Anderson-Bergman (2017) icenReg: Regression Models for Interval Censored Data in R

Summary

This Journal of Statistical Software paper introduces the R package icenReg for regression with interval-censored survival data — data in which an event time is known only to lie within an interval. It reviews the three model classes for interval-censored data — the nonparametric maximum likelihood estimator (NPMLE / Turnbull estimator), semiparametric regression (proportional hazards, proportional odds, accelerated failure time), and fully parametric regression — and provides fast, reliable fitting algorithms for all three, plus imputation of the censored responses and diagnostics for the regression effects and baseline distribution.

Key Claims

• Types of interval censoring. Current status data: each subject is inspected once, yielding only left- or right-censored observations (e.g., mice sacrificed and inspected for tumors). Mixed case interval censoring: repeated inspections give left-, right-, uncensored, or genuinely interval-censored observations (e.g., emergence of children's permanent teeth between dentist visits). The standard assumption is that inspection times are independent of the event.
• NPMLE / Turnbull estimator. The nonparametric MLE (Turnbull 1976) generalizes the Kaplan-Meier curve to interval-censored data and is preferred for diagnostics, but is notoriously inefficient — an $n^{1/3}$ convergence rate for current-status data (vs. the usual $n^{1/2}$), and something between $n^{1/3}$ and $n^{1/2}$ for mixed-case censoring depending on severity.
• Semiparametric regression is harder than in the right-censored case. For a Cox proportional-hazards model, the regression parameters cannot be separated cleanly from the baseline as they can with a partial likelihood under right censoring; icenReg's ic_sp fits PH and proportional-odds models semiparametrically and obtains standard errors by bootstrap.
• Three fitting functions. ic_np (nonparametric/Turnbull), ic_sp (semiparametric PH / proportional odds), and ic_par (fully parametric accelerated-failure-time, proportional-odds, or proportional-hazards with a choice of baseline distribution).
• Diagnostics and imputation. diag_baseline and diag_covar give visual checks of the parametric-baseline and covariate-effect assumptions against the semiparametric/nonparametric fits, and imputeCens draws imputations of the censored responses conditional on the fitted model.
• Parametric caution. Fully parametric interval-censored models are easy to fit but heavily influenced by the baseline choice, and model checking is difficult with interval data — motivating the nonparametric/semiparametric options.

Concepts Introduced or Extended

• Interval Censoring
• Parametric Survival Model
• Counting Process

Entities Mentioned

• Clifford Anderson-Bergman

Quotes

"Interval censored data occurs when an event time is known only up to an interval."

"The non-parametric maximum likelihood estimator (NPMLE; Turnbull 1976) is often preferred, a generalization of the Kaplan Meier curves… This is also referred to as the Turnbull estimator."

My Take

As a software paper its value to the wiki is mostly as a clear map of the interval-censoring problem, which is the awkward middle child of survival analysis: right censoring has clean partial-likelihood machinery, but once the event time is only bracketed, even the nonparametric estimator loses its $\sqrt n$ rate and the Cox model loses its tidy separation of baseline and regression. icenReg's three-tier design (nonparametric for honesty, semiparametric for robustness, parametric for efficiency, with diagnostics to move between them) is a sensible template. It sits naturally beside the parametric-survival and counting-process pages as the third corner of the survival cluster — the one that takes the observation scheme, not the hazard family or the martingale, as the hard part.