Hester van Eeren

| Chapter 4 4 | 70 When comparing the univariate and generalized PS methods, in which only the covariates related to the outcome were included, the MSE was smaller for the generalized PS in all simulated datasets in scenario 1 and scenario 2 (Table 2). In addition, if the sample size increased, the MSE decreased in all simulations. If the correlation increased when there was a correlation between the subgroup and covariates, the MSE increased. However, if the correlation between the subgroup and covariates was absent, the MSE showed a rather inconsistent pattern. Comparing the simulations when the correlation between the subgroup and covariates was either present or absent, gave overall lower MSE values if this correlation was absent. Univariate PS: case study The univariate PS was applied according to the protocol described by Bartak and colleagues (Bartak et al., 2009). In total, 28 covariates related to outcome ( P = 0.10) were selected in the PS estimation. We added four sociodemographic variables as these are considered highly relevant in psychotherapy research (Bartak et al., 2009). The subgroup of interest, that is, the severity of problems, was related to treatment assignment ( χ² (1)= 10.80, P =.001) and to the outcome (B = .318, P = .000; in a linear regression on the outcome). Thus, in applying the PS methods in the case study, we followed the results of scenario 2: for the univariate PS, we excluded the variable that reflected the severity of problems from the PS estimation. The PS was estimated in a logistic regression analysis on the treatment assignment and no interaction terms between the covariates were added. The distributions of the estimated PS scores showed considerable overlap (Figure 1). A lack of overlap would yield imprecise estimates of the treatment effect (Spreeuwenberg et al., 2010). The PS was then added to a regression model on the outcome GSI, in which treatment duration, severity of problems, and an interaction term were the independent variables: β β β β β = + + + + ⋅ 0 1 2 3 4 OUTCOME PS Treatment Severity Treatment Severity (5) If patients had mild problems, long-term treatment yielded more favorable results than short-term treatment (standardized coefficient of 0.092; Table 3). For patients having severe problems, both treatment options were equally effective: for patients having severe problems in the short-term treatment the standardized coefficient was 0.240, whereas for the long-term treatment, the final standardized coefficient was 0.248. The interaction effect was, however, not significant. Excluding this coefficient indicated that long-term treatment was preferred for patients with severe problems (Table 3).