Reweighted Mahalanobis distance matching for cluster‐randomized trials with missing data

Abstract

Purpose This paper introduces an improved tool for designing matched-pairs randomized trials. The tool allows the incorporation of clinical and other knowledge regarding the relative importance of variables used in matching and allows for multiple types of missing data. The method is illustrated in the context of a cluster-randomized trial. A web application and R package are introduced to implement the method and incorporate recent advances in the area. Methods Reweighted Mahalanobis Distance (RMD) matching incorporates user-specified weights and imputed values for missing data. Weight may be assigned to missingness indicators to match on missingness patterns. Three examples are presented, using real data from a cohort of 90 Veterans Health Administration sites that had at least 100 incident metformin users in 2007. Matching is utilized to balance seven factors aggregated at the site level. Covariate balance is assessed for 10,000 randomizations under each strategy: simple randomization, matched randomization using the Mahalanobis distance, and matched randomization using the RMD. Results The RMD matching achieved better balance than simple randomization or MD randomization. In the first example, simple and MD randomization resulted in a 10% chance of seeing an absolute mean difference of greater than 26% in the percent of nonwhite patients per site; the RMD dramatically reduced that to 6%. The RMD achieved significant improvement over simple randomization even with as much as 20% of the data missing. Conclusions RMD matching provides an easy-to-use tool that incorporates user knowledge and missing data.

Bagged one‐to‐one matching for efficient and robust treatment effect estimation

“…Here, we highlight three variations in particular that provide for situations in which the analyst has a great deal of uncertainty about the best distance measure and/or outcome model to use. Analysts wishing to avoid specifying either a propensity score model or an outcome model can use the BOOM estimation process with Mahalanobis distance matching or one of its variations, eg, reweighted Mahalanobis distance, and no further covariate adjustment; alternatively, machine learning techniques such as random forests could be used for estimation of propensity scores (as in the work of Lee et al) and/or predicted outcomes. Analysts wanting not only to use propensity score models and further covariate adjustment but also to account for uncertainty in the specification of those models can incorporate model selection into every iteration, thus ensuring as in the work of Efron that the SE estimates reflect this uncertainty.…”

Adaptive pair‐matching in randomized trials with unbiased and efficient effect estimation

“…“nonbipartite matching”) can be carried out with standard software. For example, the nbpMatching package [33] in R and the corresponding web application will generate the set of optimal matched pairs as function of a user-supplied matrix of covariates [35, 36]. These tools allow the user to weight covariates differently (e.g.…”

“…When the measured covariates are predictive of the outcome, this simple difference-in-means estimator tends to be inefficient as it fails to adjust for measured covariates. Despite recent advances in matching algorithms [14, 35, 36], there is likely to be some residual imbalance on pre-intervention determinants of the outcome within matched pairs. Furthermore, even if we succeeded in matching well on all available characteristics, there might be additional baseline covariates that are predictive of the outcome, but were unavailable during the matching process.…”

“…Examples include the Mwanza trial to prevent HIV [29], the PRISM trial to prevent postpartum depression [30], and the SPACE study to promote physical activity [31]. The process of selecting n /2 pairs based on the covariates of n candidates is also known in other literature as “nonbipartite matching” [14, 32] and has motivated the development of “optimal multivariate matching” algorithms to pair units based on several covariates simultaneously [33–36]. Previously, van der Laan et al [37] explored the consequences of adaptive pair-matching for estimation of the population average treatment effect.…”

Methods for developing and analyzing clinically rich data for patient‐centered outcomes research: an overview

“…Greevy et al . developed an innovative method and software to aid in the design of cluster randomized trials.…”