Sensitivity analysis for nonignorable missingness and outcome misclassification from proxy reports.

Older adults, especially those who are sick or cognitively impaired, may be unwilling or unable to respond to interview questions,1,2 potentially leading to nonignorably missing outcomes and, in most cases, inaccurate conclusions.3–5 To address this problem, investigators often recruit proxy respondents, such as relatives or caregivers, to report outcomes on behalf of nonresponding participants.6 When the objective is measuring older adults’ subjective perceptions, such as depressive symptoms or perceived ability to perform activities of daily living, gerontology researchers regard participant self-reports as the gold standard and proxy reports as error-prone alternatives. However, substituting proxy reports for missing participant self-reports may lead to misclassification error and biased estimation.7,8 The bias is sometimes large enough to reverse study conclusions.9 An additional challenge in most studies using proxies is that a response for each participant is obtained from either the participant or a proxy, but not both. Thus, proxy reports cannot be empirically validated. Bias from outcome misclassification has been well studied.10–16 However, current statistical methods for misclassification assume that gold-standard outcomes are missing by design, where researchers purposely choose instead to collect more accessible error-prone outcomes for all participants. In contrast, we consider studies where gold-standard outcomes are missing by happenstance by a possibly nonignorable mechanism, and researchers collect error-prone outcomes only for participants with missing gold-standard outcomes. The left third of Table 1 exemplifies an ideal study without outcome misclassification whereas the middle third represents the usual data structure of so-called “main-study” designs with outcome misclassification that can be analyzed using existing statistical methods. The right third of Table 1 exemplifies the typical data structure of main-study designs in gerontology research with proxy respondents. In this study design, some participants have only a gold-standard self-report, the remaining participants have only an error-prone proxy report, and the missingness mechanism for participant self-reports is unknown to investigators and unestimable from observed data. Studies with the highest percentage of nonresponse rely most heavily on proxy respondents and are therefore the most susceptible to misclassification bias. Such studies often focus on particularly vulnerable populations, including persons with stroke,17 cancer,18 or osteoporatic fractures.19 Table 1 Main Study Data Structures (Y = Gold Standard Outcome, Y* = Error-Prone Version, ? = Missing). Statistical methods for sensitivity analysis have been developed separately to address selection bias20–22 and misclassification bias;23–25 however, sensitivity-analysis methods that jointly address both sources of bias are crucially needed. We aim to provide statistical methods that address both outcome misclassification and missingness for epidemiologists working with proxy-reported outcomes. To achieve our aim, we use missing-data methods to address participants’ nonresponse while leveraging proxy reports. Specifically, we use pattern-mixture models26,27 to encode assumptions about missingness by relating an unestimable function of missing participant self-reports to an estimable function of observed proxy reports. The proposed methods for binary outcomes extend those developed by Shardell and colleagues7 for measurement error of proxy-reported continuous outcomes. We use pattern-mixture models to incorporate proxy responses into analysis, and we adapt propensity-score methods to estimate covariate-standardized proportions. We apply these methods to the Second Cohort of the Baltimore Hip Studies, an epidemiologic study of elderly hip fracture patients.28