First, by summarizing all pretreatment variables to a single score, propensity scores are an important dimension reduction tool for evaluating treatment effects. Propensity score techniques are advantageous compared with regression-based, covariate-adjustment techniquesвЂ“ which correct for imbalances between groups on pretreatment covariates by controlling for them in regression models for the outcomesвЂ“ for at least five reasons. Propensity scores have been used to match, stratify (subclassify), or weight the samples from the treatment and control groups so that the distributions (or features of the distributions such as the means) of observed pretreatment characteristics are similar across the treatment and control groups, thereby reducing or eliminating confounding. The use of propensity scores to control for pretreatment imbalances on observed variables in non-randomized or observational studies examining the causal effects of treatments or interventions has become widespread over the past decade. A case study examining the effects of three treatment programs for adolescent substance abuse demonstrates the methods. Tools for assessing balance and overlap of pretreatment variables among treatment groups in the context of multiple treatments are also provided. We present a detailed plan for using GBM to estimate propensity scores and using those scores to estimate weights and causal effects. We define the causal quantities that may be of interest to studies of multiple treatments and derive weighted estimators of those quantities. The goals of this paper are two-fold: (1) to provide step-by-step guidance for researchers who want to implement propensity score weighting for multiple treatments and (2) to propose the use of generalized boosted models (GBM) for estimation of the necessary propensity score weights. However, there is not such guidance for analyses of three or more treatments.

There are tools (e.g., the twang package in R) and guidance for implementing this method with two treatments. For settings with two conditions of interest such as a treatment and a control, inverse probability of treatment weighted (IPTW) estimation with propensity scores estimated via boosted models has been shown in simulation studies to yield causal effect estimates with desirable properties. Continued abuse of our services will cause your IP address to be blocked indefinitely.The use of propensity scores to control for pretreatment imbalances on observed variables in non-randomized or observational studies examining the causal effects of treatments or interventions has become widespread over the past decade.

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