Statistica Sinica 20 (2010), 1165-1181
MIXED CASE INTERVAL
CENSORED DATA
WITH A CURED
SUBGROUP
Shuangge Ma
Yale University
Abstract: Mixed case interval censored data arise
when the event time of interest is only known to lie in an interval
obtained from a sequence of 
random examinations, where is a
random integer. In this article, we consider mixed case interval
censored data with a cured subgroup, where subjects in this subgroup
are not susceptible to the event of interest. Such data may be
encountered in medical and demographical studies with longitudinal
followup, where the population of interest is composed of
heterogeneous subjects. We propose using a semiparametric two-part
model, where the first part is a generalized linear model that
describes the probability of cure, and the second part is a Cox
model that describes the event time for susceptible subjects. We
study maximum likelihood estimation of this two-part model. Finite
sample properties, an effective computational algorithm, and
inference with the weighted bootstrap are investigated. Asymptotic
properties, including identifiability, consistency, and weak
convergence, are established. We conduct simulations and analyze the
HDSD study using the proposed approach.
Key words and phrases: Cure rate, interval censoring,
semiparametric model.