The cox proportional hazards model with a continuous latent variable measured by multiple binary indicators

This article is motivated by the Women's Health and Aging Study, where information about physical functioning was recorded along with death information in a group of elderly women. The focus is on determining whether having difficulties in daily living tasks is accompanied by a higher mortality rate. To this end, a two-parameter logistic regression model is used for the modeling of binary questionnaire data assuming an underlying continuous latent variable, difficulty in daily living. The Cox model is used for the survival information, and the continuous latent variable is included as an explanatory variable along with other observed variables. Parameters are estimated by maximizing the likelihood for the joint distribution of the items and the time-to-event information. In addition to presenting a new statistical model, this article also illustrates the use of the model in a real data setting and addresses the more practical issues of model building, diagnostics, and parameter interpretation.