van der Laan et al. Respond to “Hypothetical Interventions to Define Causal Effects”

Abbreviations: L/F, ratio of lean body mass to fat mass; MSM, marginal structural model. Dr. Hernán (1) wrote a very insightful and educational response to our paper (2). He distinguishes between two types of epidemiologic analyses that apply marginal struc-tural models (MSMs) or any other causal model: one in which the assignment of treatment (exposure) is uniquely defined (e.g., administration of a drug) and one in which it is unclear what route a subject followed to the reported level of exposure (e.g., lean-to-fat ratio (L/F)). One could represent L/F as having two components (A1, A2), A1 being the actual level of the exposure and A2 being the manner in which the exposure level is achieved, resulting in corresponding coun-terfactuals Ya1a2: One could make the observation from our paper that we are only concerned with estimating the distri-bution of the counterfactual that sets the exposure level but leaves the assignment mechanism random to follow the course it follows in the population, that is, Ya1 Ya1A2: Since the counterfactual population distribution of Ya1a2 can, in principle, be reproduced by using a hypothetical ex-periment, we can address the question raised by Dr. Hernán (1) of how to design a randomized experiment to replicate the causal parameter for L/F as defined by an MSM. He inquires about different interventions (e.g., exercise, sur-gery) that one would use in such an experiment. We realize that none of these interventions would result in a causal parameter comparable with the one learned from the obser-vational data. However, we have that the marginal expecta-tion of Ya1 Ya1A2 equals the weighted average across the interventions a2 of the population mean of Ya1 Ya1A2 for the subpopulation of all subjects who actually took A2 a2, weighted by the population proportion of subjects taking