Survival analysis of longitudinal data: the case of English population aged 50 and over

This study considers data from 5 waves of the English Longitudinal Study of Ageing (ELSA). We aim to study the impact of demographic and self-rated health variables including disability and diseases on the survival of the population aged 50+. The disability variables that we consider are mobility impairment, difficulties in performing Activities of Daily Living (ADL) and Instrumental Activities of Daily Living (IADL). One of the problems with the survey study is missing observations. This may happen due to different reasons, such as errors, nonresponse and temporary withdrawals. We address this problem by applying single and multiple imputation methods. We then fit a Generalized Linear model (GLM) and Generalized Linear Mixed model (GLMM) to our data and show that a GLMM performs better than a GLM in terms of information criteria. We also look at the predictability of our models in terms of the time-dependent receiver operating characteristic (ROC) and the area of ROC, i.e. AUC. We conclude that among the disability factors, IADL and among the diseases, cancer significantly affect the survival of the English population aged 50 and older.