Time-dependent hazard ratio: Modeling and hypothesis testing with application in lupus nephritis

We investigate the association between duration of untreated disease and survival in lupus nephritis, a rare rheumatologic disease, In this case, as in many other studies of survival, a priori considerations suggest that the effect of the predictor on hazard may change with increasing follow-up time. To accommodate such situations, we use regression splines to model the hazard ratio as a flexible function of time. We propose model-based tests of the hypotheses of hazards proportionality and of no association. We evaluate the accuracy of estimation and inference in simulations and also present analysis of a larger medical data set.