Statistical analysis with missing exposure data measured by proxy respondents: a misclassification problem within a missing-data problem - Shardell, Michelle (2014)
In studies of older adults, researchers often recruit proxy respondents, such as relatives or caregivers, when study participants cannot provide self-reports (e.g., due to illness). Proxies are usually only sought to report on behalf of participants with missing self-reports; thus, either a participant self-report or proxy report, but not both, is available for each participant. Furthermore, the missing-data mechanism for participant self-reports is not identifiable and may be nonignorable. When exposures are binary and participant self-reports are conceptualized as the gold standard, substituting error-prone proxy reports for missing participant self-reports may produce biased estimates of outcome means. Researchers can handle this data structure by treating the problem as one of misclassification within the stratum of participants with missing self-reports. Most methods for addressing exposure misclassification require validation data, replicate data, or an assumption of nondifferential misclassification; other methods may result in an exposure misclassification model that is incompatible with the analysis model. We propose a model that makes none of the aforementioned requirements and still preserves model compatibility. Two user-specified tuning parameters encode the exposure misclassification model. Two proposed approaches estimate outcome means standardized for (potentially) high-dimensional covariates using multiple imputation followed by propensity-score methods. The first method is parametric and uses maximum likelihood to estimate the exposure misclassification model (i.e., the imputation model) and the propensity score model (i.e., the analysis model); the second method is non-parametric and uses boosted classification and regression trees to estimate both models. We apply both methods to a study of elderly hip-fracture patients.