Statistical balancing as an unconstrained optimisation problem

Summary Within the potential outcomes framework, balancing the treatment groups is a key step in estimating the average treatment effect in an observational study. Methods for optimal matching or weighting solve nonlinear programming problems. We present an alternative, related to ridge regression. Its solution has a closed form and is a smooth function of a set of tuning parameters. The method is accompanied by a simple way of exploring the sensitivity with respect to bias due to an unobserved confounder. It is applied to retrospective studies in neonatal research, concerned with clinical care for preterm born babies in the first few weeks of their lives.