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Typically, case-control studies to estimate odds-ratios associating riskfactors with disease incidence from logistic regression only include cases withnewly diagnosed disease. Recently proposed methods allow incorporatinginformation on prevalent cases, individuals who survived from disease diagnosisto sampling, into cross-sectionally sampled case-control studies underparametric assumptions for the survival time after diagnosis. Here we proposeand study methods to additionally use prospectively observed survival timesfrom prevalent and incident cases to adjust logistic models for the timebetween disease diagnosis and sampling, the backward time, for prevalent cases.This adjustment yields unbiased odds-ratio estimates from case-control studiesthat include prevalent cases. We propose a computationally simple two-stepgeneralized method-of-moments estimation procedure. First, we estimate thesurvival distribution based on a semi-parametric Cox model using anexpectation-maximization algorithm that yields fully efficient estimates andaccommodates left truncation for the prevalent cases and right censoring. Then,we use the estimated survival distribution in an extension of the logisticmodel to three groups (controls, incident and prevalent cases), to accommodatethe survival bias in prevalent cases. In simulations, when the amount ofcensoring was modest, odds-ratios from the two-step procedure were equallyefficient as those estimated by jointly optimizing the logistic and survivaldata likelihoods under parametric assumptions. Even with 90% censoring theywere as efficient as estimates obtained using only cross-sectionally availableinformation under parametric assumptions. This indicates that utilizingprospective survival data from the cases lessens model dependency and improvesprecision of association estimates for case-control studies with prevalentcases.

Incorporating survival data into case-control studies with incident and prevalent cases