Title: Learning Models from Data with Measurement Error: Tackling Underreporting,
Abstract: Measurement error in observational datasets can lead to systematic bias in
inferences based on these datasets. As studies based on observational data are
increasingly used to inform decisions with real-world impact, it is critical
that we develop a robust set of techniques for analyzing and adjusting for
these biases. In this paper we present a method for estimating the distribution
of an outcome given a binary exposure that is subject to underreporting. Our
method is based on a missing data view of the measurement error problem, where
the true exposure is treated as a latent variable that is marginalized out of a
joint model. We prove three different conditions under which the outcome
distribution can still be identified from data containing only error-prone
observations of the exposure. We demonstrate this method on synthetic data and
analyze its sensitivity to near violations of the identifiability conditions.
Finally, we use this method to estimate the effects of maternal smoking and
opioid use during pregnancy on childhood obesity, two import problems from
public health. Using the proposed method, we estimate these effects using only
subject-reported drug use data and substantially refine the range of estimates
generated by a sensitivity analysis-based approach. Further, the estimates
produced by our method are consistent with existing literature on both the
effects of maternal smoking and the rate at which subjects underreport smoking.