Generalized Propensity Scores Sample Clauses

Generalized Propensity Scores. When considering only the effect of a dichotomous treatment, standard propensity scores may be employed. However, when treatment is defined as a measure of time, we must consider a more flexible definition and model for propensity score. Imai & Van Dyk (2004) and Hirano & Imbens (2004) pro- pose generalized propensity score methods that allow for the inclusion of the . Σ information provided by covariates to control for selection bias and confound- ing when treatment assignment is non-binary (Zhao et al. 2012). In support of these generalized propensity scores, Imai & Van Dyk (2004) derive “large- sample” theoretical results of balancing properties and ignorable treatment assignment resembling those of the standard propensity score proposed by Xxxxxxxxx & Xxxxx (1983). Thus, when treatment assignment is defined as time to treatment, we may use the linear predictor of the Xxx proportional hazards model h(t) = h0(t) exp DT β as the generalized propensity score. The estimated propensity scores are included in the model for the outcome (Y), the model for missing outcome (M), and the model determining prin- cipal strata (G), to control for issues of selection bias and confounding. It is noteworthy that inclusion of the propensity scores in the principal strata model is necessary in the absence of randomization, as otherwise the principal effect is likely to be biased. To allow flexibility in the control for selection bias when including each of the propensity scores a linear predictor, the use of quadratic and cubic polynomial higher order terms are also considered when incorporateing propensity score in the models.