Efficient estimation of average causal effect with mismeasured exposures

Exposure mismeasurement is commonly seen in causal inference based on observational data. Recent evidence suggests that 35%-61% of medical studies using diagnostic tools report non-negligible exposure mismeasurement. For example, in the Global Enteric Multicenter Study, enzyme-linked immunosorbent assays (ELISA)-based rotavirus detection showed substantial discordance with polymerase chain reaction-based TaqMan Array Card (TAC) testing: 20.1% of ELISA-negative cases tested TAC-positive, whereas 19.5% of ELISA-positive cases tested TAC-negative. The existing methods handling exposure measurement error usually require that the mismeasurement distribution is known or can be estimated from a subset of study subjects with validated exposure statuses. This condition, however, is often violated when the mismeasurement mechanism is complex. In this article, we develop a novel method for estimating average causal effect using samples with exposures subject to misclassification and limited validation subsamples with correctly ascertained exposures. Our method does not require making any modeling assumptions about exposure mismeasurement. We establish some large-sample properties for the proposed method, based on which statistical inference can be easily carried out. The superiority of our proposed estimator is illustrated through extensive simulation studies. Our proposed estimator is shown to achieve a 39%-53% reduction in variance over the estimator relying solely on validation data in our simulation situations. In the application to the Global Enteric Multicenter Study, the proposed method reveals a substantial adjustment of pathogen-specific diarrhea associations that were previously distorted by inaccurate diagnoses.