Re: Estimating the Causal Effect of an Exposure on Change From Baseline Using Directed Acyclic Graphs and Path Analysis

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The recent article by Lepage et al.1 considers estimation of the causal effect of an exposure on an outcome’s change from baseline. The authors use directed acyclic graphs (DAGs) to explain how adjustment for an outcome’s measured baseline in linear regression of change analyses will influence the bias in estimation of the exposure effect.
The authors provided a very helpful appendix with the code to replicate their analyses in the article’s eAppendix; ( In reproducing their study we found minor errors in the simulation code. The fitted regression models were overspecified and coefficient values of zero were recorded in several iterations of the simulations where the exposure variable of interest was dropped. The Table presents the values reported in the article and the corrected values; our own eAppendix ( gives our corrections to the code. We applaud the authors for providing supplemental material and code that allowed for their work to be replicated. As is discussed in Peng,2 transparency of statistical procedures and code is a major component to reproducible research.
While the errors we uncovered somewhat affected the results, they did not change the conclusions of the article. DAGs provide a useful guide for deciding whether linear regression of change models should be adjusted for the outcome’s measured baseline. The setting of “nonrandomized studies where exposure starts before the beginning of the study” is of particular interest to many environmental health studies that consider exposures such as air pollutants. Lepage et al.1 used DAGs to show that “unadjusted” models of change that do not condition on the baseline outcome measurement will provide less biased estimates in this setting. However, the analysis used in Lepage et al.1 was limited to regression of change as an outcome applied to data in which all subjects have two equally spaced measurement times. In many observational studies, where a scientific interest is in rate of change or progression in an outcome measure, a more general design may be required that allows for multiple unequally spaced follow-up times, and exposure/covariate frameworks that can vary over time. It is important to be able to generalize the outcome approach to account for a more general design framework, yet maintain the “unadjusted” for measured outcome quality recommended by Lepage et al.1 We propose one option is to fit a mixed model that controls for a modeled baseline, similar to the models used in several MESA Air study analyses.3,4 Controlling for a modeled baseline will not have the same bias as that caused by controlling for the measured baseline when there is outcome measurement error. Further study should consider how various plausible analysis approaches compare to determine how to best obtain an unbiased estimate of the effect of exposure on rate of change in a more general design setting.
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