Semiparametric regression models for interval-censored survival data, with and without frailty effects

Interval-censored survival data occur when the time to an event is assessed by means of blood samples, urine samples, X-ray, or other screening methods that cannot tell the exact time of change for the disease, but only that the change has happened since the last examination. This is in contrast to the standard (naive) thinking that assumes that the change happens at the time of the first positive examination. Even though this screening setup is very common and methods to handle such data nonparametrically in the one-sample case have been suggested more than 30 years ago, it is still not a standard method. However, interval-censored methods are needed in order to consider onset and diagnosis as two different things, such as when we consider screening in order to diagnose a disease earlier. The reason for the low use of interval-censored methods is that in the nonparametric case, analysis is technically more complicated than standard survival methods based on exact or right-censored times. The same applies to proportional hazards models. This chapter covers semiparametric regression models, both of the proportional hazards type and of the corresponding frailty models, with proportional hazards conditional on a gamma-distributed frailty. With today's computing power, it is possible to handle these models and we should consider using interval-censoring methods in that case. The whole approach can also be extended to handle truncation, differential mortality with and without the disease, multivariate data, and time-dependent covariates. However, various complexities appear in these models.