Causal inference under over-simplified longitudinal causal models
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Most causal models of interest involve longitudinal exposures, confounders and mediators. However, in practice, repeated measurements are rarely available. Then, practitioners tend to overlook the time-varying nature of exposures and work under over-simplified causal models. In this work, we investigate whether, and how, the quantities estimated under these simplified models can be related to the true longitudinal causal effects. We focus on two common situations regarding the type of available data for exposures: when they correspond to (i) "instantaneous" levels measured at inclusion in the study or (ii) summary measures of their levels up to inclusion in the study. Our results state that inference based on either "instantaneous" levels or summary measures usually returns quantities that do not directly relate to any causal effect of interest and should be interpreted with caution. They raise the need for the availability of repeated measurements and/or the development of sensitivity analyses when such data is not available.
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