Adjusting for misselection using subsampling in epidemiological studies

In epidemiological research it is sometimes necessary to conduct a case-control study in a part of the population which is not exposed to certain risk factors. Such a study design may be useful to investigate the risk related to a weak carcinogen in presence of other strong risk factors. It may happen that some individuals are wrongly included in the study group due to misreporting of the true exposure status. This misselection may cause biased odds ratio estimates of the factors of interest. It is therefore recommended that an evaluation study to validate the selection procedure is undertaken. We propose a two-stage sample design, consisting of a case-control study and a validation study in a subsample. Misselection rates in cases and control for different exposure groups may be estimated in the subsample and used to correct the odds ratio estimation from the first stage. It is shown how the total sample size should be attributed to the case-control sample and to the second-stage sample in order to give an unbiased estimate with minimal variance. The allocation is shown to be dependent on a number of parameters which is illustrated numerically and graphically. Efficiency considerations are also addressed.