~ N(0, and ~ N(0, θ1 σ12) δ1 σ12) where DAS28jk is the observed individual change in DAS28 score from baseline to day 56 at Dosej for kth subject (Dose is placebo when j=1). DAS28 at Day 56 change from baseline follows a Normal distribution with mean + for each Dosej and with variance of (θj βXk) the Dosej is assumed to be spaced equally. is the estimated treatment effect at Dosej, Xk is σ2, θj the baseline DAS28 score fitted as covariate and is the coefficient for covariate. Furthermore, β has a linear relationship with neighbouring with slope of is the θj θj−1 δj−1(slope parameter). θ1 untreated or placebo response when the drug dose is equal to 0 and is the slope between placebo δ1 and the first dose. and follow Normal distributions. Bayesian NDLM method was Both θ1 δ1 used in the model estimation and it calculated the estimate based on sampled data from posterior distribution of multivariate normal distribution. Bayesian methods (Weir, 2007) offer a robust estimation of parameters in complicated model (Carlin, 2010). IN the retrospectively analysis, the priors of the effect of both the first dose and follow a θ1 δ1 Normal distribution with the mean following a vague prior of 100) and variance of N(0, distribution The prior distributions on and are vague IG(0.001,0.001)). σ2, σθ2, σδ2 inverse-gamma distribution WinBUGS code is available in Appendix 11.1.2. IG(0.001,0.001)). The results of modelling fitting of NDLM model is presented as red dashed line in Figure 6.2. Results of Retrospective Analysis Using NDLM U-shaped dose response curve was an unexpected finding from the Phase 2a PoC clinical trial of GSK123456. To investigate whether NDLM model can improve the model fitting and statistical power, the data from the GSK123456 study are retrospectively analysed using a NDLM approach. The NDLM model is applied to DAS28 change from baseline data at 56. Baseline DAS28, as a
θ1 ~ N(0, σ12) and δ1 ~ N(0, σ12) where DAS28jk is the observed individual change in DAS28 score from baseline to day 56 at Dosej for kth subject (Dose is placebo when j=1). DAS28 at Day 56 change from baseline follows a Normal distribution with mean (θj + βXk) for each Dosej and with variance of σ2, the Dosej is assumed to be spaced equally. θj is the estimated treatment effect at Dosej, Xk is the baseline DAS28 score fitted as covariate and β is the coefficient for covariate. Furthermore, θj has a linear relationship with neighbouring θj−1 with slope of δj−1(slope parameter). θ1 is the untreated or placebo response when the drug dose is equal to 0 and δ1 is the slope between placebo and the first dose. Both θ1 and δ1 follow Normal distributions. Bayesian NDLM method was used in the model estimation and it calculated the estimate based on sampled data from posterior distribution of multivariate normal distribution. Bayesian methods (Weir, 2007) offer a robust estimation of parameters in complicated model (Carlin, 2010). IN the retrospectively analysis, the priors of the effect of both the first dose θ1 and δ1 follow a Normal distribution with the mean following a vague prior of N(0, 100) and variance of distribution IG(0.001,0.001)). The prior distributions on σ2, σθ2, and σδ2 are vague inverse-gamma distribution IG(0.001,0.001)). WinBUGS code is available in Appendix 11.1.2. The results of modelling fitting of NDLM model is presented as red dashed line in Figure 6.2. Results of Retrospective Analysis Using NDLM U-shaped dose response curve was an unexpected finding from the Phase 2a PoC clinical trial of GSK123456. To investigate whether NDLM model can improve the model fitting and statistical power, the data from the GSK123456 study are retrospectively analysed using a NDLM approach. The NDLM model is applied to DAS28 change from baseline data at 56. Baseline DAS28, as a
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