Online Program

Diagnosing and Correcting Balance Assessments in High Dimensions (307861)

Presentation

*Mark Fredrickson, Dept. of Statistics, University of Michigan 
Ben Hansen, Dept. of Statistics, University of Michigan 

Keywords: Balance assessment, observational studies, randomized controlled trials, high dimensional inference

In observational studies, balance assessments check whether intervention and non-intervention subjects are comparable at baseline, often conditional on adjustments such as matching or weighting. In randomized trials, limiting treatment allocations to those with minimal imbalance can improve precision of outcome estimates. A useful measure of imbalance is the (pre-treatment) Mahalanobis distance between treated and control groups. When the number of covariates is small compared to the number of observations, this statistic has a well behaved chi-squared limit. When the number of variables grows more rapidly than the sample size, however, its distribution degenerates to a point mass, regardless of whether the Mahalanobis distance is computed using a fixed or random covariance matrix. For balance assessments with many variables, we characterize the distribution of the statistic using a Saitterthwaite-like correction, present diagnostic tools, and suggest techniques to mitigate the degeneracy. We demonstrate the problem and our solutions on example observational studies and randomized trials.