Additive gamma frailty models with applications to competing risks in related individuals
Corresponding Author
Frank Eriksson
Section of Biostatistics, University of Copenhagen, Øster Farimagsgade 5, 1014 Copenhagen, Denmark
email: [email protected]Search for more papers by this authorThomas Scheike
Section of Biostatistics, University of Copenhagen, Øster Farimagsgade 5, 1014 Copenhagen, Denmark
Search for more papers by this authorCorresponding Author
Frank Eriksson
Section of Biostatistics, University of Copenhagen, Øster Farimagsgade 5, 1014 Copenhagen, Denmark
email: [email protected]Search for more papers by this authorThomas Scheike
Section of Biostatistics, University of Copenhagen, Øster Farimagsgade 5, 1014 Copenhagen, Denmark
Search for more papers by this authorSummary
Epidemiological studies of related individuals are often complicated by the fact that follow-up on the event type of interest is incomplete due to the occurrence of other events. We suggest a class of frailty models with cause-specific hazards for correlated competing events in related individuals. The frailties are based on sums of gamma distributed variables and offer closed form expressions for the observed intensities. An inference procedure with a recursive baseline estimator is proposed, and its large sample properties are established. The estimator readily handles cluster left-truncation as occurring in the Nordic twin registers. The performance in finite samples is investigated by simulations and an example on prostate cancer in twins is provided for illustration.
Supporting Information
Additional Supporting Information may be found in the online version of this article.
| Filename | Description |
|---|---|
| biom12326-sup-0001-SuppData.pdf394.1 KB | Supplementary Materials. |
Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.
References
- Andersen, P. K., Borgan, Ø., Gill, R., and Keiding, N. (1993). Statistical Models Based on Counting Processes. Springer-Verlag, New York.
- Bandeen-Roche, K. and Liang, K.-Y. (2002). Modelling multivariate failure time associations in the presence of a competing risk. Biometrika 89, 299–314.
- Chen, B., Kramer, J., Greene, M., and Rosenberg, P. (2008). Competing risks analysis of correlated failure time data. Biometrics 64, 172–179.
- Cheng, Y. and Fine, J. (2008). Nonparametric estimation of cause-specific cross hazard ratio with bivariate competing risks data. Biometrika 95, 233–240.
- Dabrowska, D. (2005). Quantile regression in transformation models. Sankhyā 67, 153–186.
- Gorfine, M. and Hsu, L. (2011). Frailty-based competing risks model for multivariate survival data. Biometrics 67, 415–426.
- Gorfine, M., Zucker, D., and Hsu, L. (2006). Prospective survival analysis with a general semiparametric shared frailty model: A pseudo full likelihood approach. Biometrika 93, 735–741.
- Gorfine, M., Zucker, D., and Hsu, L. (2009). Case–control survival analysis with a general semiparametric shared frailty model –A pseudo full likelihood approach. Annals of Statistics 37, 1489–1517.
- Hjelmborg, J., Scheike, T., Holst, K., Skytthe, A., Penney, K., Graff, E., Pukkala, E., Christensen, K., Adami, H.-O., Holm, N., Nuttall, E., Hansen, S., Hartman, M., Czene, K., Harris, J., Kaprio, J., and Mucci, L. (2014). The heritability of prostate cancer in the Nordic twin study of cancer. Cancer Epidemiology, Biomarkers & Prevention 23, 2303–2310.
- Jensen, H., Brookmeyer, R., Aaby, P., and Andersen, P. K. (2004). Shared frailty model for left-truncated multivariate survival data. Research Report 04/02, Department of Biostatistics, University of Copenhagen.
- Jonker, M., Bhulai, S., Boomsma, D., Ligthart, R., Posthuma, D., and van der Vaart, A. (2008). Gamma frailty model for linkage analysis with application to interval-censored migraine data. Biostatistics 10, 187–200.
- Katki, A., Blackford, A., Chen, S., and Parmigiani, P. (2008). Multiple diseases in carrier probability estimation: Accounting for surviving all cancers other than breast and ovary in BRCAPRO. Statistics in Medicine 27, 4532.
- Klein, J. and Andersen, P. K. (2005). Regression modeling of competing risks data based on pseudovalues of the cumulative incidence function. Biometrics 61, 223–229.
- Korsgaard, I. R. and Andersen, A. H. (1998). The additive genetic gamma frailty model. Scandinavian Journal of Statistics 25, 225–269.
- Liu, I., Blacker, D., Xu, R., Fitzmaurice, G., Lyons, M., and Tsuang, M. (2004). Genetic and environmental contributions to the development of alcohol dependence in male twins. Archives of General Psychiatry 61, 897–903.
- Logan, B., Zhang, M.-J., and Klein, J. (2010). Marginal models for clustered time-to-event data with competing risks using pseudovalues. Biometrics 67, 1–7.
- Martinussen, T., Scheike, T., and Zucker, D. (2011). The Aalen additive gamma frailty hazards model. Biometrika 98, 831–843.
- Nielsen, G., Gill, R., Andersen, P. K., and Sørensen, T. (1992). A counting process approach to maximum likelihood estimation in frailty models. Scandinavian Journal of Statistics 19, 25–43.
- Oakes, D. (1989). Bivariate survival models induced by frailties. Journal of the American Statistical Association 84, 487–493.
-
Petersen, J. H.,
Andersen, P. K., and
Gill, R.
(1996).
Variance components models for survival data.
Statistica Neerlandica
50, 193–211.
10.1111/j.1467-9574.1996.tb01487.x Google Scholar
- Prentice, R., Kalbfleisch, J., Peterson, A., Flournoy, N., Farewell, V., and Breslow, N. (1978). The analysis of failure times in the presence of competing risks. Biometrics 34, 541–554.
- Scheike, T. (2006). A flexible semiparametric transformation model for survival data. Lifetime Data Analysis 12, 461–480.
- Scheike, T., Holst, K., and Hjelmborg, J. (2014). Estimating heritability for cause specific mortality based on twin studies. Lifetime Data Analysis 20, 210–233.
- Scheike, T., Martinussen, T., and Silver, J. (2010). Estimating haplotype effects for survival data. Biometrics 66, 705–715.
- Scheike, T., Sun, Y., Zhang, M.-J., and Jensen, T. K. (2010). A semiparametric random effects model for multivariate competing risks data. Biometrika 97, 133–145.
- Wienke, A. (2011). Frailty Models in Survival Analysis. Chapman & Hall/CRC, Boca Raton.
- Wienke, A., Christensen, K., Skytthe, A., and Yashin, A. (2002). Genetic analysis of cause of death in a mixture model of bivariate lifetime data. Statistical Modelling 2, 89–102.
- Yashin, A. and Iachine, A. (1995). Genetic analysis of durations: Correlated frailty model applied to survival of danish twins. Genetic Epidemiology 12, 529–538.
- Yashin, A, Vaupel, J., and Iachine, I. (1995). Correlated individual frailty. Mathematical Population Studies 5, 145–159.
- Zeng, D. and Lin, D. (2007). Maximum likelihood estimation in semiparametric regression models with censored data. Journal of the Royal Statistical Society Series B 69, 507–564.
- Zucker, D. (2005). A pseudo partial likelihood method for semi-parametric survival regression with covariate errors. Journal of the American Statistical Association 100, 1264–1277.
