Background: Among the large number of cohort studies that employ propensity score (PS) matching, most match patients 1:1. Increasing the matching ratio to 1:n will generally improve precision but may also increase bias.
Objectives: To evaluate via simulation study several methods of PS matching one treated patient to n untreated patients, and to evaluate differences in bias and variance.
Methods: We simulated cohorts of 20,000 patients with exposure prevalence of 10% to 50%. We simulated five dichotomous and five continuous confounders at varying levels of strength. We created a continuous outcome. We then estimated PSs and matched on PS three ways: (1) using a standard SAS-based greedy matching method; (2) using a newly-implemented exact nearest neighbor matching method; and (3) using a method that extended our nearest neighbor implementation by requiring a treated patient’s untreated matches to have alternatively higher and lower (or lower and higher) PSs. We compared variable- and fixed-ratio matching, as well as a sequential method of creating 1:n matched sets that assigned each treated patient a first untreated match before adding any second untreated patient matches, and a parallel approach in which high quality second matches could be made even if some treated patients had not yet received a first match. We performed 1,000 simulations in each of 240 scenarios. In each scenario, we recorded mean bias, mean variance, and mean squared error (MSE).
Results: Across the scenarios, increasing the match ratio beyond 1:1 generally resulted in slightly higher bias; for variable ratio matching, the increase in bias was generally <2%. Increasing the match ratio also resulted in lower variance with variable ratio matching (reductions of 20% or more), but higher variance with fixed. The parallel approach generally resulted in higher mean squared error but lower bias as compared to the sequential approach. Variable ratio parallel balanced nearest neighbor matching generally yielded the lowest bias and MSE.
Conclusions: We observed that 1:n matching increased precision in cohort studies at a small cost in bias. We recommend employing a variable-ratio, parallel balanced 1:n nearest neighbor approach
