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 or all of the 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 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. Parameter estimates are obtained by an E-M-type algorithm that essentially reduces to the iterative maximization of three complete log-likelihood functions derived from two augmented datasets 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.