Hester van Eeren

| Chapter 4 4 | 66 The covariates were multivariate normally distributed with a mean of zero and variance of 1, except for the subgroup, that followed a Bernoulli distribution with, for example, a probability of having severe problems of 0.4 (Table 1). The outcome was simulated from a linear regression model and its error term was multivariate normally distributed, just as for the error terms of the treatment assignment (Table 1). The correlation between the error terms was set to zero as only overt bias was simulated. We simulated 2 scenarios: in scenario 1 the subgroup was not related to the treatment assignment, whereas in scenario 2, this relationship was simulated. In both the scenarios, the subgroup was related to the outcome (Table 1). Within each scenario we varied the simulated data on 3 levels of the correlation between the covariates, on the presence or absence of a correlation with the subgroup, and on 3 different sample sizes (Table 1). Under each combination of characteristics of the simulated data, 1,000 datasets were created, which resulted in 18,000 datasets per scenario. In the literature there is no consensus on how to select the variables in PS estimation (Austin, Grootendorst, & Anderson, 2007; Brookhart et al., 2006). Therefore, we varied the inclusion of variables in the PS estimations (Table 1). For the univariate PS, we investigated whether the subgroup variable should be in- or excluded in the PS estimation. The subgroup variable cannot be selected for the generalized PS, as it is part of its definition (Table 1). To evaluate the performance of the 2 PS methods in the simulation study, we estimated the bias, mean squared error (MSE) and SE of the relevant effects over the total number of simulations. In Eq. (2) the relevant effects were the treatment effect, the effect of the subgroups and the interaction term. In Eq. (4), these were the coefficients related to each dummy variable. Because we were interested in 3 coefficients per regression model [Eqs (2) or (4)] and these coefficients were not comparable one-to- one, we averaged the bias, MSE and SE over the 3 relevant coefficients per regression model [Eqs (2) or (4)]. We then used this value for the bias, MSE and SE per PS method to compare the PS methods. Case study Our sample consisted of a total of 841 patients with personality disorders(Association, 2000) who had enrolled for different types of psychotherapy in 6 mental health care institutes in The Netherlands. The patients were selected for either short-term (up to 6 mo) or long-term (> 6 mo) psychotherapy in various settings (Bartak, Andrea, Spreeuwenberg, Thunnissen, et al., 2011; Bartak, Andrea, Spreeuwenberg, Ziegler, et al., 2011; Bartak et al., 2010; Soeteman et al., 2011). The mean age was 34.12 (SD 9.83, range 17 – 62y) and 68.6 % were female. To compare the PS methods, we investigated whether the treatment effect was modified by the severity of problems, that is, having mild or severe problems. Although we were aware of more recent possible classifications of severity (Crawford, Koldobsky, Mulder, & Tyrer, 2011), for comparison purposes we differentiated between the patients having personality difficulties or a simple personality disorder versus patients having complex or more severe personality disorders based on a classification of personality disorders by Tyrer and colleagues (2004; 1996).