Statistical matching as an unconstrained optimisation problem
N. T. Longford
Abstract
Within the potential outcomes framework (Rubin's causal model),
balancing the treatment groups, by purposeful subsetting or weighting,
is a key step in estimation of the average treatment effect
in an observational study.
Established methods involve an extensive search of propensity models
and distance-based matching. Their results cannot be straightforwardly
related to the best balance that might be achieved.
Methods for optimal matching or weighting solve nonlinear programming
problems by iterative algorithms.
We present an algorithm for optimal weighting of one treatment group
against a target (standard) or template, which involves no iterations.
A recursive formula is applied to avoid numerical inversion
of large matrices.
The method is applied to studies in neonatal research, concerned with
clinical care for preterm born babies in the first few weeks of their lives.
Submitted.
July 2021.