Estimation of causal effects of binary treatments in unconfounded studies with one continuous covariate

Abstract

The estimation of causal effects in nonrandomized studies should comprise two distinct phases: design, with no outcome data available; and analysis of the outcome data according to a specified protocol. Here, we review and compare point and interval estimates of common statistical procedures for estimating causal effects (i.e. matching, subclassification, weighting, and model-based adjustment) with a scalar continuous covariate and a scalar continuous outcome. We show, using an extensive simulation, that some highly advocated methods have poor operating characteristics. In many conditions, matching for the point estimate combined with within-group matching for sampling variance estimation, with or without covariance adjustment, appears to be the most efficient valid method of those evaluated. These results provide new conclusions and advice regarding the merits of currently used procedures.

Uric Acid in the Follow-Up Determines 30% Decline in Estimated GFR Over 2 Years: a Propensity Score Analysis

“…The probability to reach the threshold or above (defined as a propensity score) was determined by multivariate binary logistic regression using the aforementioned 23 baseline covariates. After estimating the propensity score, the participants whose propensity scores were non-overlapped between the higher and the lower groups of the test threshold, that is, outside the common support, were trimmed out and the remaining subsample was used for a propensity score analysis [13].…”

Estimation of causal effects of binary treatments in unconfounded studies

“…The statistical literature includes many procedures for estimating treatment effects in observational studies. Gutman and Rubin showed that when Y and X are scalar and continuous, and treatment assignment only depends on X , only a few of the common procedures are generally statistically valid, with the most promising ones being matching with replacement for effect estimation, with or without covariance adjustment, combined with within‐treatment group matching for sampling variance estimation, suggested by Abadie and Imbens , and called in Gutman and Rubin M–N–m and M–C–m (M, cross‐group matching for point estimate; C/N, with/without covariance adjustment; m, matching within treatment group for sampling variance estimate).…”

“…We compare the validity and performance of MITSS to the most promising methods identified by Gutman and Rubin using Neyman's framework of frequentist operating characteristics, in which an α ‐level interval estimate is ‘valid’ if, under repeated sampling from the population (finite or super), it covers the estimand in at least α percent of the samples. In addition to validity, we compare the accuracy, biases, and mean square errors (MSEs) of point estimates.…”

“…When X i and Y i are scalar and continuous, and the distributions of X in the control and active treatment groups differ, Gutman and Rubin identified the two most promising procedures for inference for the ATE: matching for effect estimation combined with within group matching for sampling variance estimation (M–N–m) , and matching for effect estimation with covariance adjustments combined with within group matching for sampling variance estimation (M–C–m) . This sampling variance estimation allows for heteroskedasticity across treatment groups and levels of the propensity score as described in Section 4 of Abadie and Imbens .…”

“…These five procedures are compared here with the newly proposed procedure for both scalar X and multivariate X . Other procedures such as regression adjusted subclassification were not included, because they were generally invalid even with scalar X .…”