Sequential rerandomization.

The seminal work of Morgan & Rubin (2012) considers rerandomization for all the units at one time.In practice, however, experimenters may have to rerandomize units sequentially. For example, a clinician studying a rare disease may be unable to wait to perform an experiment until all the experimental units are recruited. Our work offers a mathematical framework for sequential rerandomization designs, where the experimental units are enrolled in groups. We formulate an adaptive rerandomization procedure for balancing treatment/control assignments over some continuous or binary covariates, using Mahalanobis distance as the imbalance measure. We prove in our key result that given the same number of rerandomizations, in expected value, under certain mild assumptions, sequential rerandomization achieves better covariate balance than rerandomization at one time.

Measuring Geographic "Hot Spots" of Racial/Ethnic Disparities: An Application to Mental Health Care.

This article identifies geographic "hot spots" of racial/ethnic disparities in mental health care access. Using data from the 2001-2003 Collaborative Psychiatric Epidemiology Surveys(CPES), we identified metropolitan statistical areas(MSAs) with the largest mental health care access disparities ("hot spots") as well as areas without disparities ("cold spots"). Racial/ethnic disparities were identified after adjustment for clinical need. Richmond, Virginia and Columbus, Georgia were found to be hot spots for Black-White disparities, regardless of method used. Fresno, California and Dallas, Texas were ranked as having the highest Latino-White disparities and Riverside, California and Houston, Texas consistently ranked high in Asian-White mental health care disparities across different methods. We recommend that institutions and government agencies in these "hot spot" areas work together to address key mechanisms underlying these disparities. We discuss the potential and limitations of these methods as tools for understanding health care disparities in other contexts.

Rerandomization to Balance Tiers of Covariates.

When conducting a randomized experiment, if an allocation yields treatment groups that differ meaningfully with respect to relevant covariates, groups should be rerandomized. The process involves specifying an explicit criterion for whether an allocation is acceptable, based on a measure of covariate balance, and rerandomizing units until an acceptable allocation is obtained. Here we illustrate how rerandomization could have improved the design of an already conducted randomized experiment on vocabulary and mathematics training programs, then provide a rerandomization procedure for covariates that vary in importance, and finally offer other extensions for rerandomization, including methods addressing computational efficiency. When covariates vary in a priori importance, better balance should be required for more important covariates. Rerandomization based on Mahalanobis distance preserves the joint distribution of covariates, but balances all covariates equally. Here we propose rerandomizing based on Mahalanobis distance within tiers of covariate importance. Because balancing covariates in one tier will in general also partially balance covariates in other tiers, for each subsequent tier we explicitly balance only the components orthogonal to covariates in more important tiers.