Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of weights---the balancing weights---that balance the weighted distributions of the covariates between treatment groups. These weights incorporate the propensity score to weight each group to an analyst-selected target population. This class unifies existing weighting methods, including commonly used weights such as inverse-probability weights as special cases. General large-sample results on nonparametric estimation based on these weights are derived. We further propose a new weighting scheme, the overlap weights, in which each unit's weight is proportional to the probability of that unit being assigned to the opposite group. The overlap weights are bounded, and minimize the asymptotic variance of the weighted average treatment effect among the class of balancing weights. The overlap weights also possess a desirable small-sample exact balance property, based on which we propose a new method that achieves exact balance for means of any selected set of covariates. Two applications illustrate these methods and compare them with other approaches.Comment: 33 pages, 5 figures, 5 table

In stepped wedge cluster randomized trials, intact clusters of individuals switch from control to intervention from a randomly assigned period onwards. Such trials are becoming increasingly popular in health services research. When a closed cohort is recruited from each cluster for longitudinal follow-up, proper sample size calculation should account for three distinct types of intraclass correlations: the within-period, the inter-period, and the within-individual correlations. Setting the latter two correlation parameters to be equal accommodates cross-sectional designs. We propose sample size procedures for continuous and binary responses within the framework of generalized estimating equations that employ a block exchangeable within-cluster correlation structure defined from the distinct correlation types. For continuous responses, we show that the intraclass correlations affect power only through two eigenvalues of the correlation matrix. We demonstrate that analytical power agrees well with simulated power for as few as eight clusters, when data are analyzed using bias-corrected estimating equations for the correlation parameters concurrently with a bias-corrected sandwich variance estimator.

Evidence obtained from clinical practice settings that compares alternative treatments is an important source of information about populations and end points for which randomized clinical trials are unavailable or infeasible. 1 Unlike clinical trials, which strive to ensure patient characteristics are comparable across treatment groups through randomization, observational studies must attempt to adjust for differences (ie, confounding). This is frequently addressed with a propensity score (PS) that summarizes differences in patient characteristics between treatment groups. The PS is the probability that each individual will be assigned to receive the treatment of interest given their measured covariates. 2 Matching or weighting on the PS is used to adjust comparisons between the 2 groups being compared. 2,3 In an article in JAMA Cardiology, Mehta et al evaluated the association between angiotensin-converting enzyme inhibitors (ACEIs), angiotensin II receptor blockers (ARBs), or both with testing positive for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus that causes coronavirus disease 2019 (COVID-19), in 18 472 patients who were tested in the Cleveland Clinic Health System between March 8, 2020, and April 12, 2020. 4 Overlap weighting 5,6 based on the PS was used to adjust for confounding in the comparison of 2285 patients who had been treated with ACEIs/ARBs with 16 187 patients who did not receive ACEIs/ ARBs. After adjustment, there was no significant association between ACEI/ARB use and testing positive for SARS-CoV-2. Use of the MethodWhy Is Overlap Weighting Used? Related article at jamacardiology.com Clinical Review & Education JAMA Guide to Statistics and Methods jama.com

In group-randomized trials, a frequent practical limitation to adopting rigorous research designs is that only a small number of groups may be available, and therefore simple randomization cannot be relied upon to balance key group-level prognostic factors across the comparison arms. Constrained randomization is an allocation technique proposed for ensuring balance, and can be used together with a permutation test for randomization-based inference. However, several statistical issues have not been thoroughly studied when constrained randomization is considered. Therefore, we used simulations to evaluate key issues including: the impact of the choice of the candidate set size and the balance metric used to guide randomization; the choice of adjusted versus unadjusted analysis; and the use of model-based versus randomization-based tests. We conducted a simulation study to compare the type I error and power of the F-test and the permutation test in the presence of group-level potential confounders. Our results indicate that the adjusted F-test and the permutation test perform similarly and slightly better for constrained randomization relative to simple randomization in terms of power, and the candidate set size does not substantially affect their power. Under constrained randomization, however, the unadjusted F-test is conservative while the unadjusted permutation test carries the desired type I error rate as long as the candidate set size is not too small; the unadjusted permutation test is consistently more powerful than the unadjusted F-test, and gains power as candidate set size changes. Finally, we caution against the inappropriate specification of permutation distribution under constrained randomization. An ongoing group-randomized trial is used as an illustrative example for the constrained randomization design.