Analysis of interval-censored failure time data with long-term survivors

Abstract

Failure time data analysis, or survival analysis, is involved in various research

fields, such as medicine and public health. One basic assumption in

standard survival analysis is that every individual in the study population

will eventually experience the event of interest. However, this assumption is

usually violated in practice, for example when the variable of interest is the

time to relapse of a curable disease resulting in the existence of long-term survivors.

Also, presence of unobservable risk factors in the group of susceptible

individuals may introduce heterogeneity to the population, which is not properly

addressed in standard survival models. Moreover, the individuals in the

population may be grouped in clusters, where there are associations among observations

from a cluster. There are methodologies in the literature to address

each of these problems, but there is yet no natural and satisfactory way to

accommodate the coexistence of a non-susceptible group and the heterogeneity

in the susceptible group under a univariate setting. Also, various kinds of

associations among survival data with a cure are not properly accommodated.

To address the above-mentioned problems, a class of models is introduced to

model univariate and multivariate data with long-term survivors.

A semiparametric cure model for univariate failure time data with long-term

survivors is introduced. It accommodates a proportion of non-susceptible

individuals and the heterogeneity in the susceptible group using a compound-

Poisson distributed random effect term, which is commonly called a frailty. It

is a frailty-Cox model which does not place any parametric assumption on the

baseline hazard function. An estimation method using multiple imputation

is proposed for right-censored data, and the method is naturally extended to

accommodate interval-censored data. The univariate cure model is extended

to a multivariate setting by introducing correlations among the compound-

Poisson frailties for individuals from the same cluster. This multivariate cure

model is similar to a shared frailty model where the degree of association among

each pair of observations in a cluster is the same. The model is further extended

to accommodate repeated measurements from a single individual leading to

serially correlated observations. Similar estimation methods using multiple

imputation are developed for the multivariate models. The univariate model

is applied to a breast cancer data and the multivariate models are applied

to the hypobaric decompression sickness data from National Aeronautics and

Space Administration, although the methodologies are applicable to a wide

range of data sets.