Ecological studies, in which data are available at the level of the group, rather than at the level of the individual, are susceptible to a range of biases due to their inability to characterize within-group variability in exposures and confounders. In order to overcome these biases, we propose a hybrid design in which ecological data are supplemented with a sample of individual-level case-control data. We develop the likelihood for this design and illustrate its benefits via simulation, both in bias reduction when compared to an ecological study, and in efficiency gains relative to a conventional case-control study. An interesting special case of the proposed design is the situation where ecological data are supplemented with case-only data. The design is illustrated using a dataset of county-specific lung cancer mortality rates in the state of Ohio from 1988.


Statistical Methodology | Statistical Theory