Doubly Robust Estimation of Desirability of Outcome Ranking (DOOR) Probability with Application to MDRO Studies

In observational studies, adjusting for confounders is required if a treatment comparison is planned. A crude comparison of the primary endpoint without covariate adjustment will suffer from biases, and the addition of regression models could improve precision by incorporating imbalanced covariates and thus help make correct inference. Desirability of outcome ranking (DOOR) is a patient-centric benefit-risk evaluation methodology designed for randomized clinical trials. Still, robust covariate adjustment methods could further expand the compatibility of this method in observational studies. In DOOR analysis, each participant’s outcome is ranked based on pre-specified clinical criteria, where the most desirable rank represents a good outcome with no side effects and the least desirable rank is the worst possible clinical outcome. We develop a causal framework for estimating the population-level DOOR probability, via the inverse probability of treatment weighting method, G-Computation method, and a Doubly Robust method that combines both. The performance of the proposed methodologies is examined through simulations. We also perform a causal analysis of the Multi-Drug Resistant Organism (MDRO) network within the Antibacterial Resistant Leadership Group (ARLG), comparing the benefit:risk between Mono-drug therapy and Combination-drug therapy.

💡 Research Summary

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The manuscript introduces a causal‑inference framework for estimating the population‑level Desirability of Outcome Ranking (DOOR) probability in observational studies, where confounding is a major concern. DOOR is a patient‑centric benefit‑risk metric that ranks each subject’s clinical outcome on a pre‑specified ordinal scale (K levels) and defines the estimand
(D = P(Y_1 > Y_0) + \tfrac12 P(Y_1 = Y_0)),
the probability that a randomly selected treated patient has a more desirable outcome than a randomly selected control. While DOOR has been applied mainly to randomized trials, the authors recognize that observational data require adjustment for covariates that influence treatment assignment.

Three estimators are proposed:

1. Inverse Probability of Treatment Weighting (IPTW) – a propensity‑score (PS) model (logistic regression) estimates the probability of receiving the treatment given covariates (X). The inverse‑probability weights (w_i = Z_i/\hat\pi_i + (1-Z_i)/(1-\hat\pi_i)) are used to compute weighted cell‑probabilities for each rank (k). This estimator is consistent if the PS model is correctly specified.

2. G‑Computation (Outcome‑Model, “PO”) – a multinomial or proportional‑odds model for the conditional distribution of the DOOR outcome given treatment and covariates, (m_{iak}=P(Y=k|Z=a,X)). Averaging the fitted conditional probabilities over the observed covariate distribution yields the marginal cell‑probabilities. Consistency requires a correctly specified outcome model.

3. Doubly Robust (DR) Estimator – combines the two approaches. The DR cell‑probability for treatment arm (a) and rank (k) is
   \