Generalized propensity score for estimating the average treatment effect of multiple treatments

The propensity score method is widely used in clinical studies to estimate the effect of a treatment with two levels on patient's outcomes. However, due to the complexity of many diseases, an effective treatment often involves multiple components. For example, in the practice of Traditional Chinese Medicine (TCM), an effective treatment may include multiple components, e.g. Chinese herbs, acupuncture, and massage therapy. In clinical trials involving TCM, patients could be randomly assigned to either the treatment or control group, but they or their doctors may make different choices about which treatment component to use. As a result, treatment components are not randomly assigned. Rosenbaum and Rubin proposed the propensity score method for binary treatments, and Imbens extended their work to multiple treatments. These authors defined the generalized propensity score as the conditional probability of receiving a particular level of the treatment given the pre-treatment variables. In the present work, we adopted this approach and developed a statistical methodology based on the generalized propensity score in order to estimate treatment effects in the case of multiple treatments. Two methods were discussed and compared: propensity score regression adjustment and propensity score weighting. We used these methods to assess the relative effectiveness of individual treatments in the multiple-treatment IMPACT clinical trial. The results reveal that both methods perform well when the sample size is moderate or large.