A Bayesian Approach to Estimate a Linear Regression Model with Aggregate Data

Abstract

The main purpose of this paper is to perform linear regression analysis on a continuous aggregate outcome from a Bayesian perspective using a Markov chain Monte Carlo algorithm (Gibbs sampling). In many situations, data are partially available due to privacy and confidentiality of the subjects in the sample. So, in this study, the vector of outcomes, Y, is realistically assumed to be missing and is partially available through summary statistics, sum(Y), aggregated over groups of subjects, while the covariate values, X, are available for all subjects in the sample. The results of the simulation study highlight both the efficiency of the regression parameter estimates and the predictive power of the proposed model compared with classical methods. The proposed approach is fully implemented in an example regarding systolic blood pressure for illustrative purposes.