×

zbMATH — the first resource for mathematics

Semiparametric generalized exponential frailty model for clustered survival data. (English) Zbl 1419.62273
Summary: In this paper, we propose a novel and mathematically tractable frailty model for clustered survival data by assuming a generalized exponential (GE) distribution for the latent frailty effect. Both parametric and semiparametric versions of the GE frailty model are studied with main focus for the semiparametric case, where an EM-algorithm is proposed. Our EM-based estimation for the GE frailty model is simpler, faster and immune to a flat likelihood issue affecting, for example, the semiparametric gamma model, as illustrated in this paper through simulated and real data. We also show that the GE model is at least competitive with respect to the gamma frailty model under misspecification. A broad analysis is developed, with simulation results explored via Monte Carlo replications, to evaluate and compare models. A real application using a clustered kidney catheter data is considered to demonstrate the potential for practice of the GE frailty model.
MSC:
62N02 Estimation in survival analysis and censored data
62G05 Nonparametric estimation
62P10 Applications of statistics to biology and medical sciences; meta analysis
Software:
eha; parfm; R; snowfall; survival
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aalen, OO, Modelling heterogeneity in survival analysis by the compound Poisson distribution, Annals of Applied Probability, 4, 951-972, (1992) · Zbl 0762.62031
[2] Andersen, P. K., Klein, J. P., Knudsen, K., Palacios, R. T. (1997). Estimation of variance in Cox’s regression model with shared gamma frailties. Biometrics, 53, 1475-1484. · Zbl 0911.62030
[3] Balakrishnan, N., Peng, Y. (2006). Generalized gamma frailty model. Statistics in Medicine, 25, 2797-2816.
[4] Brostrom, G. (2016). eha: Event history analysis. R package version 2.4-4. https://CRAN.R-project.org/package=eha. Accessed March 2018.
[5] Callegaro, A., Iacobelli, S. (2012). The Cox shared frailty model with log-skew-normal frailties. Statistical Modelling, 12, 399-418.
[6] Christian, N. J., Ha, I. D., Jeong, J. H. (2016). Hierarchical likelihood inference on clustered competing risks data. Statistics in Medicine, 35, 251-267.
[7] Cox, DR, Regression models and life-tables (with discussion), Journal of the Royal Statistical Society B, 34, 187-220, (1972) · Zbl 0243.62041
[8] Crowder, M., A multivariate distribution with Weibull connections, Journal of the Royal Statistical Society B, 51, 93-107, (1989) · Zbl 0669.62029
[9] Duchateau, L., Janssen, P. (2008). The frailty model. Springer series in statistics. New York: Springer. · Zbl 1210.62153
[10] Enki, D. G., Noufaily, A., Farrington, C. P. (2014). A time-varying shared frailty model with application to infectious diseases. The Annals of Applied Statistics, \(8\), 430-447. · Zbl 1454.62328
[11] Fletcher, R. (2000). Practical methods of optimization (2nd ed.). New York: Wiley. · Zbl 0988.65043
[12] Giner, G., Smyth, G. K. (2016). statmod: Probability calculations for the inverse Gaussian distribution. R Journal, \(8\)(1), 339-351.
[13] Gupta, R. C., Gupta, P. L., Gupta, R. D. (1998). Modeling failure time data by Lehman alternatives. Communications in Statistics: Theory and Methods, 27, 887-904. · Zbl 0900.62534
[14] Gupta, R. D., Kundu, D. (1999). Generalized exponential distributions. Australian and New Zealand Journal of Statistics, 41, 173-188.
[15] Gupta, R. D., Kundu, D. (2001). Exponentiated exponential family: An alternative to gamma and Weibull distributions. Biometrical Journal, 43, 117-130. · Zbl 0997.62076
[16] Ha, I. D., Pan, J., Oh, S., Lee, Y. (2014). Variable selection in general frailty models using penalized h-likelihood. Journal of Computational and Graphical Statistics, 23, 1044-1060.
[17] Hougaard, P., Life table methods for heterogeneous populations: Distributions describing the heterogeneity, Biometrika, 71, 75-83, (1984) · Zbl 0553.92013
[18] Hougaard, P., A class of multivariate failure time distributions, Biometrika, 73, 671-678, (1986) · Zbl 0613.62121
[19] Hougaard, P. (2000). Analysis of multivariate survival data. New York: Springer. Springer series. in Statistics. · Zbl 0962.62096
[20] Hougaard, P., Harvald, B., Holm, N. V. (1992). Measuring the similarities between the lifetimes of adult danish twins born 1881-1930. Journal of the American Statistical Association, 87, 17-24.
[21] Ibrahim, J. G., Chen, M. H., Sinha, D. (2001). Bayesian survival analysis. Springer series in statistics. New York: Springer.
[22] Klein, JP, Semiparametric estimation of random effects using the Cox model based on the EM algorithm, Biometrics, 48, 795-806, (1992)
[23] Knaus, J. (2015). Snowfall: Easier cluster computing (based on snow). R package version 1.84-6.1. https://CRAN.R-project.org/package=snowfall. Accessed Mar 2018.
[24] McGilchrist, CA, REML estimation for survival models with frailty, Biometrics, 49, 221-225, (1993)
[25] McGilchrist, C. A., Aisbett, C. W. (1991). Regression with frailty in survival analysis. Biometrics, 49, 461-466.
[26] Munda, M., Rotolo, F., Legrand, C. (2012). Parfm: Parametric frailty models in R. Journal of Statistical Software, 51(11), 1-20.
[27] Nadarajah, S., Kotz, S. (2006). The beta exponential distribution. Reliability Engineering and System Safety, 91, 689-697.
[28] Nielsen, G. G., Gill, R. D., Andersen, P. K., Sorensen, T. I. A. (1992). A counting process approach to maximum likelihood estimation in frailty models. Scandinavian Journal of Statistics, 19, 25-44. · Zbl 0747.62093
[29] Parner, E., Asymptotic theory for the correlated gamma-frailty model, Annals of Statistics, 26, 181-214, (1998) · Zbl 0934.62101
[30] R Core Team (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/. Accessed Mar 2018.
[31] Therneau, T. (2015). A package for survival analysis in S. R package version 2.38. https://CRAN.R-project.org/package=survival. Accessed Mar 2018.
[32] Therneau, T. M., Grambsch, P. M. (2000). Modeling survival data: Extending the Cox model. New York: Springer. · Zbl 0958.62094
[33] Therneau, T. M., Grambsch, P. M., Fleming, T. R. (1990). Martingale-based residuals for survival models. Biometrika, 77(1), 147-160. · Zbl 0692.62082
[34] Therneau, T. M., Grambsch, P. M., Pankratz, V. S. (2003). Penalized survival models. Journal of Computational and Graphical Statistics, 12(1), 156-175.
[35] Vaupel, J., Manton, K., Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16, 439-454.
[36] Wienke, A. (2011). Frailty models in survival analysis. CRC biostatistics series. New York: Chapman and Hall.
[37] Yavuz, A. C., Lambert, P. (2016). Semi-parametric frailty model for clustered interval-censored data. Statistical Modelling, 16, 360-391.
[38] Yu, B., Estimation of shared gamma frailty models by a modified EM algorithm, Computational Statistics and Data Analysis, 50, 463-474, (2006) · Zbl 1302.62214
[39] Zeng, D., Lin, D. Y., Lin, X. (2008). Semiparametric transformation models with random effects for clustered failure time data. Statistica Sinica, 18, 355-377. · Zbl 1137.62019
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.