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Propensity score analysis is a common approach to addressing confounding in non-randomized studies. Its implementation, however, requires important assumptions (e.g., positivity). The disease risk score is an alternative confounding score that can relax some of these assumptions. Like the propensity score, the disease risk score summarizes multiple confounders into a single score, on which conditioning by matching allows the estimation of causal effects. However, matching relies on arbitrary choices for pruning out data (e.g., matching ratio, algorithm and caliper width) and may be computationally demanding. Alternatively, weighting methods, common in propensity score analysis, are easy to implement and may entail fewer choices, yet none have been developed for the disease risk score. We present two weighting approaches: one derives directly from inverse probability weighting (IPW); the other named target distribution weighting (TDW) relates to importance sampling. We empirically show IPW and TDW display a performance comparable to matching techniques in terms of bias but outperform them in terms of efficiency (mean squared error) and computational speed (up to >870 times faster in an illustrative study). We illustrate implementation of the methods in two case studies where we investigate placebo treatments for multiple sclerosis and administration of Aspirin in stroke patients.

Original publication




Journal article


Am j epidemiol

Publication Date



causal inference, confounding, density, disease risk score, weighting