Optimal survival analyses with prevalent and incident patients

Period-prevalent cohorts are often used for their cost-saving potential in epidemiological studies of survival outcomes. Under this design, prevalent patients allow for evaluations of long-term survival outcomes without the need for long follow-up, whereas incident patients allow for evaluations of short-term survival outcomes without the issue of left-truncation. In most period-prevalent survival analyses from the existing literature, patients have been recruited to achieve an overall sample size, with little attention given to the relative frequencies of prevalent and incident patients and their statistical implications. Furthermore, there are no existing methods available to rigorously quantify the impact of these relative frequencies on estimation and inference and incorporate this information into study design strategies. To address these gaps, we develop an approach to identify the optimal mix of prevalent and incident patients that maximizes precision over the entire estimated survival curve, subject to a flexible weighting scheme. In addition, we prove that inference based on the weighted log-rank test or Cox proportional hazards model is most powerful with an entirely prevalent or incident cohort, and we derive theoretical formulas to determine the optimal choice. Simulations confirm the validity of the proposed optimization criteria and show that substantial efficiency gains can be achieved by recruiting the optimal mix of prevalent and incident patients. The proposed methods are applied to assess waitlist outcomes among kidney transplant candidates.