The Challenges of Parameterizing Direct Effects in Individual-Level Simulation Models

Abstract

Individual-level simulation models are used to assess the effects of health interventions in complex settings. However, estimating valid causal effects using these models requires correct parametrization of the relationships between time-varying treatments, outcomes, and other variables in the causal structure. To parameterize these relationships, individual-level simulation models typically need estimates of the direct effects of treatment. However, direct effects of treatment are often not well- defined and therefore cannot be validly estimated from any data. In this paper, we explain the causal meaning of the parameters of individual-level simulation models as direct effects, describe why direct effects may be difficult to define unambiguously in some settings, and conclude with some suggestions for the design of individual-level simulation models in those settings.

Figure 1

The structure of the simulated example as (A) a decision model and (B) directed acyclic graph (DAG). (A) The decision model depicts the decision process at a single time-step, with the circular decision nodes indicating probabilistic events and the colored square decision node indicating an intervention point. (B) The directed acyclic graph depicts two arbitrary time points of the same causal structure for a time- varying treatment, A0 and At, an outcome, Y, a time-varying confounder, Lt, affected by prior treatment (A0), and an unmeasured outcome cause, U.

Figure 2

The structure of an alternate simulation model which does not require parameterizing the controlled direct effect of treatment when CD4 count is held constant, as (A) a decision model and (B) directed acyclic graph (DAG). (A) The decision model depicts a single time-step. Note that, unlike Figure 1b, the model and transition probabilities in Figure 2b do not depend on the time-varying covariate. (B) The directed acyclic graph depicts two arbitrary time points of the causal structure for a time-varying treatment, A0 and At, an outcome, Y, and an unmeasured outcome cause, U.