Non-parametric treatment effect bounds for left-censored outcomes: estimating the effect of herbicide use on 2,4-D exposure

Causal inference is concerned with defining and estimating the effect of a exposure on an outcome. For example, the Average Treatment Effect (ATE), a causal inference concept, is defined as the population mean outcome had all participants been exposed vs. not exposed. Estimating the ATE is challenging when the outcome exhibits left-censoring, which arises when the outcome is measured by a process that cannot distinguish values below a limit of detection (LOD). Left-censored data arise frequently in many environmental datasets incorporating chemical measurements. We show that, under left-censoring of the outcome, the ATE has lower and upper bounds that provide a range of ATEs consistent with the observed degree of left-censoring. The bounds make no assumptions on the underlying distribution of the censored outcome. Standard software for causal inference can be used to estimate these bounds, and we provide sample code. Empirical results from a simulation study validate our approach in finite samples. We illustrate by estimating the effect of recent home herbicide use on urine levels of the herbicide 2,4-dichlorophenoxyacetic acid (2,4-D) using data from the National Health and Nutrition Examination Survey.