Overlap Weights for Causal Inference/Comparative Effectiveness Research

Basic Idea

To compare two treatments (say one treatment and one control), the overlap weight (OW) for each unit is the probability that unit is assigned to the opposite group, that is, 1-PS for the treated units, and PS for the control units, where PS is the propensity score of that unit. Overlap weights focus on the causal effects on the population with the most overlap in covariates between two treatments. The procedure involves three simple steps, no hidden caveats: Compared to the traditional inverse probability of treatment weights (IPW or IPTW) and associated trimming methods, overlap weights have several advantages:

Extensions to multiple treatments, binary outcomes, time-to-event outcomes, and dynamic treatment regime have also been established.

Some graphical illustration of the target population of the overlap weights (the tilting function h(x))

Fig.1 - Overlap weights for two normally distributed groups with different means. In the upper panel, the red, blue, black dashed, and blue lines represent the density of the covariate in the control, treated, combined (h(x) = 1), and overlap weighted populations (h(x) = e(x)(1 − e(x))), respectively (e(x) is the propensity score). In the lower panel, the red and green lines represent the overlap weights for treated and control units, and the tilting function h(x) = e(x)(1 − e(x)).

Fig.2 - Ternary plot of the tilting function of the overlap weights with three treatments. Each point in the triangular plane represents a unit with certain values of the generalized propensity scores. The value of each generalized propensity score is proportional to the orthogonal distance from that point to each edge. Overlap weights emphasize the centroid region with good overlap, e.g., units with e(x)=(1/3, 1/3, 1/3), and smoothly down-weights the edges, e.g., units with e(x)=(0, 1/2, 1/2).

R package

PSweight [CRAN]: a R package that provides a comprehensive analysis platform for causal inference based on propensity score weighting methods, including overlap weighting, inverse probability weighting, trimming. It accommodates both binary and multiple treatments as well as different types of estimands (difference, odds ratio, risk ratio, relative risk). A detailed manual and illustration is given in the R vignette Zhou et al. (2022) [R vignette] and arxiv [arxiv].

SAS code

  • An example SAS code that simulates a case with two treatments and a binary outcome [SAS code for binary outcome].
  • An example SAS code that simulates a case with two treatments and a survival outcome. The analysis includes (1) a Cox proportional hazard model on OW-weighted sample; (2) a Breslow (Nelson-Aalen) estimator of the survival curves on the OW-weighted sample [SAS code for survival/time-to-event outcome].
  • Tutorial

    An accessible tutorial on overlap weights that includes binary, multiple treatments, subgroup analysis, code demo, and real examples is [OW Tutorial].

    Papers and Slides