Separating Algorithms From Questions and Causal Inference With Unmeasured Exposures: An Application to Birth Cohort Studies of Early Body Mass Index Rebound

Abstract

Observational studies reporting on adjusted associations between childhood body mass index (BMI; weight (kg)/height (m)2) rebound and subsequent cardiometabolic outcomes have often not paid explicit attention to causal inference, including definition of a target causal effect and assumptions for unbiased estimation of that effect. Using data from 649 children in a Boston, Massachusetts-area cohort recruited in 1999-2002, we considered effects of stochastic interventions on a chosen subset of modifiable yet unmeasured exposures expected to be associated with early (<age 4 years) BMI rebound (a proxy measure) on adolescent cardiometabolic outcomes. We considered assumptions under which these effects might be identified with available data. This leads to an analysis where the proxy, rather than the exposure, acts as the exposure in the algorithm. We applied targeted maximum likelihood estimation, a doubly robust approach that naturally incorporates machine learning for nuisance parameters (e.g., propensity score). We found a protective effect of an intervention that assigns modifiable exposures according to the distribution in the observational study of persons without (vs. with) early BMI rebound for fat mass index (fat mass (kg)/ height (m)2; -1.39 units, 95% confidence interval: -1.63, -0.72) but weaker or no effects for other cardiometabolic outcomes. Our results clarify distinctions between algorithms and causal questions, encouraging explicit thinking in causal inference with complex exposures.

Keywords: body mass index; body mass index rebound; cardiometabolic outcomes; causal inference; life course epidemiology; targeted maximum likelihood estimation.

Figure 1

Causal directed acyclic graph representing a data-generating assumption relating a time-varying exposure A, a proxy measure R, an outcome Y, and other covariates U, Project Viva, Boston, Massachusetts, 1999–2002. With all solid arrows present, exchangeability requires dashed arrows to be absent. With all solid black arrows present, proxy separation may fail by the presence of the red arrow.