Sample size and power determination in joint modeling of longitudinal and survival data

Owing to the rapid development of biomarkers in clinical trials, joint modeling of longitudinal and survival data has gained its popularity in the recent years because it reduces bias and provides improvements of efficiency in the assessment of treatment effects and other prognostic factors. Although much effort has been put into inferential methods in joint modeling, such as estimation and hypothesis testing, design aspects have not been formally considered. Statistical design, such as sample size and power calculations, is a crucial first step in clinical trials. In this paper, we derive a closed-form sample size formula for estimating the effect of the longitudinal process in joint modeling, and extend Schoenfeld's sample size formula to the joint modeling setting for estimating the overall treatment effect. The sample size formula we develop is quite general, allowing for p-degree polynomial trajectories. The robustness of our model is demonstrated in simulation studies with linear and quadratic trajectories. We discuss the impact of the within-subject variability on power and data collection strategies, such as spacing and frequency of repeated measurements, in order to maximize the power. When the within-subject variability is large, different data collection strategies can influence the power of the study in a significant way. Optimal frequency of repeated measurements also depends on the nature of the trajectory with higher polynomial trajectories and larger measurement error requiring more frequent measurements.