Time-modified confounding

Abstract

According to the authors, time-modified confounding occurs when the causal relation between a time-fixed or time-varying confounder and the treatment or outcome changes over time. A key difference between previously described time-varying confounding and the proposed time-modified confounding is that, in the former, the values of the confounding variable change over time while, in the latter, the effects of the confounder change over time. Using marginal structural models, the authors propose an approach to account for time-modified confounding when the relation between the confounder and treatment is modified over time. An illustrative example and simulation show that, when time-modified confounding is present, a marginal structural model with inverse probability-of-treatment weights specified to account for time-modified confounding remains approximately unbiased with appropriate confidence limit coverage, while models that do not account for time-modified confounding are biased. Correct specification of the treatment model, including accounting for potential variation over time in confounding, is an important assumption of marginal structural models. When the effect of confounders on either the treatment or outcome changes over time, time-modified confounding should be considered.

Figure 1.

Causal diagrams representing confounding (A), time-modified confounding by a time-fixed covariate (B), time-varying confounding (C), time-varying confounding affected by prior treatment (D), and time-modified confounding (E and F).

Figure 2.

Scatterplot of standard (pooled) inverse probability weights against proposed (time-stratified) inverse probability weights, for example, scenario 2 (Figure 1C).