Moving towards best practice when using inverse probability of treatment weighting (IPTW) using the propensity score to estimate causal treatment effects in observational studies

Abstract

The propensity score is defined as a subject's probability of treatment selection, conditional on observed baseline covariates. Weighting subjects by the inverse probability of treatment received creates a synthetic sample in which treatment assignment is independent of measured baseline covariates. Inverse probability of treatment weighting (IPTW) using the propensity score allows one to obtain unbiased estimates of average treatment effects. However, these estimates are only valid if there are no residual systematic differences in observed baseline characteristics between treated and control subjects in the sample weighted by the estimated inverse probability of treatment. We report on a systematic literature review, in which we found that the use of IPTW has increased rapidly in recent years, but that in the most recent year, a majority of studies did not formally examine whether weighting balanced measured covariates between treatment groups. We then proceed to describe a suite of quantitative and qualitative methods that allow one to assess whether measured baseline covariates are balanced between treatment groups in the weighted sample. The quantitative methods use the weighted standardized difference to compare means, prevalences, higher-order moments, and interactions. The qualitative methods employ graphical methods to compare the distribution of continuous baseline covariates between treated and control subjects in the weighted sample. Finally, we illustrate the application of these methods in an empirical case study. We propose a formal set of balance diagnostics that contribute towards an evolving concept of 'best practice' when using IPTW to estimate causal treatment effects using observational data.

Keywords: IPTW; causal inference; inverse probability of treatment weighting; observational study; propensity score.

Figure 1

Number of published IPTW studies.

Figure 2

Absolute standardized differences in unweighted and weighted samples.

Figure 3

Distribution of age between treated and control subjects.

Figure 4

Distribution of respiratory rate between treated and control subjects.

Figure 5

Distribution of creatinine between treated and control subjects.

Figure 6

Distribution of hemoglobin between treated and control subjects.

Figure 7

Distribution of log‐creatinine between treated and control subjects.