Joint analysis of multivariate interval-censored survival data and a time-dependent covariate

Abstract

We develop a joint modeling method for multivariate interval-censored survival data and a time-dependent covariate that is intermittently measured with error. The joint model is estimated using nonparametric maximum likelihood estimation, which is carried out via an expectation–maximization algorithm, and the inference for finite-dimensional parameters is performed using bootstrap. We also develop a similar joint modeling method for univariate interval-censored survival data and a time-dependent covariate, which excels the existing methods in terms of model flexibility and interpretation. Simulation studies show that the model fitting and inference approaches perform very well under realistic sample sizes. We apply the method to a longitudinal study of dental caries in African-American children from low-income families in the city of Detroit, Michigan.

Keywords

Dental caries expectation–maximization algorithm frailty model interval censoring joint model nonparametric maximum likelihood estimation

Get full access to this article

View all access options for this article.

References

Zeng

Mao

Lin

DY.

Maximum likelihood estimation for semiparametric transformation models with interval-censored data.

Biometrika 2016; 103: 253–271.

Zeng

Gao

Lin

DY.

Maximum likelihood estimation for semiparametric regression models with multivariate interval-censored data.

Biometrika 2017; 104: 505–525.

Sparling

Younes

Lachin

, et al. Parametric survival models for interval-censored data with time-dependent covariates. Biostatistics 2006; 7: 599–614.

Tsiatis

Davidian

Joint modeling of longitudinal and time-to-event data: an overview. Stat Sin 2004; 14: 809–834, https://www-jstor-org.web.bisu.edu.cn/stable/24307417 (accessed 15 November 2020).

Chen

Shen

P-S

Tseng

YK.

Semiparametric transformation joint models for longitudinal covariates and interval-censored failure time. Comput Stat Data Anal 2018; 128: 116–127, https://www-sciencedirect-com.web.bisu.edu.cn/science/article/pii/S0167947318301671 (15 November 2020).

Tang

Sun

Regression analysis of interval-censored failure time data with time-dependent covariates. Comput Stat Data Anal 2020; 144: 106848, https://www-sciencedirect-com.web.bisu.edu.cn/science/article/pii/S0167947319302038 (accessed 15 November 2020).

Wang

McMahan

Hudgens

, et al. A flexible, computationally efficient method for fitting the proportional hazards model to interval-censored data. Biometrics 2016; 72: 222–231.

Pak

Todem

Adaptive lasso for the cox regression with interval censored and possibly left truncated data.

Stat Methods Med Res 2020; 29: 1243–1255.

Rizopoulos

Joint models for longitudinal and time-to-event data. London: Chapman and Hall, 2012.

10.

Lin

McCulloch

Mayne

ST.

Maximum likelihood estimation in the joint analysis of time-to-event and multiple longitudinal variables.

Stat Med 2002; 21: 2369–2382.

11.

Zeng

Cai

Asymptotic results for maximum likelihood estimators in joint analysis of repeated measurements and survival time. Ann Stat 2005; 33: 2132–2163.

12.

Box

GEP

Cox

DR.

An analysis of transformations revisited, rebutted. J Am Stat Assoc 1982; 77: 209–210, https://www-tandfonline-com-s.web.bisu.edu.cn/doi/abs/10.1080/01621459.1982.10477788; https://www-tandfonline-com-s.web.bisu.edu.cn/doi/pdf/10.1080/01621459.1982.10477788 (accessed 15 November 2020).

13.

Delyon

Lavielle

Moulines

Convergence of a stochastic approximation version of the EM algorithm. Ann Stat 1999; 27: 94–128.

14.

Vaida

Harrington

DP.

Using profile likelihood for semiparametric model selection with application to proportional hazards mixed models. Stat Sin 2009; 19: 819–842, https://www-jstor-org.web.bisu.edu.cn/stable/24308858 (15 November 2020).

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

0.19 MB