Hester van Eeren

Subgroup analysis using the propensity score | 4 75 | Discussion The present study illustrates the use of the univariate and generalized PS in subgroup analyses in non-randomized outcomes research, and describes how the generalized PS could be used in subgroup analysis. The results indicate that the generalized PS – estimated by crossing the treatment options with a subgroup variable – could be a feasible option and should be seriously considered when assessing subgroup effects while correcting for observed pre-treatment differences. In the Monte Carlo simulation study, the generalized PS gave more efficient results overall than the univariate PS, regardless of whether there was a relationship between the subgroup and treatment assignment. In both PS methods, the variables related to the outcome should be included in the PS estimation. These results follow earlier studies of Brookhart and colleagues (2006) and Austin and colleagues (2007) in selecting only the covariates related to the outcome. Furthermore, when the univariate PS was used, the subgroup of interest should be excluded from the PS estimation. Applying the 2 PSs estimations on real-world data produced almost equal model results, illustrating the modifying effect of the severity of problems on the differential effectiveness of 2 psychotherapy treatment arms. In applying the generalized PSwhen analyzing subgroups effects, a researcher should take into account additional characteristics of their datasets. Firstly, the characteristics of the subgroup variable should be taken into account. For example, the independence of irrelevant alternatives (IIA) assumption can be violated. This assumption will be violated if, for example, short-term psychotherapy for patients having mild problems is no longer available and this influences the relative risks of the remaining categories. We tested this assumption in our study and it was not violated. However, when it is violated, a nested structure can overcome this violation by first defining the probability that a patient belongs to a particular subgroup and is subsequently assigned to a treatment option. Fuji and colleagues (2012) focused on a 2-stage structure (i.e. a nested structure), in which patients could be assigned sequentially to 2 treatment options, each consisting of 2 sub-options. Yet, if for example a patient characteristic evolves after treatment, it could mediate the relationship between the independent and dependent variable (i.e. a mediator) and should be analyzed differently from the proposed methods (VanderWeele & Vansteelandt, 2009). Secondly, for various reasons, other application methods when using the PS could be more advantageous (Austin, 2011; Rubin, 1979). For example, the PS can be estimated in each subgroup separately (Kreif et al., 2012; Radice et al., 2012), requiring a large study population to have sufficient power. If the sample size is large enough, a multivariable adjusted model including interaction terms for the subgroup effects can also be a valid alternative (Liem et al., 2010). In this study we applied the PS using covariate adjustment, as sample sizes in clinical practice can be small and this method uses the complete sample size. However, covariate adjustment inherently assumes a correctly specified outcome regression model (Rubin, 2004), whereas for matching this is not required. Inverse probability weighting on the PS is a third and efficient method to control for selection bias (Hirano et al., 2003). The latter 2 methods can indeed eliminate most systematic differences between treated and untreated subjects (Austin, 2009), but