Extension of the Peters-Belson method to estimate health disparities among multiple groups using logistic regression with survey data

Abstract

Determining the extent of a disparity, if any, between groups of people, for example, race or gender, is of interest in many fields, including public health for medical treatment and prevention of disease. An observed difference in the mean outcome between an advantaged group (AG) and disadvantaged group (DG) can be due to differences in the distribution of relevant covariates. The Peters-Belson (PB) method fits a regression model with covariates to the AG to predict, for each DG member, their outcome measure as if they had been from the AG. The difference between the mean predicted and the mean observed outcomes of DG members is the (unexplained) disparity of interest. We focus on applying the PB method to estimate the disparity based on binary/multinomial/proportional odds logistic regression models using data collected from complex surveys with more than one DG. Estimators of the unexplained disparity, an analytic variance-covariance estimator that is based on the Taylor linearization variance-covariance estimation method, as well as a Wald test for testing a joint null hypothesis of zero for unexplained disparities between two or more minority groups and a majority group, are provided. Simulation studies with data selected from simple random sampling and cluster sampling, as well as the analyses of disparity in body mass index in the National Health and Nutrition Examination Survey 1999-2004, are conducted. Empirical results indicate that the Taylor linearization variance-covariance estimation is accurate and that the proposed Wald test maintains the nominal level.