A joint modeling approach for multivariate survival data with random length

• Type of Material: Article
• Authors: Shuling Liu, Emory University; Amita Manatunga, Emory University; Limin Peng, Emory University; Michele Marcus, Emory University
• Language: English
• Date: 2017-06-01
• Publisher: Wiley: Biometrics
• Publication Version: Author Accepted Manuscript (After Peer Review)
• Copyright Statement: © 2016, The International Biometric Society
• Final Published Version (URL): http://dx.doi.org/10.1111/biom.12588
• Title of Journal or Parent Work: Biometrics
• ISSN: 0006-341X
• Volume: 73
• Issue: 2
• Start Page: 666
• End Page: 677
• Grant/Funding Information: This research is partly supported by NIH grant R01HL113548.
• Keywords: Joint models; Approximate EM algorithm; Physical Sciences; FAILURE TIME MODEL; Semi-parametric transformation model; MAXIMUM-LIKELIHOOD ESTIMATORS; LINEAR TRANSFORMATION MODELS; Menstrual cycle length; MENSTRUAL-CYCLE LENGTH; Time-to-pregnancy; Statistics & Probability; REGRESSION-MODEL; Clayton-Oakes model; CENSORED-DATA; Science & Technology; 2-STAGE ESTIMATION; Mathematical & Computational Biology; TO-PREGNANCY; Life Sciences & Biomedicine - Other Topics; Mathematics; EVENT TIMES; SEMIPARAMETRIC ANALYSIS; Life Sciences & Biomedicine; Random length data; Biology
• Research Categories: Health Sciences, Epidemiology; Biology, Biostatistics; Health Sciences, Public Health

Abstract

In many biomedical studies that involve correlated data, an outcome is often repeatedly measured for each individual subject along with the number of these measurements, which is also treated as an observed outcome. This type of data has been referred as multivariate random length data by Barnhart and Sampson (1995). A common approach to handling such type of data is to jointly model the multiple measurements and the random length. In previous literature, a key assumption is the multivariate normality for the multiple measurements. Motivated by a reproductive study, we propose a new copula-based joint model which relaxes the normality assumption. Specifically, we adopt the Clayton–Oakes model for multiple measurements with flexible marginal distributions specified as semi-parametric transformation models. The random length is modeled via a generalized linear model. We develop an approximate EM algorithm to derive parameter estimators and standard errors of the estimators are obtained through bootstrapping procedures and the finite-sample performance of the proposed method is investigated using simulation studies. We apply our method to the Mount Sinai Study of Women Office Workers (MSSWOW), where women were prospectively followed for 1 year for studying fertility.