Abstract : In the risk analysis of sequential events, the successive gap times from the same subject are often correlated, e.g. as a result of an individual heterogeneity. These correlations are usually accounted for by using a shared gamma frailty model, where the variance of the random individual effect quantifies the correlation between gap times. It has been shown that this method yields satisfactory estimates of covariates effects, but underestimates the variance of the frailty, which could result in a lack of power of the test of independence.
We propose a new test of independence acrossbetween two sequential gap times that is based on a
proportional hazards approximation of the hazard of second event given the first gap-time in a frailty model, with a frailty distributionthat is assumed to belong to the power variance function (PVF) family. Simulation results show an increased power of the new test by comparison with the usual test. In the realistic case where hazards are event-specific, and using event-specific approaches, the proposed estimation of the variance of the frailty is less biased than the gamma-frailty based estimation for a wide range of values of the variance, and similar for higher values. For illustration, the methods are applied to a previously analysed asthma prevention trial with results showing a significant association in the sample of asthmatic children. We also analyse data from a cohort of HIV-seropositive patients in order to assess the effect of risk factors on the occurrence of two successive markers of progression of the HIV-disease. Results exemplify the ability of the proposed model for taking into account negative correlations between gap times.