. The distribution of death by other causes is an additional parameter that can be estimated based on peer-reviewed literature. PanelPRO outputs crude future risk estimates by default.

\subsection{Computation}
The integration step over the counselee genotypes in computing the probabilities in a Mendelian model is usually obtained by applying the Elston-Stewart peeling algorithm \citep{elston1971general}. The peeling algorithm is broadly used and generalizable to any number of heritable sites specified in the model. It is linear with respect to the number of relatives $I$ in the counselee's family, but sums over all possible genotypes in the pedigree. Therefore, computation time is exponential with respect to the number of genes $K$, making integration challenging for even a moderate number of genes. The peeling and paring algorithm \citep{madsen2018efficient} restricts the set of possible genotypes $\mathcal{G}$ to the set of genotypes $\mathcal{G}_M$ that contain up to $M$ deleterious variants. Then, one applies local integration over the ``pared'' set of genotypes $\mathcal{G}_M$ to approximate $\mathbb{P}(\boldsymbol{H} | \boldsymbol{G}_1 = \boldsymbol{g}_1, \boldsymbol{U})$ as
\begin{align}
    & \sum_{\boldsymbol{g}_2, \dots, \boldsymbol{g}_I \in \mathcal{G}_M} \mathbb{P}(\boldsymbol{H} | \boldsymbol{G}_1=\boldsymbol{g}_1, \dots, \boldsymbol{G}_I=\boldsymbol{g}_I, \boldsymbol{U}) \mathbb{P}(\boldsymbol{G}_2=\boldsymbol{g}_2, \dots, \boldsymbol{G}_I=\boldsymbol{g}_I | \boldsymbol{G}_1=\boldsymbol{g}_1).
\end{align}
When $M \geq K$, the peeling-paring algorithm is equivalent to the peeling algorithm.

For example, if the model has $K=11$ genes, each of which is fairly uncommon in the population, it would be very rare to observe an individual with all 11 variants, or even 9 or 10 variants. It is also possible that many genotypes with several such pathogenic variants may not be viable. Illustrating again with the scenario of two states for each gene, if $M=2$ and $K=11$, there are only $\sum_{m=0}^M \binom{K}{m} = 78$ admissible genotypes in $\mathcal{G}_M$ that need to be summed over. This is a substantial reduction compared to the $M^K = 2048$ in the original space $\mathcal{G}$.

There are trade-offs in selecting the value for $M$. Higher values of $M$ lead to more precise approximations of the posterior genotypic distribution, but as $M$ approaches $K$, the computational complexity approaches $2^K$ once again. A smaller value of $M$ leads to higher efficiency, but this simplifying assumption has the cost of lower precision. These trade-offs are discussed in greater detail by \cite{madsen2018efficient}. Our PanelPRO implementation allows users to set the value for $M$, but in both our simulations and data application, we used $M=2$. Even as the number of genes in PanelPRO increases to 5, 7, 11, and potentially more, the computational expense of the integration step is kept feasible by imposing this restriction. The Lander-Green algorithm \citep{lander1987construction} is an alternative algorithm that is expected to be more efficient when the number of genes $K$ exceeds the number of family members $I$ in the pedigree. Further discussion of genetic linkage algorithms and their computational considerations can be found in \cite{lee2021panelpro}.

\subsection{Additional Modifiers}

\subsubsection{Secondary Cancers}
Separate from the general approach of including primary cancers in a model, secondary cancers such as contralateral breast cancer modify risk estimation based on years since the primary cancer diagnosis. Suppose that primary breast cancer is indexed by $r = b$ and contralateral breast cancer by $r = c$. Then $\mathbb{P} \left(\boldsymbol{H}_{ci} \middle| \boldsymbol{G}_i, U_i \right)$ can be expressed in terms of the contralateral breast cancer net penetrances $\mathbb{P} \left(T_{ci} = t \middle| \boldsymbol{G}_i, U_i \right)$ as
\begin{align}
    \mathbb{P} \left(\boldsymbol{H}_{ci} \middle| \boldsymbol{G}_i, U_i \right) =
    \begin{cases}
        1 - \sum_{s=T_{bi}^{obs}}^{C_i} \mathbb{P} \left(T_{ci} = s \middle| \boldsymbol{G}_i, U_i \right) & \text{ if } \delta_{bi} = 1, \delta_{ci} = 0 \\
        \mathbb{P} \left(T_{ci} = T_{ci}^{obs} - T_{bi}^{obs} \middle| \boldsymbol{G}_i, U_i \right) & \text{ if } \delta_{bi} = 1, \delta_{ci} = 1 \\
        1 & \text{ if } \delta_{bi} = 0.
    \end{cases}
\end{align}
$T_{ci}$ is a random variable, whereas $T_{bi}^{obs}$ and $T_{ci}^{obs}$ are the observed ages of diagnosis for breast and contralateral breast cancer, respectively.

\subsubsection{Risk Modifiers}
Our implementation supports modifying risk at the cancer penetrance level using risk or hazard ratios for interventions such as prophylactic mastectomies, oophorectomies, and hysterectomies. When calculating carrier probabilities, simply use the modified penetrances $\mathbb{P}^{\text{mod}} \left(T_{ri} \middle| \boldsymbol{G}_i, U_i \right)$ in place of the raw penetrances $\mathbb{P} \left(T_{ri} \middle| \boldsymbol{G}_i, U_i \right)$. Suppose family member $i$ received a preventive intervention at age $T_{\text{int},i}$, and let $\text{RR}_{r,\text{int}} \left(T_{\text{int},i} \middle| \boldsymbol{G}_i, U_i \right)$ be the relative risk of developing cancer $r$ for those that receive the intervention at age $T_{\text{int},i}$, computed based on probabilities that are conditional on genotype and sex. Their modified penetrance for cancer $r$ is
\begin{align}
    \mathbb{P}^{\text{mod}} \left(T_{ri} = t \middle| \boldsymbol{G}_i, U_i \right) & = \mathbb{P} \left(T_{ri} = t \middle| \boldsymbol{G}_i, U_i \right) \nonumber \\
    & \qquad \cdot \left[ \mathbb{I}(t < T_{\text{int},i}) +  \text{RR}_{r,\text{int}} \left(T_{\text{int},i} \middle| \boldsymbol{G}_i, U_i \right) \mathbb{I}(t \geq T_{\text{int},i}) \right].
\end{align}

Suppose that instead of a relative risk, the hazard ratio for the intervention at age $T_{\text{int},i}$, $\text{HR}_{r,\text{int}} \left(T_{\text{int},i} \middle| \boldsymbol{G}_i, U_i \right)$, is available. Define $S_r \left(t \middle| \boldsymbol{G}_i, U_i \right) = 1 - \sum_{s=1}^t \mathbb{P} \left(T_{ri} = s \middle| \boldsymbol{G}_i, U_i \right)$ as the survival function for cancer $r$ (conditional on sex and genotype), and let $\lambda_r \left(t \middle| \boldsymbol{G}_i, U_i \right) = \mathbb{P} \left(T_{ri} = t \middle| \boldsymbol{G}_i, U_i \right)/S \left(t \middle| \boldsymbol{G}_i, U_i \right)$ be the corresponding hazard. Then the modified hazard, survival, and penetrance functions at age $t$ for this intervention are:
\begin{align}
    \lambda_r^{\text{mod}} \left(t \middle| \boldsymbol{G}_i, U_i \right) & = \lambda_r \left(t \middle| \boldsymbol{G}_i, U_i \right) \left[ \mathbb{I}(t < T_{\text{int},i}) + \text{HR}_r(T_{\text{int},i}) \mathbb{I}(t \geq T_{\text{int},i}) \right] \nonumber \\
    S_r^{\text{mod}} \left(t \middle| \boldsymbol{G}_i, U_i \right) & = \prod_{s=1}^t (1 - \lambda_r^{\text{mod}} \left(s \middle| \boldsymbol{G}_i, U_i \right)) \nonumber \\
    \mathbb{P}^{\text{mod}} \left(T_{ri} = t \middle| \boldsymbol{G}_i, U_i \right) & = S_r^{\text{mod}} \left(t + 1 \middle| \boldsymbol{G}_i, U_i \right) - S_r^{\text{mod}} \left(t \middle| \boldsymbol{G}_i, U_i \right).
\end{align}

\subsubsection{Germline and tumor biomarker testing}
When germline or tumor marker testing results are available for some family members, this information can also be incorporated into the probability estimates. For each relative $i$, one substitutes $\mathbb{P}(\boldsymbol{H}_{i} | \boldsymbol{G}_i, U_i) = \prod_{r=1}^R \mathbb{P}(\boldsymbol{H}_{ri} | \boldsymbol{G}_i, U_i)$ with
\begin{align}
    \mathbb{P}^{\text{mod}}(\boldsymbol{H}_{i} | \boldsymbol{G}_i, U_i) & = \mathbb{P}(\boldsymbol{H}_{i} | \boldsymbol{G}_i, U_i) \cdot \mathbb{P} (\boldsymbol{V}_i |\boldsymbol{G}_i) \cdot \mathbb{P} (\boldsymbol{W}_i |\boldsymbol{G}_i),
\end{align}
where $\boldsymbol{V}_i$ is the observed germline testing results and $\boldsymbol{W}_i$ is the observed tumor marker testing results for relative $i$. The probabilities $\mathbb{P} (\boldsymbol{W}_i |\boldsymbol{G}_i)$ can be interpreted as test sensitivities and specificities. In practice, we often assume conditional independence of the different germline and marker testing results when robust joint estimates are not available. Currently, our implementation allows for modifying risk based on germline testing for any of the genes included in the model. It also supports modifying the risk of breast cancer conditional on BRCA1 or BRCA2 carrier status based on breast cancer tumor markers, ER, CK5/6, CK14, HER, and PR; and the risk of colorectal cancer conditional on MLH1, MSH2, MSH6, or PMS2 carrier status based on the colorectal cancer tumor marker, MSI. The implementation is designed to make it straightforward to extend risk modification to additional tumor markers or to modify the values according to user inputs.

\subsection{Conditions for Collapsibility}

It is possible to collapse a larger ``full'' model into a smaller submodel that contains a subset of the specified genes and/or cancers. In this section we derive the following important facts:

\begin{enumerate}
    \item If the submodel contains a subset of the genes in the full model, both models will return the same posterior probabilities if the allele frequency for being a noncarrier is 1 for all genes not present in the submodel. In other words, the probability of carrying a pathogenic variant is zero for any of the genes that are absent in the submodel.

    \item If the submodel contains a subset of the cancers in the full model, the submodel can be collapsed within the full model if the penetrances of the cancers not included in the submodel do not change depending on genotype.
\end{enumerate}

Suppose that one has fit a model with $K$ genes and wishes to collapse it into a submodel that only includes the genes with indices in the set $\mathcal{K}^{(*)}$. Let $\mathcal{K}^{(-*)}$ be the index set for genes not included in the submodel, such that $\mathcal{K}^{(*)} \cup \mathcal{K}^{(-*)}$ is the full set of $K$ gene indices. Similarly, $\boldsymbol{G}_i$ can be partitioned as as $\boldsymbol{G}_i = \left( \boldsymbol{G}_i^{(*)}, \boldsymbol{G}_i^{(-*)} \right)$, where $\boldsymbol{G}_i^{(*)}$ is the genotype vector for the genes included in the submodel and $\boldsymbol{G}_i^{(-*)}$ is the genotype vector for the genes not included in the submodel. For the $i$th individual and $k$th gene, let $G_{ki} = 0$ represent a noncarrier and allow carriers of pathogenic variants to be represented using numbers other than zero. In order to obtain the same results from both the full model and submodel, a sufficient condition for collapsibility is that $\mathbb{P} \left( G_{ki}^{(*)} = 0 \right) = 1$ for all genes $k \in \mathcal{K}^{(-*)}$ and all individuals $i$ in the family.

Under this condition, the counselee's genotype frequency is
\begin{align}
    \mathbb{P}(\boldsymbol{G}_1 = \boldsymbol{g}_1) & = \prod_{i=1}^K \mathbb{P}(G_{k1} = g_{k1}) = \begin{cases}
        0 & \text{if } g_{k1} \neq 0 \text{ for at least one } k \in K^{(-*)} \\
        \mathbb{P} \left(G_{k1}^{(*)} = g_{k1}^{(*)} \right) & \text{if } g_{k1} = 0 \text{ for all } k \in K^{(-*)}.
    \end{cases}
\end{align}
Under the Mendelian model's conditional independence assumptions for the genotypes in the pedigree, we can also obtain
\begin{align}
    \mathbb{P}(\boldsymbol{G}_2=\boldsymbol{g}_2, ..., \boldsymbol{G}_I=\boldsymbol{g}_I | \boldsymbol{G}_1=\boldsymbol{g}_1) = \mathbb{P}\left( \boldsymbol{G}_2^{(*)}=\boldsymbol{g}_2^{(*)}, ..., \boldsymbol{G}_I^{(*)}=\boldsymbol{g}_I^{(*)} \middle| \boldsymbol{G}_1^{(*)}=\boldsymbol{g}_1^{(*)} \right)
\end{align}
when $g_{ki} = 0$ for all $k \in K^{(-*)}$ and $i = 1, \dots, I$; and $\mathbb{P}(\boldsymbol{G}_2=\boldsymbol{g}_2, ..., \boldsymbol{G}_I=\boldsymbol{g}_I | \boldsymbol{G}_1=\boldsymbol{g}_1) = 0$ otherwise.

Let $\mathcal{K}_{i,1}$ be the set of gene indices that satisfy $g_{ki} = 1$ for a given individual $i$, and let $\mathcal{K}_{i,1}^{(*)}$ be the analogous index set for only the genes that are included in the submodel. In the case where $g_{ki} = 0$ for all $k \in K^{(-*)}$, it follows that $\mathcal{K}_{i,1} = \mathcal{K}_{i,1}^{(*)}$ and
\begin{align}
    \mathbb{P}(\boldsymbol{H}_{ri} | \boldsymbol{G}_i=\boldsymbol{g}_i, U_i) & = \prod_{k \in \mathcal{K}_{i,1}} \mathbb{P}(\boldsymbol{H}_{ri} | G_{ki} = g_{ki}, U_i) \nonumber \\
    & = \prod_{k \in \mathcal{K}_{i,1}^{(*)}} \mathbb{P} \left( \boldsymbol{H}_{ri} | G_{ki} = g_{ki}, U_i \right) \nonumber \\
    & = \mathbb{P} \left(\boldsymbol{H}_{ri} \middle| \boldsymbol{G}_{i}^{(*)} = g_{i}^{(*)}, U_i \right).
\end{align}

Using these findings to compute Eq.~\ref{eq:totalprob}, the expression for the posterior probabilities (Eq.~\ref{eq:bayes}) can be shown to be equivalent for the full model with $K$ genes and the submodel with $| \mathcal{K}^{(*)} |$ genes. Note that the equality below holds because the terms in the summation where $g_{ki} \neq 0$ for at least one $k \in \mathcal{K}^{(-*)}$ are zero, and therefore do not contribute.
\begin{align}
    & \qquad \mathbb{P}(\boldsymbol{G}_1=\boldsymbol{g}_1 | \boldsymbol{H}, \boldsymbol{U}) \nonumber \\
    & \propto \mathbb{P}(\boldsymbol{G}_1=\boldsymbol{g}_1) \sum_{\boldsymbol{g}_2, \dots, \boldsymbol{g}_I \in \mathcal{G}} \left[ \prod_{i=1}^I \prod_{r=1}^R \mathbb{P}(\boldsymbol{H}_{ri} | \boldsymbol{G}_i=\boldsymbol{g}_i, U_i) \right] \nonumber \\
    & \hspace{40mm} \cdot \mathbb{P}(\boldsymbol{G}_2=\boldsymbol{g}_2, ..., \boldsymbol{G}_I=\boldsymbol{g}_I | \boldsymbol{G}_1=\boldsymbol{g}_1) \nonumber \\
    & = \mathbb{P} \left( \boldsymbol{G}_1^{(*)}=\boldsymbol{g}_1^{(*)} \right) \sum_{\boldsymbol{g}_2^{(*)}, \dots, \boldsymbol{g}_I^{(*)} \in \mathcal{G}^{(*)}} \left[ \prod_{i=1}^I \prod_{r=1}^R \mathbb{P} \left(\boldsymbol{H}_{ri} | \boldsymbol{G}_i^{(*)}=\boldsymbol{g}_i^{(*)}, U_i \right) \right] \nonumber \\
    & \hspace{54mm} \cdot \mathbb{P} \left( \boldsymbol{G}_2^{(*)}=\boldsymbol{g}_2^{(*)}, ..., \boldsymbol{G}_I^{(*)}=\boldsymbol{g}_I^{(*)} \middle| \boldsymbol{G}_1^{(*)}=\boldsymbol{g}_1^{(*)} \right) \nonumber \\
    & \propto \mathbb{P}\left( \boldsymbol{G}_1^{(*)}=\boldsymbol{g}_1^{(*)} \middle| \boldsymbol{H}, \boldsymbol{U} \right)
\end{align}

Now suppose that the full model has $R$ cancers or other phenotypes and that the submodel of interest contains only the phenotypes with indices in the set $\mathcal{R}^{(*)}$. Denote the complementary set as $\mathcal{R}^{(-*)}$. Let $\boldsymbol{H}_{i}^{(*)}$ be the phenotype vector for individual $i$ corresponding to the phenotypes included in the submodel.
In order to collapse the submodel within the full model, we require $\mathbb{P} \left( \boldsymbol{H}_{ri} | \boldsymbol{G}_i = \boldsymbol{g}_i, U_i \right)$ to be constant for all $\boldsymbol{g}_i \in \mathcal{G}$ with respect to each individual $i$ and cancer $r \in \mathcal{R}^{(-*)}$. In words, each relative's penetrances for the cancers/phenotypes not included in the submodel must not depend on genotype. When this value is constant across genotypes, the additional cancers do not contribute to the posterior probabilities (Eq.~\ref{eq:bayes}) after normalization:
\begin{align}
    & \qquad \mathbb{P}(\boldsymbol{G}_1=\boldsymbol{g}_1 | \boldsymbol{H}, \boldsymbol{U}) \nonumber \\
    & \propto \mathbb{P}(\boldsymbol{G}_1=\boldsymbol{g}_1) \sum_{\boldsymbol{g}_2, \dots, \boldsymbol{g}_I \in \mathcal{G}} \left[ \prod_{i=1}^I \prod_{r=1}^R \mathbb{P}(\boldsymbol{H}_{ri} | \boldsymbol{G}_i=\boldsymbol{g}_i, U_i) \right] \nonumber \\
    & \hspace{40mm} \cdot \mathbb{P}(\boldsymbol{G}_2=\boldsymbol{g}_2, ..., \boldsymbol{G}_I=\boldsymbol{g}_I | \boldsymbol{G}_1=\boldsymbol{g}_1) \nonumber \\
    & \propto \mathbb{P}(\boldsymbol{G}_1=\boldsymbol{g}_1) \sum_{\boldsymbol{g}_2, \dots, \boldsymbol{g}_I \in \mathcal{G}} \left[ \prod_{i=1}^I \prod_{r \in \mathcal{R}^{(*)}} \mathbb{P}(\boldsymbol{H}_{ri} | \boldsymbol{G}_i=\boldsymbol{g}_i, U_i) \prod_{r \in \mathcal{R}^{(-*)}} \mathbb{P}(\boldsymbol{H}_{ri} | \boldsymbol{G}_i=\boldsymbol{g}_i, U_i) \right] \nonumber \\
    & \hspace{40mm} \cdot \mathbb{P}(\boldsymbol{G}_2=\boldsymbol{g}_2, ..., \boldsymbol{G}_I=\boldsymbol{g}_I | \boldsymbol{G}_1=\boldsymbol{g}_1) \nonumber \\

    & = \mathbb{P}(\boldsymbol{G}_1=\boldsymbol{g}_1) \left[ \prod_{i=1}^I \prod_{r \in \mathcal{R}^{(-*)}} \mathbb{P}(\boldsymbol{H}_{ri} | \boldsymbol{G}_i=\boldsymbol{g}_i, U_i) \right] \nonumber \\
    & \qquad \cdot \sum_{\boldsymbol{g}_2, \dots, \boldsymbol{g}_I \in \mathcal{G}} \left[ \prod_{i=1}^I \prod_{r \in \mathcal{R}^{(*)}} \mathbb{P}(\boldsymbol{H}_{ri} | \boldsymbol{G}_i=\boldsymbol{g}_i, U_i) \right] \mathbb{P}(\boldsymbol{G}_2=\boldsymbol{g}_2, \dots, \boldsymbol{G}_I=\boldsymbol{g}_I | \boldsymbol{G}_1=\boldsymbol{g}_1) \nonumber \\
    & \propto \mathbb{P}(\boldsymbol{G}_1=\boldsymbol{g}_1) \sum_{\boldsymbol{g}_2, \dots, \boldsymbol{g}_I \in \mathcal{G}} \left[ \prod_{i=1}^I \prod_{r \in \mathcal{R}^{(*)}} \mathbb{P}(\boldsymbol{H}_{ri} | \boldsymbol{G}_i=\boldsymbol{g}_i, U_i) \right] \nonumber \\
    & \hspace{40mm} \cdot \mathbb{P}(\boldsymbol{G}_2=\boldsymbol{g}_2, \dots, \boldsymbol{G}_I=\boldsymbol{g}_I | \boldsymbol{G}_1=\boldsymbol{g}_1) \nonumber \\
    & = \mathbb{P}(\boldsymbol{G}_1=\boldsymbol{g}_1) \mathbb{P} \left( \boldsymbol{H}^{(*)} \middle| \boldsymbol{G}_1=\boldsymbol{g}_1, \boldsymbol{U} \right) \nonumber \\
    & \propto \mathbb{P}\left( \boldsymbol{G}_1=\boldsymbol{g}_1 \middle| \boldsymbol{H}^{(*)}, \boldsymbol{U} \right)
\end{align}

When the peeling-paring algorithm is used to restrict the possible genotypes to those in $\mathcal{G}_M$, one can simply substitute $\mathcal{G}_M$ for $\mathcal{G}$ in the derivations.

redpajama_set_name: RedPajamaArXiv


text:
Clinicopathological Description of a Urinary Bladder Leiomyosarcoma in a Dog
Derick S Alves1, Fabiana Elias2, Helvécio L S Junior3, Guilherme Thizen3, Rômulo S A Eloi4, Carlos E Fonseca-Alves1*
1Institute of Health Science, Paulista University – UNIP, Bauru – SP, Brazil.
2Universidade Federal da Fronteira Sul (UFFS), Realeza, PR, Brazil.
3Departamento de Medicina Veterinária, Faculdade UPIS, Brasília, DF - Brazil.
4HistoPato-Análise Anatomopatológica Veterinária, Brasília, DF, Brazil.
Urinary bladder cancer is uncommon in dogs, corresponding to 1% of all reported canine malignancies. Smooth muscle neoplasms can be benign (leiomyomas) or malignant (leiomyosarcoma) and are rare in humans and animals. As the incidence of urinary bladder leiomyosarcoma in dogs is low, our report presents the clinical and pathological aspects of primary urinary bladder leiomyosarcoma in a dog. A 10-year-old boxer breed dog was referred to the veterinary hospital presenting with dysuria for a month, appetite loss for seven days, abdominal distension for two weeks, and anuria for the last three days. After a physical examination and laboratory tests, an abdominal mass was diagnosed, and a laparotomy was performed. During the surgery, it was found that the urinary bladder neoplasm occupied the bladder trigone region, involving the ureters, and causing obstruction. The urinary bladder was reconstructed successfully, and the patient was kept under post-operative evaluation. In the post-operative recovery, an acute kidney disease was observed, which was irresponsive to the clinical treatment. Due to the advanced stage of the disease and the non-response to treatment, euthanasia was performed after surgery, and the animal was sent for necropsy. In this case, leiomyosarcoma was manifested as an expansive, low infiltration, and non-metastatic disease, causing obstruction of the ureters and consequent hydronephrosis.
Leiomyosarcoma is an uncommon malignant mesenchymal neoplasm originating from the smooth muscle. It commonly presents as a slow-growing tumor, being an expansive disease with a low metastatic rate1. It can affect the intestinal and reproductive tracts, being more common in the urinary bladder in comparison with the other parts of the urogenital system2. It is histologically characterized by spindle cells with marginalized fascicles, an abundant eosinophilic cytoplasm, and elongated and hyperchromatic nuclei. Macroscopically, the neoplasm does not have a capsule, and usually, areas of necrosis are observed. Metastases are not common, but when present, can affect the spleen, duodenum, mesentery, and mesenteric lymph nodes1-3. Bladder neoplasms can block or invade the ureters, which obstruct the urinary flow and increase ureteral pressure, causing hydronephrosis4.
This neoplasm is rare in dogs, accounting for less than 1% of malignant neoplasms associated with the species and being less common in cats5. It has no racial predisposition, being common in animals aged six and 11 years old1,6. A higher occurrence was observed in females. Obesity, insecticides, herbicides, use of cyclophosphamide, and urine retention are considered predisposing factors3,5. The clinical signs include hematuria, dysuria, pollakiuria, urinary incontinence, and a mass in the urinary vesicle on rectal examination7,8. The blood count and biochemical tests can be normal or can present with azotemia7.
Ultrasound is the most used diagnostic imaging method for the identification of neoplastic alterations in animals with clinical signs such as hematuria; however, cytological or histopathological evaluation is necessary for the definitive diagnosis9. Intraluminal masses of the bladder can originate in the bladder trigone, urethra, or prostate, and these structures must be carefully evaluated4. Due to a lack of information about leiomyosarcoma in the urinary bladder of canine patients, the aim of this study was to report a case of primary bladder leiomyosarcoma in a dog.
A 10-year-old, female, boxer breed dog presented with dysuria for one month, hyporexia for seven days, abdominal distension for two weeks, and anuria for the last three days. On physical examination, an abdominal mass of consistent aspect was identified, occupying a large part of the abdominal cavity in the hypogastric region. Complete blood count, serum urea, creatinine, alanine aminotransferase, and alkaline phosphatase were performed, in addition to abdominal radiography and ultrasound.
The blood count showed no abnormalities, while urea (351 mg/dL) and creatinine (10 mg/dL) levels were found to be increased. The abdominal radiographic examination identified a large mass occupying the abdominal cavity. Thoracic 3-view radiographic examination revealed no abnormalities in the lungs (no evidence of metastasis). Ultrasound showed an immeasurable mass with no distinct limit associated with hydronephrosis in the right kidney. The bladder was displaced caudally to the pelvic floor, moderately filled with homogeneous anechogenic content, with a thin and regular wall and the presence of an echogenic, heterogeneous mass with hypoechogenic areas occupying the abdominal cavity. Due to the dimensions of the mass, it was not possible to specify the organ from which the mass originated via ultrasound examination.
Based on the suspicion of neoplasm, the patient underwent an exploratory laparotomy procedure. During the procedure, a neoplastic mass was identified, with a vascularized and irregular appearance and areas of necrosis (Figure 1). The animal had a urethral obstruction and accumulation of urine in the bladder, and cystocentesis was performed (Figure 2). After this procedure, it was noticed that the mass originated in the bladder trigone and due to the involvement of the ureter, a surgical procedure was performed to replant the ureter in the urinary bladder. Figure 3 shows the urinary bladder after reimplantation. After total mass removal, the bladder mass became evident with a dimension of 80x40x30 cm and weight of 4,6 kg, with an irregular aspect and an intense vascularization. Right nephrectomy was performed due to the hydronephrosis resulting from the obstruction due to the expansive growth of the neoplasm (Figure 4).
Figure 1: Exploratory laparotomy procedure revealing neoplastic mass with irregular appearance, vascularized and with areas of necrosis (arrows).
Figure 2: During laparotomy and identification of a bladder mass, cystocentesis procedure was performed due to accumulation of urine in urinary bladder. After cystocenteses, it was performed tumor removal and bladder reconstruction.
Figure 3: After tumor removal, urinary bladder was reconstructed and the ureter was reimplanted in the bladder mucosa.
Figure 4: Evaluation of the kidney and ureter after surgical procedure. It is possible to observe the dilated ureter and kidney and shape modification.
During the surgical procedure, urethral catheterization was performed, and the patient was kept in the intensive care unit. After 24 hours of the surgical procedure, the patient did not show urine production, and presented with intense azotemia (creatinine: 9.0 mg/dL and urea: 350 mg/dL). The patient was maintained with a permanent urinary catheter to measure the urinary volume, and saline solution (NaCl 0.9%) was administered intravenously with a continuous infusion of furosemide (1 mg/kg/h) in a period of six hours. The patient did not pass out urine, and dopamine at a dose of 2 μg/kg/min was administered without success. Due to the poor clinical condition, failure to replant the ureter in the urinary bladder, and the neoplastic extension, euthanasia was chosen.
The macroscopic findings of the neoplastic mass and kidney revealed dilation of the left ureter and stenosis of the lumen due to neoplastic infiltration. The left kidney was swollen, with a preserved capsule, and when sliced, there was total loss of the renal parenchyma with the presence of intense serosanguinous fluid inside. The neoplasm invaded the right ureter lumen, causing total obstruction. The right kidney was increased in volume, with preservation of the renal capsule and medullary cortical region. The mass was encapsulated with an irregular shape and several peripheral blood vessels with a high caliber. Necropsy was performed and no macroscopic abnormalities were observed. Tissue fragments from the spleen, liver, lungs, kidneys, ureters, and three mesenteric lymph nodes were randomly collected.
Histopathological examination of the neoplasm revealed spindle cell proliferation, moderately pleomorphic and elongated nucleus, dispersed chromatin, and evident nucleoli (Figure 5). Some of these cells had a fusiform and hyperchromatic nucleus, the cells were arranged in multidirectional bundles, and the cytoplasm of these cells was eosinophilic and indistinct. There were mitotic figures noting discreet and diffuse bleeding with discreet necrotic areas. The special Masson's Trichrome tumor cells stained red, indicating a tumor of muscle origin. To confirm the diagnosis, immunohistochemistry analysis was performed according to the previous literature5 for the markers S100 (Dako Cytomation, Carpinteria, CA, USA) at 1:400 dilution, MyoD1 (Novocastra, Wetzlar, Germany) at a 1:200 dilution and Alpha-actin (Dako Cytomation, Carpinteria, CA, USA) at a 1:100 dilution. The tumor cells were negative for S100 and MyoD1 and presented a diffuse cytoplasmic positive expression for alpha-actin (Figure 6). The association of morphological findings, Masson's trichrome, and immunohistochemistry supported the leiomyosarcoma diagnosis.
Figure 5: Morphological evaluation of the urinary bladder mass showing neoplastic cells with spindle-cell morphology, with moderate pleomorphism and anisokaryosis. It was also observed nucleolus evident and mitotic figures (arrows). Hematoxylin and eosin staining, 400x.
Figure 6: Alpha-actin immunostaining in the urinary bladder tumor. Note the intense cytoplasmic expression (brown color) by neoplastic cells. Harris hematoxylin, 400x.
Bladder leiomyosarcoma is a rare mesenchymal neoplasm with few reports in the literature8-13. The clinical signs of dysuria and anuria were related to the mechanical compression of the urethra by the neoplasm. Anuria was attributed to the fact that the neoplasm affects the bladder trigone causing obstruction in the ureters. During the laparotomy, the urinary bladder was observed to be full of urine, and after tumor exposure (from the abdominal cavity), bladder catheterization was performed and there were no signs of obstruction.
The animal presented with hydronephrosis and due to its irreversible nature, associated with ureteral obstruction, we opted for the surgical removal of the kidney. Due to the enlarged right kidney and the necessity to perform tumor removal associated with nephrectomy, prolongation of anesthesia could contribute to acute kidney failure. Based on the macroscopic and histopathological findings, a bladder leiomyosarcoma of the urinary vesicle was diagnosed. The leiomyosarcoma presented expansive growth, with ureteral obstruction and consequent hydronephrosis, and it showed a little infiltrative and non-metastatic neoplasm. In a previous report by our group, we described a case of bladder leiomyosarcoma in the urinary bladder of a cat that was successfully removed by a surgical procedure (Buzatto et al., 2019). However, the tumor that was removed was a small tumor (1.5 cm) with margins of 1.0 cm.
The immunohistochemistry analysis revealed tumor cells expression Alpha-actin, indicating a tumor from smooth muscle fibers. The bladder submucosa has a muscular layer, which is probably the origin of this tumor. In this report, we observed an expansive tumor growth, with a large intraabdominal mass, and we believe the tumor appeared several months ago. Even as a chronic lesion, the dog did not show any evidence of metastasis, corroborating with the literature indicating that leiomyosarcomas is a tumor with a low metastatic rate.
Regarding the surgical procedure, the urinary bladder reconstruction was successfully performed. However, the patient had one kidney left with the reimplanted ureter. We believe that due surgical manipulation and inflammation, the remaining reimplanted ureter could be swollen or edematous due manipulation, obstructing the urinary flow. Besides that, we performed a protocol for urinary production with no success. Thus, due the prolonged surgical procedure and anesthesia, the dog could develop acute kidney disease.
We would like to thank Editage (www.editage.com) for English language editing.
Layane SMJ. Leiomiossarcoma Vaginal em Cadela: Relato de Caso. UFRB, 2018. Available from: http://www.repositoriodigital.ufrb.edu.br//handle/123456789/1408.
Kapatkin AS. Leiomyosarcoma in dogs: 44 cases (1983-1988). J Am Vet Med Assoc. 1 out 1992; 201: 1077-1079.
Hanzaike T, ITO I, Ishikawa T, et al. Leiomyosarcoma of soft tissue in a cow. J Comp Path. 2006; 112(3): 237-242.
Heng HG, Lowry JE, Boston S, et al. Smooth muscle neoplasia of the urinary bladder wall in three dogs. Veterinary Radiology & Ultrasound. 2006; 47: 83-86.
Buzatto AB, Elias F, Franzoni MS, et al. Long-Term Survival of a Cat with Primary Leiomyosarcoma of the Urinary Bladder. Vet Sci. 2019 Jun 27; 6(3): 60. doi: 10.3390/vetsci6030060. PMID: 31252551; PMCID: PMC6789653.
Norris AM, Laing EJ, Valli VEO. Canine bladder and urethral tumors: A retrospective study of 115 cases (1980-1985). Journal of veterinary internal medicine. 1992; 6: 145-153.
Vetchten M. Embryonal rhabdomyosarcoma of the urinary bladder in dogs. Compendium of continuing education practice in veterinary. 1990; 12: 783.
Fondacaro JV, Richter KP, Carpenter JL. Feline gastrointestinal well differentiated lymphocytic lymphoma: 39 cases. Proceedings of the 17th annual ACVIM. 1999; 722.
Walker M, Breider M. Intraoperative radiotherapy of canine bladder cancer. Veterinary Radiology & Ultrasound. 2005; 28(6): 200 – 204.
Yuki M, Naitoh E. Complete Remission of Associative Immune-Mediated Hemolytic Anemia in a Dog Following Surgical Resection of Intestinal Leiomyosarcoma. Vet Sci. 2019; 6(2): 55.
Aleksandra Sobczyńska-Rak, Izabela Polkowska, Beata Żylińska, et al. Case report of leiomyosarcoma, a very rare type of urinary bladder tumour. Med Weter. 2017; 73 (7): 439-444.
Souza junior P, Teixeira ALS, Menezes L. Urinary bladder leiomyoma in a bitch (canis lupus familiaris): Case report. Ars veterinaria jaboticabal sp. 2011; 27(1): 007-010.
Cartagena Albertus JC, Moya García S, Moise A, et al. Urethral Leiomyosarcoma in a Bitch. Israel Journal of Veterinary Medicine. June 2018; 73 (2).
Journal of Nephrology and Dialysis Medicine
Leiomyosarcoma
Urinary bladder
*Correspondence:
Dr. Carlos Eduardo Fonseca Alves
Institute of Health Science, Paulista University – UNIP, Bauru – SP, Brazil
Email: carlos.e.alves@unesp.br.

redpajama_set_name: RedPajamaCommonCrawl


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NHL Rookie Radar: Team-by-team Calder Trophy candidates and freshman hopefuls for 2018-19
A team-by-team peek at the Calder Trophy candidates and rookie hopefuls for the 2018-19 NHL season.
Sam McCaig
There's a plethora of Calder Trophy contenders and first-year arrivals entering the 2018-19 NHL season. Here's a team-by-team look at this year's rookie crop:
Sam Steel is gunning for a job at center, especially with Ryan Kesler's status for 2018-19 up in the air, and the 30th overall draft pick in 2016 could score his way into the Calder Trophy conversation. Forwards Max Jones (24th overall in 2016) and Troy Terry (148th overall in 2015) are also knocking on the door. Jacob Larsson (27th overall in 2015) endured an injury-plagued campaign last season, but should be ready for work on the Ducks' third defense pairing.
Center Dylan Strome isn't rookie-eligible after playing seven and 21 NHL games in the past two seasons, but the third overall pick in 2015 is the Coyotes' most promising up-and-comer. Right winger Nick Merkley (30th overall in 2015) isn't real big, but he is real skilled and should be able to crack the roster. Kyle Capobianco, 21, and former KHLer Ilya Lyubushkin, 24, are in the mix for depth spots on the blueline.
The Bruins employed five rookies on a regular basis last season, and that doesn't include promising winger Anders Bjork, who was limited to 30 games due to injuries and no longer qualifies as an NHL rookie. Boston won't have that kind of quantity this season, but they have quality in Calder candidate Ryan Donato (56th overall in 2014). Donato put up nine points in 12 games when he jumped to the NHL late last season after leaving Harvard, and has a chance at top-six ice time this year.
There's help on the way. The Sabres' bid for respectability will be aided by not one, but two bona fide Calder contenders. Rasmus Dahlin, the No. 1 draft pick last June, arrives as a do-it-all defenseman with superstar potential. The NHL isn't an easy league for 18-year-old blueliners, but all signs point to Dahlin bucking the trend and making an immediate impact. He's joined by Casey Mittelstadt (eighth overall in 2017), who had five points in a six-game NHL debut last spring and enters training camp as the projected second-line center. Fleet-footed Brendan Guhle (51st overall in 2015) played 18 NHL games last year and should find work on the blueline. The best-case scenario? Buffalo's best rookie crop ever.
The Flames don't have any sure-thing freshmen, but Rasmus Andersson (53rd overall in 2015) looks good for depth work on the blueline. Forwards Andrew Mangiapane, Morgan Klimchuk and Spencer Foo have a chance at a bottom-six spot.
The Hurricanes are young up front, and they're going to get even younger with full-time jobs anticipated for Andrei Svechnikov (second overall in 2018), Martin Necas (12th overall in 2017), Valentin Zykov (37th overall by Los Angeles in 2013) and perhaps Warren Foegele (67th overall in 2014). Svechnikov, Necas and maybe even Zykov could score their way into the Calder race.
Chicago needs an infusion of young talent, and this season it's coming in the form of skilled-but-small left winger Dylan Sikura (178th overall in 2014). He had a cup of coffee in the NHL at the end of last season, along with Blake Hillman (173rd overall in 2016), who has a chance for a depth role on defense. Neither player figures to rise into Calder contention.
Skilled center Vladislav Kamenev, obtained in the Matt Duchene trade, and physical left winger A.J. Greer (39th overall in 2015) are both on track for NHL jobs. Kamenev could end up as the Avs' second-line center – and a Calder candidate -- when all is said and done. Conor Timmins (32nd overall in 2017) might break in on the blueline. If he does, he'll add mobility and an offensive bent to Colorado's defense corps.
Already stocked with young talent, the Blue Jackets might have to make room for a couple more kids. Gabriel Carlsson (29th overall in 2015) is in line as a third-pairing defender, while speedy Vitaly Abramov (65th overall in 2016) could force his way into the lineup after ripping up the QMJHL.
There's only one rookie on the radar in Dallas, but he's a good one. Miro Heiskanen (third overall in 2017) is expected to seize a top-four job on the blueline and don't be surprised if he's a Calder candidate.
It looks rough for the Red Wings, but at least there's promise in a flock of first-year hopefuls. Detroit got a steal at the 2018 NHL draft when winger Filip Zadina fell to sixth overall, and the teen sniper might make some noise in the Calder race. He could be joined up front by forwards Evgeny Svechkikov (19th overall in 2015) and Michael Rasmussen (ninth overall in 2017), while Dennis Cholowski (20th overall in 2016), Joe Hicketts (free-agent signing in 2014) and Filip Hronek (53rd overall in 2016) could see some time on the blueline.
Kailer Yamamoto (22nd overall in 2017) had some chemistry with Connor McDavid in a nine-game NHL audition at the start of last season. If he makes the team and sees time with McDavid in 2018-19, the points will come and perhaps some Calder hype, too. Evan Bouchard (10th overall in 2018) has the mobility and offensive skill set to play in the NHL, but the Oilers will be wary of rushing an 18-year-old defenseman. Ethan Bear (124th overall in 2015) is a few years older and fared well in an 18-game look last season, so he might be a better bet to stick around.
Henrik Borgstrom (23rd overall in 2016) and Owen Tippett (10th overall in 2017) should make the roster, and perhaps Maxim Mamin (175th overall in 2016) as well, with Borgstrom the best bet to make a Calder push. Bogdan Kiselevich, 28, is too old to be considered a rookie, but the KHL veteran brings defensive acumen to the blueline.
Center Gabe Vilardi (11th overall in 2017) and defenseman Kale Clague (51st overall in 2016) are the most likely rookies to make the team, but neither player is guaranteed a spot.
Left winger Jordan Greenway (50th overall in 2015) turned pro after his Boston University season ended last year, and played a handful of games -- plus all five playoff contests – for the Wild. He's 6-foot-6 and 226 pounds and should bump his way into the middle-six. Luke Kunin (15th overall in 2016) is an all-around center coming back from ACL surgery and has a chance to stick. Nick Seeler (131st overall in 2011) played 22 games on the blueline and didn't back down from anybody.
Left winger Nikita Scherbak (26th overall in 2014) and defenseman Noah Juulsen (26th overall in 2015) acquitted themselves well when they were called up down the stretch last season and should remain with the team for the long haul in 2018-19. Goalie Charlie Lindgren is biding his time behind Carey Price and Antti Niemi.
The Predators are loaded, but who couldn't use a little more scoring pop from the wing? That's what Eeli Tolvanen (30th overall in 2017) brings to the table, and he should find a spot on Nashville's deep roster.
The Devils ran with a handful of rookies last season, led by 2017 No. 1 pick Nico Hischier and quarterback defenseman Will Butcher. The new faces this season won't be as plentiful -- or as talented -- as last year, but one or two of John Quenneville (30th overall in 2014), Michael McLeod (12th overall in 2016) and Joey Anderson (73rd overall in 2016) could earn a spot up front.
Unfortunately for the Islanders, there's no John Tavares Jr. joining the team this season. Defenseman Devon Toews (108th overall in 2014), no relation to Chicago's Jonathan, might stick as a third-pairing defender. Up front, scoring winger Kieffer Bellows (19th overall in 2016), son of retired NHLer Brian, has a chance, too, but he might need another year of seasoning.
It's all about the rebuild for the Rangers and there's no shortage of rookie options. A couple of 2017 first-round picks, Lias Andersson (seventh overall) and Filip Chytil (21st overall), look good to claim jobs at center. Both players got into some early games last year as 18-year-olds, and they represent hope for New York's future forward corps. Give Andersson a slight edge, both in his ability to make the team as well as contend for the Calder. Neal Pionk forfeited his rookie status playing 28 NHL games last season, but he fared so well that he skates into training camp as one of the team's top-four defenseman. Alexandar Georgiev (free-agent signing in 2017) had a 10-game audition in net and appears ready to back up Henrik Lundqvist.
The reeling Senators need someone to send in the cavalry, but a cavalcade of rookies will have to do for now. The one that everyone is watching is Brady Tkachuk (fourth overall in 2018), a power winger in the grand Tkachuk tradition. Do the Sens want to expose a teenager to the trials and tribulations that likely lie ahead this season? Well, they signed him to an entry-level deal, thereby ending his NCAA career, so the signs point to another Tkachuk in the big leagues. Centers Colin White (21st overall in 2015) and Logan Brown (11th overall in 2016) should find full-time work up front, while wingers Drake Batherson (121st overall in 2017) and Alex Formenton (47th overall in 2017) also have a shot.
No sure things, but Philippe Myers (free-agent signing in 2015) and Samuel Morin (11th overall in 2013) will battle for spots on the blueline. Morgan Frost (27th overall in 2017) is a shifty center who's on the cusp. But the youngster who's most in the spotlight in Philadelphia is goalie-of-the-future Carter Hart (48th overall in 2016). Expect some spot starts this season, and then full-time graduation to the NHL next year.
The Penguins have regularly cycled in young players in a supporting role during their decade of Stanley Cup contention, and that will continue this season. Zach Aston-Reese (free-agent signee in 2017) played 16 games last year, plus nine more in the playoffs, and the gritty winger should have a job locked up. Daniel Sprong (46th overall in 2015) gives Pittsburgh another offensive weapon if he's able to stick for good. Teddy Blueger (52nd overall in 2012) is another AHL-to-NHL option.
The Blues bolstered their forward group with a slew of veteran free agents this summer, but St. Louis might want to make room for some rookies up front, too. Two-way center Robert Thomas (20th overall in 2017) is the headliner and has Calder potential, while Jordan Kyrou (35th overall in 2016) and Klim Kostin (31st overall in 2017) could accelerate their NHL ascension with a strong showing in camp. Jordan Schmaltz (25th overall in 2012) is hoping to break into a stacked blueline.
Full-grown fish only, please, everything else gets thrown back. The veteran Sharks aren't expecting an influx of rookies, with 24-year-old free-agent signing Antti Suomela, who led the Finnish League in scoring last season, the lone legitimate candidate. He's the early favorite to center San Jose's fourth line.
Good luck finding work with the top-to-bottom loaded Lightning, kids. Anthony Cirelli (72nd overall in 2015) ended up as Tampa Bay's third-line center down the stretch and in the playoffs, but he's still considered a rookie. Mitchell Stephens (33rd overall in 2015) will have to leapfrog some veterans to stick around.
Andreas Johnsson (202nd overall in 2015) got a late-season call-up and then they couldn't take him out of the lineup, including in the playoffs. And when Toronto's post-season ended, Johnsson returned to the AHL and led the Toronto Marlies to the Calder Cup, claiming playoff MVP honors in the process. He's got speed and skill and could be a Calder dark horse. Free-agent signee Par Lindholm, 27, is too old for official NHL rookie status, but he comes over from Sweden with designs on the fourth-line center job. Another import, 25-year-old Russian defenseman Igor Ozhiganov, is trying to make the jump from the KHL.
Brock Boeser's rookie breakout was last year, and now Vancouver is hoping that it is Elias Pettersson's turn. The fifth overall pick in 2017 dominated the Swedish League last season, leading the loop in scoring and winning MVP honors in both the regular season and playoffs. He'll get every chance to center a scoring line, and enters the 2018-19 NHL season as one of the Calder favorites. Better yet for the Canucks, Pettersson isn't the only kid expected to make an impact in 2018-19. The blueline will get a lot more mobile if Olli Juolevi (fifth overall in 2016) and perhaps even 2018 first-rounder Quinn Hughes (seventh overall) make the grade. Jonathan Dahlen, obtained from Ottawa at the 2017 trade deadline in the Alex Burrows deal, and Adam Gaudette (149th overall in 2017) are also expected to contend for spots up front.
The NHL's newest franchise might not have any new young faces. It makes sense. When you make it to the Stanley Cup final as an expansion team, you probably don't want to change things up too much. Cody Glass, the Golden Knights' first-ever draft pick (sixth overall in 2017), has a chance to earn a job at center, but Vegas isn't going to rush him so he'll have to really shine in camp.
Teams that win the Cup don't usually ice too many rookies the following season, so don't look for a rookie wave in Washington. The one to watch is goalie-of-the-future Ilya Samsonov (22nd overall in 2015), although he's expected to marinate in the AHL in his first North American campaign. Travis Boyd (177th overall in 2011) and Shane Gersich (134th overall in 2014) are depth options at center.
The Jets have been churning out rookie stars in recent years, but don't expect another Patrik Laine, Kyle Connor or Nikolaj Ehlers to come down the pipe this season. Any freshmen who make it onto Winnipeg's stacked roster will arrive as depth support. Sami Niku (198th overall in 2015) and Tucker Poolman (127th overall in 2013) are among a group of hopefuls for the No. 6-7 spots on the blueline, while grinding Brendan Lemieux and offensively inclined Mason Appleton are in the mix for fourth-line duty. Eric Comrie (59th overall in 2013) could be called upon to back up starting goalie Connor Hellebuyck.
awardsnhl
Bo Horvat Trade Has Huge Effect in Fantasy Hockey
The ripple effect from the New York Islanders acquiring Bo Horvat from the Vancouver Canucks could be huge in fantasy hockey. Which players are affected?
By Jason Chen Jan 30, 2023
Canucks Trade Bo Horvat to Islanders
The Vancouver Canucks have traded captain Bo Horvat to the New York Islanders in exchange for Anthony Beauvillier, Aatu Raty, and a protected first-round pick.
By Mike Stephens Jan 30, 2023
Hockey Things: What Caught Our Eye (Jan. 30)
The Oilers played an Alberta Golden Bears goalie, Luke Hughes had a big night for the Michigan Wolverines and a Czech hockey fan won a car with a perfect shot.
By Avry Lewis-McDougall Jan 30, 2023
THE HOCKEY NEWS MAGAZINE
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This package includes a fix for the HMC V9 R1.921.0 service pack. You can also reference this package by PTF MH01804 and APAR MB04190. This image can be installed on top of HMC Version 9 Release 1 921.0 Service Pack (PTF MH01789) with or without additional fixes.
NOTE: This PTF supersedes MH01800.
This package includes a fix for the HMC V9 R1.921.0 service pack. You can also reference this package PTF MH01805 and APAR MB04191. This image can be installed on top of HMC Version 9 Release 921.0 Service Pack (PTF MH01790) with or without additional fixes.
NOTE: This PTF supersedes MH01801.
Added support to allow administrators to specify the Client Adapter Id while attaching virtual storage using virtual fiber channel in order to allow for their desired mapping rules. Previously, only the next available adapter was possible.
Fixed an issue that prevented users from adding additional VLAN to an existing load group using HMC GUI for systems that are not VSN (Virtual Server Network) capable.
Fixed an issue where the Logical Partition list is missing in the Software Service Information Transmission. This occurs when the HMC is managing multiple systems and a few of the systems do not have any logical partitions.
During Day Light Saving (DST), the timestamp in HMC's Performance and Capacity Monitoring (PCM) dashboard and some of the HMC log files show one hour lag as compared to actual HMC's system time. Fixed the issue to synchronize the time in application server with the system time when DST change occurs.
Fixed an issue where the user specified a Client adapter Id which was not honored and the SCSI mapping was created with the next available slot instead while associating a Virtual Optical Device to the partition.
Fixed an issue where applying a HMC update would reset the lpar_rmc_comm_ifs value to default.


An rss reader that mimics the interface of the NYTimes Chrome app ( https://chrome.google.com/webstore/detail/ecmphppfkcfflgglcokcbdkofpfegoel ).
MySQL Forge is a repository of tools, projects, roadmap tasks, and wiki content that is created and maintained by the MySQL user and developer community. It is intended to be a resource for learning, contributing, and sharing information and code with each other.