Hester van Eeren

| Chapter 4 4 | 64 used to estimate subgroup effects. These 2 PS estimations were subsequently compared using data from a Dutch research project on psychotherapy effectiveness: SCEPTRE (Study on Cost-Effectiveness of Personality Disorder TREatment) (Bartak et al., 2010). Methods First, we describe the univariate propensity score (PS), the generalized PS and the simulation study in which we tested these methods. Then, we describe the case study where we compare the 2 PS methods. To estimate the treatment effects for subgroups of patients, we used the 2 PS estimations in covariate adjustment, as this method is the most frequently used PS method in the medical literature (Austin, 2009; Shah, Laupacis, Hux, & Austin, 2005; Stürmer et al., 2006; Weitzen, Lapane, Toledano, Hume, & Mor, 2004) because it leaves the sample size intact. Univariate PS method The univariate PS is defined according to Rosenbaum and Rubin (Rosenbaum & Rubin, 1983) as: PS(x)=pr D=1|X=x (1) where if D = 1 the PS defines the conditional probability of assignment to the treatment of interest, given a set of observed covariates (X) (Rosenbaum & Rubin, 1983). The ignorability assumption defines that the potential outcomes and the treatment assignment are independent given the observed covariates (X) (Rosenbaum & Rubin, 1983; Rubin, 1997). The PS was estimated in a univariate logistic regression function (Hirano & Imbens, 2001). To estimate the treatment effect for subgroups of patients, this PS estimation was used as an extra predictor in a linear regression model with treatment outcome (Y) as the dependent variable: 0 1 3 4 β β β β = + + Ζ + OUTCOME D DZ (2) The treatment groups (D), subgroups (Z) and the interaction between these (DZ) were the independent variables, and the effects of interest (Liem et al., 2010). Generalized PS method The generalized PS is an extension of the univariate PS defined by Rosenbaum and Rubin (Rosenbaum & Rubin, 1983) and is further defined by Imbens (2000). To calculate the generalized PS used in this study, we estimated the joint conditional probability of the treatment assignment (D) and subgroup (Z) given all covariates (X): PS(d,z,x)=pr D=d,Z=z|X=x (3) Using 2 treatment options and 2 subgroups, the PS was estimated for 4 groups. The assumption on the strongly ignorable treatment assignment is crucial (Imbens, 2000; Rosenbaum & Rubin, 1983; Rubin, 1997). When this assumption was adjusted to the combined categories on which the generalized PS was estimated, the joint distributions of