Joint Modeling Subject to Dependent Censoring and Group Sequential Designs by Prespecifying Cumulative Power Levels with Uncertainties in Effect Size

In biomedical studies, investigators are typically interested in the relationship between the independent variable and both longitudinal outcomes and survival endpoints. One effective statistical method to model such outcomes is the joint random effects model. A conditional independent censoring assumption is made for dropouts within the study. However, the conditional independent censoring assumption may not hold in cases where the censoring process is dependent on some factors that are not in the main models of interest (termed as auxiliary variables). We propose an inverse probability weighted estimation approach to account for the dependent censoring that uses the EM algorithm and quadrature techniques. We show the benefits of this approach through simulations and provide an example of how it can be applied to clinical trial data. In clinical trials, group sequential designs (GSDs) are commonly used. The typical GSD requires specification of an alpha-spending function, overall power level, overall type I error, alternative effect size, and information fractions. Traditionally, the cumulative power is typically assessed retrospectively and there is no method for directly specifying the cumulative power with a corresponding alpha-spending function directly. We propose a method of minimizing a defined objective function using the Nelder-Mead simplex method to construct GSDs such that the cumulative power at each sequential analysis can be prespecified by the investigator at the design stage while maintaining the overall type I error and adhering to a prespecified alpha-spending function. When designing a clinical trial, investigators are often uncertain about the effect of the new treatment. The ability to account for the uncertainties in alternative hypotheses has become of interest. Current methods that attempt to address this issue lack some favorable elements from the traditional GSD, such as the ability to prespecify an alpha-spending function. We propose a method that optimizes an objective function that allows the specification of a sequence of alternative hypotheses to construct a GSD such that a prespecified power level is achieved at each sequential analysis for a corresponding alternative. We use a method similar to the previous work but adapted to handle a sequence of alternative hypotheses.