On the treatment of grouped observations in life studies.

Assuming a model of proportional failure rates, Cox (1972) presents a systematic study of the use of covariates in the analysis of life time. The treatment of tied observations is a particularly troublesome point in both theory and application. It appears that grouping rather than discrete time is the right way to handle ties. This paper studies methodology for grouped observations. A logistic model, which makes explicit use of Cox's earlier binary data methods, is introduced and illustrated with a numerical example. The model leads back to Cox's proportional failure rates when the lengths of the grouping intervals approach zero. This limiting process provides some enlightenment on controversial issues such as ignoring intervals in which no failures occur, determining whether the covariates may be functions of time, and treating ties.