Hester van Eeren

Subgroup analysis using the propensity score | 4 63 | Introduction In non-randomized studies, the propensity score (further denoted as PS) method has gained popularity as a statistical method to overcome selection bias due to differences in observed pre-treatment variables of patient groups (Winship & Mare, 1992) and the “dimensionality” problem of alternative methods such as stratification and matching (D'Agostino, 1998). The univariate propensity score (Rosenbaum & Rubin, 1983) is a valid solution to compare 2 treatment categories (Bartak et al., 2009; Rubin, 1974), whereas the generalized PS can be used if >2 treatment categories are compared (Feng, Zhou, Zou, Fan, & Li, 2012; Imbens, 2000; Spreeuwenberg et al., 2010). An equal distribution on the covariates is assumed after adjustment on the PS (Austin, 2009; Rubin, 1997; Spreeuwenberg et al., 2010). Although the PS can control for overt bias due to (many) observed pre-treatment variables (Rosenbaum, 1991; Rubin, 1997), hidden bias could still be present (Rosenbaum, 1991). The PS is predominantly used to estimate treatment effects (Austin, 2011; Hirano, Imbens, & Ridder, 2003). However, it may also be important to define which treatment is specifically effective for a (sub)group of patients (Norcross & Wampold, 2011). Treatment options can then be applied more efficiently by directly allocating a group of patients to a relevant treatment. For instance, one could argue that long-term psychotherapy is more effective than short-term psychotherapy for patients having severe problems. Because the patients are not randomly assigned to the treatment options, patients having either mild or severe problems can differ on the observed pre-treatment variables. Therefore, there is a need to apply PS modelling methods when studying subgroup effects. Several authors have described methods to estimate treatment effects for particular subgroups while using the univariate PS. Rosenbaum and Rubin already recommended sub-classifying or matching on additional covariates to identify differences in treatment effect between subgroups. To reduce bias in the estimated treatment effect, Rubin and Thomas (2000) and Stürmer and colleagues (2006) advised that the covariate together with the PS be included when estimating the treatment effect. Such an additional covariate could define subgroups. The treatment effect can also vary according to quantiles of the PS estimations. Effect modification (e.g. interaction effects) can result in different estimated treatment effects for different PS quantiles (Glynn, Schneeweiss, & Sturmer, 2006; Kurth et al., 2006; Lunt et al., 2009; Sturmer, Rothman, & Glynn, 2006; Ye, Bond, Schmidt, Mulia, & Tam, 2012). However, it is not possible to relate a specific subgroup to the PS quantiles. More recently, Liem and colleagues (2010) determined the treatment effect for subgroups by adding interaction terms in a multivariable adjusted model in which the PS was also included. Another method was described by Radice and colleagues (2012) and Kreif and colleagues (2012) who estimated the univariate PS within each subgroup separately. Yet, only the univariate PS was used in subgroup analyses and the PS was not made multiple, as a generalized PS, by crossing the treatment options with a subgroup variable. Because the univariate PS is mainly used in subgroup analyses, this study investigated whether a generalized PS could be used to estimate subgroup effects in outcomes research, and compared it to using a univariate PS. We first used Monte Carlo simulations to investigate whether and how the generalized or univariate PS could be