Pragmatic trials: ignoring a mediator and adjusting for confounding

In pragmatic trials, the new treatment is compared with usual care (heterogeneous control arm) that makes the comparison of the new treatment with each treatment within the control arm more difficult. The usual assumption is that we can fully capture the relations between different quantities. In this paper we use simulation to assess the performance of statistical methods that adjust for confounding when the assumed relations are not true. The true relations contain a mediator and heterogeneity with or without confounding, but the assumption is that there is no mediator and that confounding and heterogeneity are fully captured. The statistical methods that are compared include multivariable logistic regression, propensity score, disease risk score, inverse probability weighting, doubly robust inverse probability weighting and standardisation.

The misconception that there is no mediator can cause to misleading comparative effectiveness of individual treatments when a method that estimates the conditional causal effect is used. Using a method that estimates the marginal causal effect is a better approach, but not for all scenarios.