Page 52 - Contributed Paper Session (CPS) - Volume 2

CPS1419 Jinheum K. et al.

A multi-state model for analyzing doubly
interval-censored semi-competing risks
1
2
Jinheum Kim , Jayoun Kim
1 Jinheum Kim, Department of Applied Statistics, University of Suwon, Suwon, 18323, South
Korea
2 Jayoun Kim, Medical Research Collaborating Center, Seoul National University Hospital,
Seoul, 03080, South Korea

Abstract
In biomedical or clinical studies, we often encounter semi-competing risks
data in which one type of event may censor another event, but not vice versa.
We propose a multi-state model for analyzing these semi-competing risks
data in the presence of interval censoring on both intermediate and terminal
events, so-called doubly censored scenarios. In this article, we utilize the
conventional Cox proportional hazards model by incorporating a frailty effect.
Thus, the proposed model can reflect diversities for which real data might
frequently possess. Marginalization of the full likelihood is accomplished using
adaptive importance sampling, and the optimal solution of the regression
parameters is achieved through the iterative quasi-Newton algorithm. The
proposed methodology is illustrated on several simulation studies and real
data.

Keywords
Doubly interval-censored; Illness-death model; Intermediate event; Multi-
state model; Normal frailty; Semi-competing risks data

1. Introduction
In time-to-event or survival analysis, patients with certain diseases are
asked to make clinic visits and are monitored during periodic follow-up. This
makes it virtually impossible to observe the event time exactly. Under these
situations the event time is at least known to lie on a time interval, i.e., the
interval between the last and current visits; this is often called interval
censoring. Further, in a considerable number of medical studies, we encounter
situations in which two series of events are interval censored, which is known
as doubly interval-censored (DIC). The most well-known DIC data are acquired
immunodeficiency syndrome (AIDS) data which motivated several papers,
including Gruttola and Lagakos (1989), Kim et al. (1993), and Zeng et al. (2006).
The study was designed to analyze the doubly interval-censored incubation
time between the originating event, infection with the human
immunodeficiency virus (HIV) and onset of the terminating event, AIDS.

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