Power and sample size determinations in dynamic risk prediction

Dynamic risk prediction is a powerful tool to estimate the future risk of study subjects with data involves time-dependent information, including repeatedly measured covariates, intermediate events, and time-varying covariate effects. The quantity of interest for dynamic risk prediction is the probability of failure at the prediction horizon time conditional on the status at the prediction baseline (aka landmark time}. For a clinical study, a series of horizon and landmark time points are usually planned in the design stage. This conditional probability can be estimated from a standard Cox proportional hazards model (for data without competing risks) or a Fine and Gray subdistributional hazards model (for data with competing risks) by appropriately setting up a landmark dataset. In this dissertation, I propose test statistics for testing the equal conditional probability between two patient groups according to their response to treatment at the prediction baseline under the scenarios of data with and without competing risks, respectively. The dissertation provides three different methods for estimating the variance of risk difference. In designing a randomized clinical trial for comparing risk difference between the two study arms, I derived formulas for power, the number of events, and the total sample size required with respect to the aforementioned hypothesis tests. Simulations were conducted to evaluate the impact of each design parameter on the power and sample size calculations. Public health significance: This study aims to introduce new risk prediction methods that can incorporate time-dependent information and update risk estimation during the course of study follow-up, also provide researchers with references on the power and sample size requirements at the planning phase of studies involving dynamic risk prediction