Sieve Estimation for Mixture Cure Rate Model with Informatively Interval-Censored Failure Time Data

Abstract

In biomedical and public health studies, interval-censored data arise when the failure time of interest is not exactly observed and instead only known to lie within an interval. Furthermore, the failure time and censoring time may be dependent. There may also exist a cured subgroup, meaning that a proportion of study subjects are not susceptible to the failure event of interest. Many authors have investigated inference procedure for interval-censored data. However, most existing methods either assume no cured subgroup or apply only to limited situations such that the failure time and the observation time have to be independent. To take both cured subgroups and informative censoring into consideration for regression analysis of interval-censored data, we employ a mixture cure model and propose a sieve maximum likelihood estimation approach using Bernstein Polynomials. A novel expectation-maximization algorithm with the use of subject-specific independent log-normal latent variable is developed to obtain the numerical solutions of the model. The robustness and finite-sample performance of the proposed method in terms of estimation accuracy and predictive power is evaluated by an extensive simulation study which suggest that the proposed method works well for practical situations. In addition, we provide an illustrative example using NASA’s hypobaric decompression sickness database (HDSD).