×

A flexible, computationally efficient method for fitting the proportional hazards model to interval-censored data. (English) Zbl 1393.62105

Summary: 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.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62N01 Censored data models

Software:

SAS; Intcox
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Allison, Survival analysis using SAS: A practical guide (2010)
[2] Andriole, Prostate cancer screening in the randomized Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial: mortality results after 13 years of follow-up, Journal of the National Cancer Institute 104 pp 125– (2012) · doi:10.1093/jnci/djr500
[3] Betensky, A local likelihood proportional hazards model for interval-censored data, Statistics in Medicine 21 pp 263– (2002) · doi:10.1002/sim.993
[4] Cai, Bayesian proportional hazards model for current status data with monotone splines, Computational Statistics and Data Analysis 55 pp 2644– (2011) · Zbl 1464.62034 · doi:10.1016/j.csda.2011.03.013
[5] Cai, Hazard regression for interval-censored data with penalized spline, Biometrics 59 pp 570– (2003) · Zbl 1210.62130 · doi:10.1111/1541-0420.00067
[6] Cox, Regression models and life-tables, Journal of the Royal Statistical Society: Series B 4 pp 187– (1972) · Zbl 0243.62041
[7] Finkelstein, A proportional hazards model for interval-censored failure time data, Biometrics 42 pp 845– (1986) · Zbl 0618.62097 · doi:10.2307/2530698
[8] Goeteghebeur, Semiparametric regression analysis of interval-censored data, Biometrics 56 pp 1139– (2000) · Zbl 1060.62616 · doi:10.1111/j.0006-341X.2000.01139.x
[9] Goggins, A Markov chain Monte Carlo EM algorithm for analyzing interval-censored data under the Cox proportional hazards model, Biometrics 54 pp 1498– (1998) · Zbl 1058.62555 · doi:10.2307/2533674
[10] Gómez, Tutorial on methods for interval-censored data and their implementation in R, Statistical Modeling 9 pp 259– (2009) · doi:10.1177/1471082X0900900402
[11] Groeneboom, Information Bounds and Non-Parametric Maximum Likelihood Estimation (1992) · Zbl 0757.62017 · doi:10.1007/978-3-0348-8621-5
[12] Henschel , V. Mansmann , U. 2013 http://CRAN.R-project.org/package=intcox
[13] Li, Chapman & Hall/CRC Biostatistic Series (2013)
[14] Lin, A semiparametric probit model for case 2 interval-censored failure time data, Statistics in Medicine 29 pp 972– (2010)
[15] Liu, A semiparametric regression cure model for interval-censored data, Journal of the American Statistical Association 104 pp 1168– (2009) · Zbl 1388.62283 · doi:10.1198/jasa.2009.tm07494
[16] Louis, Finding the observed information matrix when using the EM algorithm, Journal of the Royal Statistical Society: Series B 44 pp 226– (1982) · Zbl 0488.62018
[17] McMahan, Regression analysis for current status data using the EM algorithm, Statistics in Medicine 32 pp 4452– (2013) · doi:10.1002/sim.5863
[18] Odell, Maximum likelihood estimation for interval-censored data using a Weibull-based accelerated failure time model, Biometrics 48 pp 951– (1992) · doi:10.2307/2532360
[19] Pan, Extending the iterative convex minorant algorithm to the Cox model for interval-censored data, Journal of Computational and Graphical Statistics 8 pp 109– (1999)
[20] Pan, A multiple imputation approach to Cox regression with interval-censored data, Biometrics 56 pp 199– (2000) · Zbl 1060.62649 · doi:10.1111/j.0006-341X.2000.00199.x
[21] Ramsay, Monotone regression splines in action, Statistical Science 3 pp 425– (1988) · doi:10.1214/ss/1177012761
[22] Rosen, The gradient projection method for nonlinear programming, Journal of the Society for Industrial and Applied Mathematics 8 pp 181– (1960) · Zbl 0099.36405 · doi:10.1137/0108011
[23] Rosenberg, Hazard function estimation using B-splines, Biometrics 51 pp 874– (1995) · Zbl 0875.62489 · doi:10.2307/2532989
[24] Rucker, Remission duration: an example of interval-censored observations, Statistics in Medicine 7 pp 1139– (1988) · doi:10.1002/sim.4780071106
[25] Satten, Rank based inference in the proportional hazards model for interval-censored data, Biometrika 83 pp 355– (1996) · Zbl 0864.62079 · doi:10.1093/biomet/83.2.355
[26] Shao, Semiparametric varying-coefficient model for interval-censored data with a cured proportion, Statistics in Medicine 33 pp 1700– (2014) · doi:10.1002/sim.6054
[27] Sun, The Statistical Analysis of Interval-Censored Data (2006) · Zbl 1127.62090
[28] Turnbull, The empirical distribution function with arbitrarily grouped, censored and truncated data, Journal of the Royal Statistical Society: Series B 38 pp 290– (1976) · Zbl 0343.62033
[29] Wang, Semiparametric Bayes proportional odds models for current status data with under-reporting, Biometrics 67 pp 1111– (2011) · Zbl 1226.62131 · doi:10.1111/j.1541-0420.2010.01532.x
[30] Wang, A Bayesian approach for analyzing case 2 interval-censored failure time data under the semiparametric proportional odds model, Statistics and Probability Letters 81 pp 876– (2011) · Zbl 1219.62054 · doi:10.1016/j.spl.2011.02.034
[31] Zhang, A spline-based semiparametric maximum likelihood estimation method for the Cox model with interval-censored data, Scandinavian Journal of Statistics 37 pp 338– (2010) · Zbl 1224.62108 · doi:10.1111/j.1467-9469.2009.00680.x
[32] Zhang, On algorithms for the nonparametric maximum likelihood estimator of the failure function with censored data, Journal of Computational and Graphical Statistics 13 pp 123– (2004) · doi:10.1198/1061860043038
[33] Zhang, Interval-censoring, Statistical Methods in Medical Research 19 pp 53– (2010) · doi:10.1177/0962280209105023
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.