Using the Peters--Belson method to measure health care disparities from complex survey data

The Peters-Belson (PB) method uses regression to assess wage discrimination and can also be used to analyse disparities for a variety of health care issues, e.g. cancer screening. The PB method estimates the proportion of an overall disparity that is not explained by the covariates in the regression, e.g. education, which may be due to discrimination. This method first fits a regression model with individual-level covariates to the majority/advantaged group and then uses the fitted model to estimate the expected values for minority-group members had they been members of the majority group. The data on disparities in health care available to biomedical researchers differ from data used in legal cases as it is often obtained from large-scale studies or surveys with complex sample designs involving stratified multi-stage cluster sampling. Sample surveys with a large representative sample of various racial/ethnic groups and the extensive collection of important social-demographic variables provide excellent sources of data for assessing disparity for a wide range of health behaviours. We extend the PB method for multiple logistic and linear regressions of simple random samples to weighted data from complex designed survey samples. Because of the weighting and complex sample designs, we show how to apply the Taylor linearization method and delete-one-group jackknife methods to obtain estimates of standard errors for the estimated disparity. Data from the 1998 National Health Interview Survey on racial differences in cancer screening among women is used to illustrate the PB method.