Analysis of follow-up data in large biobank cohorts: a review of methodology.

This study focuses on key methodological challenges in genome-wide association studies (GWAS) of biobank data with time-to-event outcomes, analyzed using the Cox proportional hazards (CPH) model. We address four primary issues: left-truncation of the data, computational inefficiency of standard model-fitting algorithms, relatedness among individuals, and model misspecification. To manage left-truncation, the common practice is to use age as the timescale, with individuals entering the risk set at their age of recruitment. We assess how this choice of timescale influences bias and statistical power, under realistic GWAS conditions of varying effect sizes and censoring rates. In addition, to alleviate the computational burden typical in large-scale data, we propose and evaluate a two-step martingale residual (MR) approach for high-dimensional CPH modeling. Our results show that the timescale choice has minimal effect on accuracy for small hazard ratios, though using time since birth as the timescale - ignoring recruitment age - yields the highest power for association detection. We find that relatedness, when ignored, does not substantially bias effect size estimates, while omitting key covariates introduces significant bias. The two-step MR approach proves to be computationally efficient, retaining power for detecting small effect sizes, making it suitable for large-scale association studies. However, when precise effect size estimates are critical, particularly for moderate or larger effect sizes, we recommend recalculating these estimates using the conventional CPH model, with careful attention to left-truncation and relatedness. These conclusions are drawn from simulations and illustrated with data from the Estonian Biobank cohort.