Emerging Topics in Modeling Interval-Censored Survival Data

We review our recently developed pointwise confidence intervals for the distribution of event times for current status data. Previous existing methods were based on asymptotic distributions, but our new approach is based on binomial properties. This binomial approach can be applied with continuous and discrete assessment distributions. We discuss confidence interval (CI) versions using the binomial approach, a valid (i.e., exact) CI and an ABA (Approximate Binomial Approach) confidence interval. The valid confidence interval guarantees the nominal rate. Although the valid confidence interval is necessarily conservative for small sample sizes, asymptotically its coverage rate approaches the nominal one. The ABA confidence interval does not guarantee the nominal rate, but its coverage rate asymptotically approaches the nominal rate under certain conditions. Extensive and systematic simulations are presented to compare these new confidence intervals with existing intervals (likelihood ratio test [LRT] CIs and smoothed maximum likelihood estimation [SMLE] CIs). The valid CI has been theoretically shown to guarantee the nominal coverage rate, while simulations show where other methods can have less than nominal coverage. The ABA CIs generally have coverage rates closer to the nominal level with shorter length than existing intervals in most cases. Based on the anti-hepatitis A antibody responses in Bulgaria (Keiding, J R Stat Soc Ser A 154:371–412, 1991, Table 2), we compare our new confidence intervals with the LRT CIs and SMLE CIs for the distribution of age at which people were first exposed to hepatitis A. We introduce the R package csci and provide R code to reproduce examples in this chapter.

Bivariate event time data are constantly encountered in biomedical research. In many real-life applications, both event times are possibly subject to interval censoring that gives rise to bivariate interval-censored data. Nonparametric inference of bivariate interval-censored data focuses on estimation of the joint distribution function of event times or the joint survival function. The conventional nonparametric maximum likelihood estimator suffers non-uniqueness of the estimates as well as computation inefficiency due to searching for maximal intersections and high-dimensional convex programming. A spline-based sieve nonparametric maximum likelihood estimator for the joint cumulative distribution function with bivariate interval-censored data has been developed to resolve the non-uniqueness issue in estimation. Numerically, it leads to a convex programming with complicated linear constraints but much reduced number of unknown parameters. In this project, we will illustrate the key characteristics of the sieve nonparametric maximum likelihood estimation with emphasis on numerical computation. We will develop an R-based software to facilitate the public use for computing the spline-based sieve nonparametric maximum likelihood estimator of the joint cumulative distribution function.

Joint models for longitudinal and survival data are a class of models that jointly analyze an outcome of interest repeatedly observed over time along with the associated event times. These models are useful in two practical applications; firstly focusing on survival outcome whilst accounting for time-varying covariates measured with error and secondly focusing on the longitudinal outcome while controlling for informative censoring. The joint modeling framework has mainly been focused on right-censored data in the survival outcome for the last decade. This chapter is then aimed to extend the classical joint modeling framework to interval-censored data using a cardiology multi-center clinical trial. We illustrate our approach using R statistical software.