Statistica Sinica 28 (2018), 2167-2187
Abstract: Nonresponse is an important practical problem in epidemiological surveys and clinical trials. Common methods for dealing with missing data rely on untestable assumptions. In particular, non-ignorable modeling, which derives inference from the likelihood function based on a joint distribution of the variables and the missingness indicators, can be sensitive to misspecification of this distribution and may also have problems with identifying the parameters. Nonresponse two-phase sampling (NTS), which re-contacts and collects data from a subsample of the initial nonrespondents, has been used to reduce nonresponse bias. The additional data collected in phase II provide important information for identifying the parameters in the non-ignorable models. We propose a Bayesian selection model which utilizes the additional data from phase II and develop an efficient Markov chain Monte Carlo algorithm for the posterior computation. We illustrate the proposed model on simulation studies and a Quality of Life (QOL) dataset.
Key words and phrases: Bayesian selection model, Markov chain Monte Carlo, missing not at random, quality of life, two-phase sampling.