Time-to-event data are common in clinical trials to evaluate survival benefit of a new drug, biological product, or device. The commonly used parametric models including exponential, Weibull, Gompertz, log-logistic, log-normal, are simply not flexible enough to capture complex survival curves observed in clinical and medical research studies. On the other hand, the nonparametric Kaplan Meier (KM) method is very flexible and successful on catching the various shapes in the survival curves but lacks ability in predicting the future events such as the time for certain number of events and the number of events at certain time and predicting the risk of events (eg, death) over time beyond the span of the available data from clinical trials. It is obvious that neither the nonparametric KM method nor the current parametric distributions can fulfill the needs in fitting survival curves with the useful characteristics for predicting. In this paper, a full parametric distribution constructed as a mixture of three components of Weibull distribution is explored and recommended to fit the survival data, which is as flexible as KM for the observed data but have the nice features beyond the trial time, such as predicting future events, survival probability, and hazard function.

Censored survival data are common in clinical trial studies. We propose a unified framework for sensitivity analysis to censoring at random in survival data using multiple imputation and martingale, called SMIM. The proposed framework adopts the 𝛿-adjusted and control-based models, indexed by the sensitivity parameter, entailing censoring at random and a wide collection of censoring not at random assumptions. Also, it targets a broad class of treatment effect estimands defined as functionals of treatment-specific survival functions, taking into account missing data due to censoring. Multiple imputation facilitates the use of simple full-sample estimation; however, the standard Rubin's combining rule may overestimate the variance for inference in the sensitivity analysis framework. We decompose the multiple imputation estimator into a martingale series based on the sequential construction of the estimator and propose the wild bootstrap inference by resampling the martingale series. The new bootstrap inference has a theoretical guarantee for consistency and is computationally efficient compared to the nonparametric bootstrap counterpart. We evaluate the finite-sample performance of the proposed SMIM through simulation and an application on an HIV clinical trial.

There has been an increased interest in borrowing information from historical control data to improve the statistical power for hypothesis testing, therefore reducing the required sample sizes in clinical trials. To account for the heterogeneity between the historical and current trials, power priors are often considered to discount the information borrowed from the historical data. However, it can be challenging to choose a fixed power prior parameter in the application. The modified power prior approach, which defines a random power parameter with initial prior to control the amount of historical information borrowed, may not directly account for heterogeneity between the trials. In this paper, we propose a novel approach to pick a power prior based on some direct measures of distributional differences between historical control data and current control data under normal assumptions. Simulations are conducted to investigate the performance of the proposed approach compared with current approaches (e.g. commensurate prior, meta-analytic-predictive, and modified power prior). The results show that the proposed power prior improves the study power while controlling the type I error within a tolerable limit when the distribution of the historical control data is similar to that of the current control data. The method is developed for both superiority and non-inferiority trials and is illustrated with an example from vaccine clinical trials.

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Censored survival data are common in clinical trial studies. We propose a unified framework for sensitivity analysis to censoring at random in survival data using multiple imputation and martingale, called SMIM. The proposed framework adopts the δ-adjusted and control-based models, indexed by the sensitivity parameter, entailing censoring at random and a wide collection of censoring not at random assumptions. Also, it targets for a broad class of treatment effect estimands defined as functionals of treatment-specific survival functions, taking into account of missing data due to censoring. Multiple imputation facilitates the use of simple full-sample estimation; however, the standard Rubin's combining rule may over estimate the variance for inference in the sensitivity analysis framework. We decompose the multiple imputation estimator into a martingale series based on the sequential construction of