Sample size and power determination for assessing overall SNP effects in joint modeling of longitudinal and time-to-event data

Longitudinal biomarkers are frequently collected in clinical studies due to their strong association with time-to-event outcomes. While considerable progress has been made in methods for jointly modeling longitudinal and survival data, comparatively little attention has been paid to statistical design considerations, particularly sample size and power calculations, in genetic studies. Yet, appropriate sample size estimation is essential for ensuring adequate power and valid inference. Genetic variants may influence event risk through both direct effects and indirect effects mediated by longitudinal biomarkers. In this paper, we derive a closed-form sample size formula for testing the overall effect of a single nucleotide polymorphism within a joint modeling framework. Simulation studies demonstrate that the proposed formula yields accurate and robust performance in finite samples. We illustrate the practical utility of our method using data from the Diabetes Control and Complications Trial.