More on "Biased selection of controls for case-control analyses of cohort studies"

The authors consider several aspects of the design and analysis of synthetic case-control studies of cohort data under a proportional hazards model. First, in highly stratified data, consistent estimates of the relative risk are shown to result only if controls are sampled randomly with replacement from the entire risk set or without replacement from the noncases. Second, if previous controls are excluded from consideration as future controls but are included as cases if they fail, then inconsistent estimates of the relative risk can occur if "time" in the proportional hazards model represents an individual's chronological age and age at entry into follow-up is variable. On the other hand, if "time" represents time since the beginning of follow-up, estimates of the relative risk will be consistent, but the usual variance estimator will be inconsistent.