Using Propensity Scores to Reduce Case-control Selection Bias

Abstract

To the Editor: When sampling frames differ for cases and controls in a population based study, there are several analytical options to increase study validity. One is to exclude cases not found in the sampling frame for controls. Another, when the case sampling frame is nearly complete, is to link cases to the sampling frame for controls in order to obtain the information needed to model coverage propensity scores.1 Propensity scores have been used to address selection bias due to non-response and treatment-selection,2, 3 but we have found no studies that used propensity scores to address selection bias due to inadequate sampling frame coverage. We describe such an application here. Our analyses use data from the Wisconsin Women’s Health Study. Cases were women with incident invasive breast cancer reported to Wisconsin’s mandatory cancer registry. Controls were identified using a master file of licensed drivers who consented to have their private information released by the Wisconsin Department of Transportation. An estimated 68% of Wisconsin women with valid driver’s licenses provided this consent in 2008.4 Case eligibility was limited to women with a Wisconsin driver’s license (verified by self-report). We calculated odds ratio (OR) estimates of breast cancer risk using 3 established methods to correct selection bias, and compared these with published estimates.5, 6 The 3 methods were (1) excluding cases not in the control sampling frame, (2) applying propensity scores as weights, and (3) using quintiles of propensity scores to stratify analyses. We calculated standard errors of OR estimates to compare their precision. Additional details, including study inclusion criteria, are described elsewhere.4 The 2,988 breast cancer cases were linked to the driver’s license file to determine whether cases matched a record from the master-file of drivers (sampling frame for controls).4, 7 Propensity scores for inclusion in the sampling frame were calculated using logistic regression of 24 potential confounding factors ascertained through interviews with participants. The Table shows results of applying the 3 correction methods to a re-analysis of antidepressant medications and breast cancer risk.6 Of the 3 methods, stratifying by quintile of propensity score produced odds ratio3 with the best precision. Weighting, stratification and exclusion produced odds ratio3 with a similar degree of bias correction. However, the odds ratio3 changed only slightly after applying any of the correction methods. Similar results were found in another re-analysis of breast cancer risk, that one in relation to reproductive factors.4 Historically, the standard procedure in epidemiologic case-control studies has been to exclude cases that could not have been approached to serve as controls.8 This procedure assumes that factors that predict inclusion in the control sampling frame are similar for cases and potential controls. The two propensity-score-based methods implemented here also require this assumption and in addition, require correct model specification for propensity score estimation. The advantage of the propensity score methods is that they preserve the study base by allowing all cases to be used. Selection bias caused by incomplete sampling-frame coverage is frequently overlooked. In this study we linked the case and control sampling frames to demonstrate the use of propensity scores to adjust for selection bias due to incomplete study-base coverage of the sampling frames.