TIME-DEPENDENT HAZARD RATIO - MODELING AND HYPOTHESIS-TESTING WITH APPLICATION IN LUPUS NEPHRITIS

We investigate the association between duration of untreated disease a nd survival in lupus nephritis, a rare rheumatologic disease, In this case, as in many other studies of survival, a priori considerations su ggest that the effect of the predictor on hazard may change with incre asing follow-up time. To accommodate such situations, we use regressio n splines to model the hazard ratio as a flexible function of time. We propose model-based tests of the hypotheses of hazards proportionalit y and of no association. We evaluate the accuracy of estimation and in ference in simulations and also present analysis of a larger medical d ata set.