Design consideration for complex survival models

Various complex survival models, such as joint models of survival and longitudinal data and multivariate frailty models, have gained popularity in recent years because these models can maximally utilize the information collected. It has been shown that these methods can reduce bias and improve efficiency, and thus can increase the power for statistical inference. Statistical design, such as sample size and power calculations, is a crucial first step in clinical trials. However, compared to the large number of papers on the analysis methods, papers that focus on design considerations are very limited. We derived a closed form sample size formula for estimating the effect of the longitudinal process (any p-degree polynomial trajectories) in joint modeling, and extended Schoenfeld's (1983) sample size formula to the joint modeling setting for estimating the overall treatment effect. The robustness of the formula was demonstrated in simulation studies with a linear and a quadratic trajectory. We discussed the impact of the within subject variability on the power, and the data collection strategies, such as spacing and frequency of the repeated measurements, in order to maximize power. We also developed a sample size determination method for the shared frailty model to investigate the treatment effect on multivariate time to events, including recurrent events. We first assumed a common treatment effect on multiple event times, and the sample size determination was based on testing the common treatment effect. We then considered testing the treatment effect on one time-to-event while treating the other time-to-events as nuisance, and compared the power from a multivariate frailty model versus that from a univariate parametric and semi-parametric survival model. The multivariate frailty model has significant advantage over the univariate survival model when the time-to-event data is highly correlated. Group sequential methods had been developed to control the overall type I error rate in multiple analyses of accumulating data in a clinical trial. Typically group sequential methods mainly apply to testing the same hypothesis at different interim analyses. Finally, we extended the methodology of the alpha spending function to group sequential stopping boundaries when the hypotheses could be different between analyses. We found that when testing different parameters from the same likelihood function, the stopping boundaries depend on the Fisher's Information matrix. Application to a bivariate frailty model and a joint model was considered.