Pattern‐mixture models for analyzing normal outcome data with proxy respondents

Studies of older adults often involve interview questions regarding subjective constructs such as perceived disability. In some studies, when subjects are unable (e.g. due to cognitive impairment) or unwilling to respond to these questions, proxies (e.g. relatives or other care givers) are recruited to provide responses in place of the subject. Proxies are usually not approached to respond on behalf of subjects who respond for themselves; thus, for each subject, data from only one of the subject or proxy are available. Typically, proxy responses are simply substituted for missing subject responses, and standard complete-data analyses are performed. However, this approach may introduce measurement error and produce biased parameter estimates. In this paper, we propose using pattern-mixture models that relate non-identifiable parameters to identifiable parameters to analyze data with proxy respondents. We posit three interpretable pattern-mixture restrictions to be used with proxy data, and we propose estimation procedures using maximum likelihood and multiple imputation. The methods are applied to a cohort of elderly hip-fracture patients.