Hester van Eeren

Subgroup analysis using the propensity score | 4 65 | the potential outcomes and the covariates X should be equal between the 4 groups (Fujii, Henmi, & Fujita, 2012). The generalized PS was estimated in a multinomial regression model. To estimate the treatment effects, 3 estimated generalized PSs and 3 dummy variables indicating group membership (G) were adjusted for in a regression model with treatment outcome (Y) as the dependent variable: 0 1 1 2 2 3 3 4 1 5 2 6 3 OUTCOME PS PS PS G G G β β β β β β β = + + + + + + (4) The coefficients related to the 3 dummy variables were the effects of interest. Monte Carlo simulation study A Monte Carlo simulation study was designed to test the 2 PS estimations. Therefore, we simulated 2 treatment categories, a subgroup variable with 2 categories and 3 additional variables that served as covariates. These 3 covariates were continuous variables (such as age, length, or body weight) related to (a) only the treatment assignment, (b) both treatment assignment and outcome, such that it is a true confounder (Brookhart et al., 2006), or (c) outcome alone (Table 1). Table 1. Variables and characteristics of Monte Carlo simulation* Variables Type Function X1 Covariate Multivariate normal distribution (0, 1) X2 Covariate Multivariate normal distribution (0, 1) X3 Covariate Multivariate normal distribution (0, 1) Z Covariate – forms subgroups Bernoulli distribution (1, 0.4) D Treatment assignment Defined in treatment assignment, values 0 or 1 Y Outcome Defined in outcome ε ε 1 2 , Error terms Multivariate normal distribution (0, 1) Treatment assignment Scenario 1: ε + +  1 0.5 1 0.5 2 f X X ; if f<0, D=0; otherwise D=1 Scenario 2: ε + +  1 0.5 1 0.5 2 0,3Z+ f X X ; if f<0, D=0; otherwise D=1 Outcome α α α ε + + +  1 2 3 2 0.5 2 0.5 3 D+ DZ+ Y X X Z ; linear regression model where α α α = = = 1 2 3 0.7, 0.4, 0.2 Characteristics that define simulated datasets Categories Correlation between covariates ( X 1- X 3) 0; 0.3; 0.7 Correlation Z – covariates ( X 1- X 3) yes; no Sample size 250; 500; 1000 Variables selected in PS Univariate PS Generalized PS X2,X3; X1,X2,X3; X2,X3,Z; X1,X2,X3,Z; X1,X2; X1,X2,Z; X2; X2,Z X2,X3; X1,X2,X3; X1,X2; X2 * The parameter values related to the different variables in the description of the treatment assignment and outcome are arbitrary. PS indicates propensity score