Incorporating group-level exposure information in case-control studies with missing data on dichotomous exposures

In case-control studies with exposure data obtained from interviews, participation is an issue of concern. Use of external group-level exposure information, available for all cases and controls (including nonparticipants), can reduce participation bias and improve precision of effect estimates. Our methodologic investigation was motivated by a population-based case-control study on occupational exposures and leukemia. We assessed exposure using dichotomous data collected in interviews, and also using census data on past and current occupational groups for all subjects. Based on information from a job-exposure database, a group-level probability of exposure was assigned to each subject. We studied the performance of the iterative expectation-maximization method for estimating the odds ratio (OR) by using the individual-level exposure data on the interviewed participants together with the assigned group-level exposure probabilities for the nonparticipants. In each iteration, the expected numbers of exposed and unexposed among the nonparticipating cases and controls were calculated from their assigned exposure probabilities and, for the cases only, from the current OR estimate. We then estimated the OR based on the total (observed plus expected) numbers and repeated the procedure until convergence. The expectation-maximization method eliminated participation bias and improved precision for scenarios with error-free group-level exposures and individual-level exposure data missing at random conditional on disease status and group affiliation. We specifically addressed consequences of assigning erroneous exposure probabilities to the nonparticipating subjects. In such situations, the expectation-maximization method can produce biased estimates if the participation rates among the cases and controls differ substantially.