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Generalized Additive Models with Interval‐Censored Data and Time‐Varying Covariates: Application to Human Immunodeficiency Virus Infection in Hemophiliacs
Author(s) -
Bacchetti Peter,
Quale Christopher
Publication year - 2002
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2002.00443.x
Subject(s) - covariate , proportional hazards model , truncation (statistics) , nonparametric statistics , parametric statistics , event (particle physics) , statistics , mathematics , smoothness , confidence interval , data set , hazard , censoring (clinical trials) , interval (graph theory) , biology , ecology , physics , quantum mechanics , combinatorics , mathematical analysis
Summary. We describe a method for extending smooth nonparametric modeling methods to time‐to‐event data where the event may be known only to lie within a window of time. Maximum penalized likelihood is used to fit a discrete proportional hazards model that also models the baseline hazard, and left‐truncation and time‐varying covariates are accommodated. The implementation follows generalized additive modeling conventions, allowing both parametric and smooth terms and specifying the amount of smoothness in terms of the effective degrees of freedom. We illustrate the method on a well‐known interval‐censored data set on time of human immunodeficiency virus infection in a multicenter study of hemophiliacs. The ability to examine time‐varying covariates, not available with previous methods, allows detection and modeling of nonproportional hazards and use of a time‐varying covariate that fits the data better and is more plausible than a fixed alternative.