Calculating a Propensity Score Sample Clauses

Calculating a Propensity Score. In a randomized trial, the treatment assignment mechanism is known, and therefore the propensity score e(x) has one known definition for that trial. In observational studies the assignment mechanism must be estimated from the observed data, and therefore numerous different definitions of e(x) may be suggested. Translated into Bayesian language, the propensity score may be considered the “. . . posterior predictive probabilities of assignment to treatment 1 for a unit with vector x of covariates [Xxxxxxxxx and Xxxxx, 1983a].” For the case of a dichotomous treatment assignment (only treatment and control groups), the propensity score may be calculated based on a logistic regression model. All pre- treatment covariates should be considered for this model, and any preferred model-building procedure may be used (see chapter 3 of this paper, Xxxxxxxxx and Xxxxx, 1984, D’Xxxxxxxx Xx., 1998, among others for specific examples). Once a preliminary model has been chosen, the resulting balance of covariates between the treated and control groups should be assessed, and the propensity score model updated appropriately until sufficient balance is achieved. Of course, propensity scores can only balance samples for observed covariates - only ran- domization can plausibly account for unobserved covariates as well. There is some debate in the literature regarding whether propensity score models should include all potential confounding variables or only those that remain significantly associated with the treatment or exposure indicator. As Miettinen [1976] states with regard to a multivariate confounder score (a precursor to the propensity score) [w]ith the initial, full model fitted to the data, the statistical significance of the coefficients for many of the (potential) confounding factors is often found to be quite low. In these situations there may be a temptation to reduce the model in a stepwise fashion until all remaining terms have (nominally) ‘significant’ coefficients. Such reduction of the model would tend to defeat the purpose of multivariate control of confounding, since ‘nonsignificance’ does not mean lack of confounding, and the deletion of many ‘nonsignificant’ terms from the model may lead to substantial confounding by the aggregate of the deleted factors. Moreover, the deletion, even if not detrimental, would not serve a purpose of parsimony analogous to that in other contexts. For, the (potential) confounding factors are extraneous to the real issue - con...