Survival Function Estimation for Multiple Sequential Time-to-Events

Data on multiple time-to-events occurring in a natural sequence are observed in many prospective clinical studies. The estimation of survival functions for such time-to-events gained the attention of many researchers, and the related literature has recorded many developments. This study revisits the problem of survival function estimation for multiple sequentially observed time-to-events and discusses two very easy to straightforward and easy to implement methods. One of these approaches, being non-parametric, assumes independence between the consecutive event times, and the estimators are derived based on well known Kaplan–Meier estimates. The other method is fully parametric, accounts for the dependence between consecutive event times, and assumes the event times to be log-normally distributed. We have studied the finite sample properties of both the non-parametric and parametric approaches at different sample sizes and censoring rates through statistical simulations. Applications of the methods are demonstrated using data from a sample of HIV/AIDS patients in South Carolina. For the patients diagnosed with detectable viral load, we have analyzed their viral load rebound behavior in 24 months post-diagnosis. The marginal and conditional survival curves of viral suppression following diagnosis and viral rebound following viral suppression are estimated and discussed.