Multiple Imputation to Account for Missing Data in a Survey: Estimating the Prevalence of Osteoporosis

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Abstract
Nonresponse bias is a concern in any epidemiologic survey in which a subset of selected individuals declines to participate. We reviewed multiple imputation, a widely applicable and easy to implement Bayesian methodology to adjust for nonresponse bias. To illustrate the method, we used data from the Canadian Multicentre Osteoporosis Study, a large cohort study of 9423 randomly selected Canadians, designed in part to estimate the prevalence of osteoporosis. Although subjects were randomly selected, only 42% of individuals who were contacted agreed to participate fully in the study. The study design included a brief questionnaire for those invitees who declined further participation in order to collect information on the major risk factors for osteoporosis. These risk factors (which included age, sex, previous fractures, family history of osteoporosis, and current smoking status) were then used to estimate the missing osteoporosis status for nonparticipants using multiple imputation. Both ignorable and nonignorable imputation models are considered. Our results suggest that selection bias in the study is of concern, but only slightly, in very elderly (age 80+ years), both women and men. Epidemiologists should consider using multiple imputation more often than is current practice.