Time-to-event analysis when the event is defined on a finite time interval.

Acute graft-versus-host disease (GVHD) is a frequent complication following hematopoietic cell transplantation (HCT). Research on risk factors for acute GVHD has tended to ignore two important clinical issues. First, post-transplant mortality is high. In our motivating data, 100-day post-HCT mortality was 15.4%. Second, acute GVHD in its classic form is only diagnosed within 100 days of the transplant; beyond 100 days, a patient may be diagnosed with late onset acute or chronic GVHD. Standard modeling of time-to-event outcomes, however, generally conceive of patients being able to experience the event at any point on the time scale. In this paper, we propose a novel multi-state model that simultaneously: (i) accounts for mortality through joint modeling of acute GVHD and death, and (ii) explicitly acknowledges the finite time interval during which the event of interest can take place. The observed data likelihood is derived, with estimation and inference via maximum likelihood. Additionally, we provide methods for estimating the absolute risk of acute GVHD and death simultaneously. The proposed framework is compared via comprehensive simulations to a number of alternative approaches that each acknowledge some but not all aspects of acute GVHD, and illustrated with an analysis of HCT data that motivated this work.