Confounding is widely recognized in settings where all variables are fully observed, yet recognition of and statistical methods to address confounding in the context of latent class regression are slowly emerging. In this study we focus on confounding when regressing a distal outcome on latent class; extending standard confounding methods is not straightforward when the treatment of interest is a latent variable. We describe a recent 1-step method, as well as two 3-step methods (modal and pseudoclass assignment) that incorporate propensity score weighting. Using simulated data, we compare the performance of these three adjusted methods to an unadjusted 1-step and unadjusted 3-step method. We also present an applied example regarding adolescent substance use treatment that examines the effect of treatment service class on subsequent substance use problems. Our simulations indicated that the adjusted 1-step method and both adjusted 3-step methods significantly reduced bias arising from confounding relative to the unadjusted 1-step and 3-step approaches. However, the adjusted 1-step method performed better than the adjusted 3-step methods with regard to bias and 95% CI coverage, particularly when class separation was poor. Our applied example also highlighted the importance of addressing confounding - both unadjusted methods indicated significant differences across treatment classes with respect to the outcome, yet these class differences were not significant when using any of the three adjusted methods. Potential confounding should be carefully considered when conducting latent class regression with a distal outcome; failure to do so may results in significantly biased effect estimates or incorrect inferences.
Keywords: confounding; latent class; latent treatment; propensity scores.