The Use of Auxiliary Information to Deal with Informatively Missing Data
[slides - 110 KB pdf]

Informatively missing or observed data present significant inferential challenges. Structures to characterize observation processes have been suggested, perhaps the most well-known being that associated with the terms, missing completely at random, missing at random and missing not at random. These terms are sometimes further extended to incorporate covariate dependence. To make use of such structures for inference, significant assumptions are usually required. If there is auxiliary information that is closely linked to the observation process, then specific and plausible assumptions may be of particular value. Three examples of this are considered.

The first example deals with estimation of the level of virginity from a population survey for which interviewer acquired information on the embarassment of respondents in answering questions of a sexual nature is available. The results of assuming covariate dependent missingness at random is illustrated and extended based on distributional assumptions about embarassment levels.

The second example relates to the modelling of disease progression in Hepatitis C patients. Motivated by assumptions similar to those associated with covariate dependent missingness at random, the use of routine clinical data is shown to allow the estimation of a partially hidden Markov model for liver damage when damage is defined by biopsy and therefore not observed at all clinic visits.

A final example illustrates how changes in response bias might be examined in repeated population surveys involving sensitive questions. This auxiliary information can then be used to help interpret observed differences in survey responses over time, differences perhaps influenced by accompanying changes in bias over time.

References:
Copas, A.J., Farewell, V.T.: Dealing with non-ignorable non-response by using an `enthusiasm-to-respond' variable. J. Roy. Stat. Soc. A, 161, 385-396, 1998.
Copas, A.J., Farewell, V.T., Mercer, C.H., Yao, G.: The sensitivity of estimates of the change in population behavious to realistic changes in bias in repeated surveys. J. Roy. Stat. Soc. A, 167, 579-595, 2004.
Sweeting, M.J., Farewell, V.T., De Angelis, D.: Multi-state Markov models for categorical disease progression data in the presence of informative examination times: an application to hepatitis C. (In preparation, MRC Biostatistics Unit, Cambridge)