REML and ML estimation for clustered grouped survival data

Clustered grouped survival data arise naturally in clinical medicine and biological research. For example, in a randomized clinical trial, the variable of interest is the time to occurrence of a certain event with or without a new treatment and the data are collected from possibly correlated subjects from independent clusters. However it is sometimes impossible or too expensive to monitor the experimental subjects continuously. The subjects are examined regularly and the continuous survival data are thus grouped into a discrete time scale. With such a design, researchers are mainly interested in the effectiveness of the new treatment as well as the correlation among subjects from the same cluster, namely the intracluster correlation. This paper suggests a random effects approach to the estimation of the regression parameter with various choices of regression model and also the dependence parameter which characterizes the intracluster correlation. Time dependent covariates can be accommodated in the proposed model, and the estimation procedure will not be further complicated with large cluster sizes. The proposed method is applied to the data from the Diabetic Retinopathy Study, the objective of which is to evaluate the effectiveness of laser photocoagulation in delaying or preventing the onset of blindness in the left and right eyes of individuals with diabetes-associated retinopathy. The intracluster correlation using a grouped proportional hazards regression model can be estimated and the relationship between the regression parameter estimates based on the random effects approach and the marginal approach using a dynamic logistic regression model are discussed. Results from a simulation study of the proposed method are also presented.