One-to-many propensity score matching in cohort studies. 
Among the large number of cohort studies that employ propensity score matching, most match patients 1:1.  Increasing the matching ratio is thought to improve precision but may come with a trade-off with respect to bias.  To evaluate several methods of propensity score matching in cohort studies through simulation and empirical analyses.  We simulated cohorts of 20,000 patients with exposure prevalence of 10%-50%.  We simulated five dichotomous and five continuous confounders.  We estimated propensity scores and matched using digit-based greedy ("greedy"), pairwise nearest neighbor within a caliper ("nearest neighbor"), and a nearest neighbor approach that sought to balance the scores of the comparison patient above and below that of the treated patient ("balanced nearest neighbor").  We matched at both fixed and variable matching ratios and also evaluated sequential and parallel schemes for the order of formation of 1:n match groups.  We then applied this same approach to two cohorts of patients drawn from administrative claims data.  Increasing the match ratio beyond 1:1 generally resulted in somewhat higher bias.  It also resulted in lower variance with variable ratio matching but higher variance with fixed.  The parallel approach generally resulted in higher mean squared error but lower bias than the sequential approach.  Variable ratio, parallel, balanced nearest neighbor matching generally yielded the lowest bias and mean squared error.  1:n matching can be used to increase precision in cohort studies.  We recommend a variable ratio, parallel, balanced 1:n, nearest neighbor approach that increases precision over 1:1 matching at a small cost in bias.