Model-based Bayesian inference under computer assisted balance-improving designs.

To improve covariate balance over a complete randomization, a number of methods have been proposed recently to utilize modern computational capabilities to find allocations with balance in observed covariates. Asymptotic inference on treatment effects based on these designs is more complicated than that under complete randomization, and this is why Fisher randomization tests often are suggested. This article suggests model-based Bayesian inference as a general method of inference in these designs, which can deal with complications such as arbitrary covariate balancing criteria and complex estimands. As an illustration, we focus on the case when the outcome is linearly related to the covariates and the estimand of interest is the Sample Average Treatment Effect (SATE). We use a large Monte Carlo simulation to compare the finite sample performance of the model-based Bayesian inference with that of two previous methods which are valid for asymptotic inference of SATE under Mahalanobis distance based rerandomization. We find that for experiments with small to moderate sample sizes, Bayesian inference is to be preferred to the previous methods. As a byproduct, we also find that regression adjustment together with small sample adjusted estimators of standard errors perform better than the previous methods.

Subgroup balancing propensity score.

This paper concerns estimation of subgroup treatment effects with observational data. Existing propensity score methods are mostly developed for estimating overall treatment effect. Although the true propensity scores balance covariates in any subpopulations, the estimated propensity scores may result in severe imbalance in subgroup samples. Indeed, subgroup analysis amplifies a bias-variance tradeoff, whereby increasing complexity of the propensity score model may help to achieve covariate balance within subgroups, but it also increases variance. We propose a new method, the subgroup balancing propensity score, to ensure good subgroup balance as well as to control the variance inflation. For each subgroup, the subgroup balancing propensity score chooses to use either the overall sample or the subgroup (sub)sample to estimate the propensity scores for the units within that subgroup, in order to optimize a criterion accounting for a set of covariate-balancing moment conditions for both the overall sample and the subgroup samples. We develop two versions of subgroup balancing propensity score corresponding to matching and weighting, respectively. We devise a stochastic search algorithm to estimate the subgroup balancing propensity score when the number of subgroups is large. We demonstrate through simulations that the subgroup balancing propensity score improves the performance of propensity score methods in estimating subgroup treatment effects. We apply the subgroup balancing propensity score method to the Italy Survey of Household Income and Wealth (SHIW) to estimate the causal effects of having debit card on household consumption for different income groups.