Proxy Pattern-Mixture Analysis for Survey Nonresponse

We propose proxy pattern-mixture analysis (PPMA), a simple method for assessing nonresponse bias for the mean of a survey variable Y subject to nonresponse, when there is a set of covariates observed for nonrespondents and respondents. The covariates are reduced to a proxy variable X that has the highest correlation with Y, estimated from a regression analysis of respondent data. The impact of nonresponse on bias depends primarily on three factors: the nonresponse rate, the strength of the proxy variable in predicting Y, and the difference in proxy mean for respondents and nonrespondents. The PPMA method combines all three elements in an intuitively reasonable way. Adjusted estimators of the mean of Y are based on a pattern-mixture model with different mean and covariance matrix of Y and X for respondents and nonrespondents, assuming missingness is an arbitrary function of a known linear combination of X and Y. The method does not assume the missing-data mechanism is missing at random (λ = 0), and provides a sensitivity analysis for different values of λ. Maximum likelihood, Bayesian and multiple imputation versions of PPMA are described. Properties are examined through simulation and with data from the third National Health and Nutrition Examination Survey (NHANES III) and the Ohio Family Health Survey (OFHS).