Using the Prognostic Score to Reduce Heterogeneity in Observational Studies

In large sample observational studies, the control population often greatly outnumbers the treatment population. Typical practice is to match several control observations to a single treated observation, with the goal of reducing variability of the resulting treatment effect estimate. However, increasing the control to treated ratio yields diminishing returns in terms of variance reduction and in practice leads to poorer quality matches. In line with Rosenbaum's argument on the importance of reducing heterogeneity to strengthen causal inference against unobserved bias, we suggest first expending some of the controls to fit a prognostic model, then matching with the resulting prognostic score to produce matched sets with lower heterogeneity. We propose methodological alternatives for fitting the prognostic model that help avoid concerns of overfitting and extrapolation, then we demonstrate in a simulation setting how this alternative use of the control observations can lead to gains in terms of both treatment effect estimation and design sensitivity.