title: A flexible, computationally efficient method for fitting the proportional hazards model to interval-censored data.
abstract: The proportional hazards model (PH) is currently the most popular regression model for analyzing time-to-event data. Despite its popularity, the analysis of interval-censored data under the PH model can be challenging using many available techniques. This article presents a new method for analyzing interval-censored data under the PH model. The proposed approach uses a monotone spline representation to approximate the unknown nondecreasing cumulative baseline hazard function. Formulating the PH model in this fashion results in a finite number of parameters to estimate while maintaining substantial modeling flexibility. A novel expectation-maximization (EM) algorithm is developed for finding the maximum likelihood estimates of the parameters. The derivation of the EM algorithm relies on a two-stage data augmentation involving latent Poisson random variables. The resulting algorithm is easy to implement, robust to initialization, enjoys quick convergence, and provides closed-form variance estimates. The performance of the proposed regression methodology is evaluated through a simulation study, and is further illustrated using data from a large population-based randomized trial designed and sponsored by the United States National Cancer Institute.
authors.affiliation: Department of Statistics, University of South Carolina, Columbia, South Carolina 29208, U.S.A.
authors.forename: Lianming
authors.initials: L
authors.lastname: Wang
authors.affiliation: Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634, U.S.A.
authors.forename: Christopher S
authors.initials: CS
authors.lastname: McMahan
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, U.S.A.
authors.forename: Michael G
authors.initials: MG
authors.lastname: Hudgens
authors.affiliation: Department of Health Services Policy and Management, University of South Carolina, Columbia, South Carolina 29208, U.S.A.
authors.forename: Zaina P
authors.initials: ZP
authors.lastname: Qureshi
mesh_terms: D000368:Aged; D000465:Algorithms; D016477:Artifacts; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D015233:Models, Statistical; D009369:Neoplasms / Q000401:mortality*; D009716:Numerical Analysis, Computer-Assisted; D011247:Pregnancy; D016016:Proportional Hazards Models; D015203:Reproducibility of Results; D018401:Sample Size; D012680:Sensitivity and Specificity; D015996:Survival Rate; D014481:United States / Q000453:epidemiology
keywords: EM algorithm; Interval-censored data; Latent Poisson random variables; Monotone splines; Proportional hazards model