A case-control study compares cases of some disease or disorder to some group of controls (non-cases), looking backwards in time to contrast the frequency of treatment among cases and controls. Cases are typically matched to controls on measured pretreatment covariates. However, in an observational study, there may be unmeasured pretreatment covariates that affect both treatment and outcomes. A sensitivity analysis asks: What magnitude of bias from unmeasured covariates would need to be present to materially alter the conclusions of a naïve analysis that presumes adjustments for measured covariates suffice to remove all bias?
The first step in designing a case-control study is to define a case of disease and a control. For example, the disease may have different severities and one needs to choose how severe a person’s disease needs to be for the person to be a case. We examine the effects of this design decision on the sensitivity of conclusions to unmeasured biases. We develop an adaptive procedure for choosing the case definition based on the data to make the study as insensitive to unmeasured biases as possible asymptotically. This is joint work with Jing Cheng, Betz Halloran and Paul Rosenbaum.