Causal Inference for Latent Markov Models Using the Parametric G-Formula

The parametric g-formula can be used to estimate causal effects of time-varying exposures or treatments on observable outcomes. In such a longitudinal setting, time-varying confounders that are affected by prior exposures need to be adjusted for. The parametric g-formula does this by specifying several parametric models, one each for every time-varying variable, and by performing micro-simulations. However, its restriction to use cases of observable outcomes limits the possibility for applications of the parametric g-formula in the social sciences. In the social sciences, many variables of interest are unobservable constructs. In such cases, measurement models are needed. Here, we propose a new approach of using bias-adjusted three-step latent Markov models (LMMs) within the parametric g-formula. LMMs estimate the probability of membership in an unobservable state based on a number of observed indicator variables. Additionally, estimates for the probabilities of transitions between these latent states are obtained. We show that by replacing the parametric models in the g-formula with LMMs, the micros-simulations can be performed as usual. We illustrate the use of this new approach by estimating the average treatment effect of unemployment on the probabilities for several mental health states utilizing longitudinal data from the LISS panel.