A missing composite covariate in survival analysis: a case study of the Chinese Longitudinal Health and Longevity Survey.

We estimate a Cox proportional hazards model where one of the covariates measures the level of a subject's cognitive functioning by grading the total score obtained by the subject on the items of a questionnaire. A case study is presented where the sample includes partial respondents, who did not answer some questionnaire items. The total score takes, hence, the form of an interval-censored variable and, as a result, the level of cognitive functioning is missing on some subjects. We handle the partial respondents by taking a likelihood-based approach where survival time is jointly modelled with the censored total score and the size of the censoring interval. Estimates are obtained by an E-M-type algorithm that reduces to the iterative maximization of three complete log-likelihood functions derived from two augmented data sets with case weights, alternated with weights updating. This methodology is exploited to assess the Mini-Mental State Examination index as a prognostic factor of survival in a sample of Chinese older adults.