Joint Frailty Mixing Model for Recurrent Event Data with an Associated Terminal Event: Application to Hospital Readmission Data
DOI:
https://doi.org/10.6000/1929-6029.2023.12.25Keywords:
Frailty, Proportional hazard model, Proportional intensity model, Mixture distribution, Recurrent eventsAbstract
Recurrent events like repeated hospitalization, cancer tumour recurrences, and many others occur frequently. The follow-up on recurrent events may be stopped by a terminal event like death. It is obvious that if the frequencies of recurrent events are more, then it may lead to a terminal event and in this case terminal event becomes ‘dependent’. In this article, we study a joint modelling and analysis of recurrent events with a dependent terminal event. Here, the proportional intensity model for the recurrent events process and the proportional hazard model for the terminal event time are taken. To account for the association between recurrent events and terminal events, mixing frailty or random effect is studied rather than available pure frailty. In our case, the distribution of frailty is introduced as a mixture of folded normal distribution and gamma distribution rather than using pure gamma distribution. An estimation procedure in the joint frailty model is applied to estimate the parameters of the model. This method is close to the method of minimum chi-square rather than a complicated one. An extensive simulation study has been performed to estimate the model parameters and the performances are evaluated based on bias and MSE criteria. Further from an application point of view, the method is illustrated to a hospital readmission data for colorectal cancer patients.
References
Prentice RL, Williams BJ, Peterson AV. On the regression analysis of multivariate failure time data. Biometrika 1981; 68: 373-379. https://doi.org/10.1093/biomet/68.2.373 DOI: https://doi.org/10.1093/biomet/68.2.373
Pepe MS, Cai J. Some graphical displays and marginal regression analysis for recurrent failure times and time-dependent covariates. J Am Statist Assoc 1993; 88: 811-820. https://doi.org/10.2307/2290770 DOI: https://doi.org/10.1080/01621459.1993.10476346
Lawless JF, Nadeau C. Some simple robust methods for the analysis of recurrent events. Technometrics 1995; 37: 158-168. https://doi.org/10.2307/1269617 DOI: https://doi.org/10.1080/00401706.1995.10484300
Sun L, Zhao X, Zhou J. A class of mixed models for recurrent event data. Canad J Statist 2011; 39: 578-590. https://doi.org/10.1002/cjs.10132 DOI: https://doi.org/10.1002/cjs.10132
Ghosh D, Lin DY. Nonparametric analysis of recurrent events and death. Biometrics 2000; 56: 554-562. https://doi.org/10.1111/j.0006-341x.2000.00554.x DOI: https://doi.org/10.1111/j.0006-341X.2000.00554.x
Miloslavsky M, Keles S, Van der Laan MJ, et al. Recurrent events analysis in the presence of time-dependent covariates and dependent censoring. J R Statist Soc 2004; 66B: 239-257. https://doi.org/10.1111/j.1467-9868.2004.00442.x DOI: https://doi.org/10.1111/j.1467-9868.2004.00442.x
Zeng D, Lin DY. Semiparametric transformation models with random effects for joint analysis of recurrent and terminal events. Biometrics 2009; 65: 746-752. https://doi.org/10.1111/j.1541-0420.2008.01126.x DOI: https://doi.org/10.1111/j.1541-0420.2008.01126.x
Zeng D, Cai J. A semiparametric additive rate model for recurrent events with informative terminal event. Biometrika 2010; 97: 699-712. https://doi.org/10.1093/biomet/asq039 DOI: https://doi.org/10.1093/biomet/asq039
Wang MC, Qin J, Chiang CT. Analyzing recurrent event data with informative censoring. J Am Statist Assoc 2001; 96: 1057-1065. https://doi.org/10.1198/016214501753209031 DOI: https://doi.org/10.1198/016214501753209031
Huang CY, Wang MC. Joint Modeling and estimation of recurrent event process and failure time. J Am Statist Assoc 2004; 99: 1153-1165. https://doi.org/10.1198/016214504000001033 DOI: https://doi.org/10.1198/016214504000001033
Ye Y, Kalbfleisch JD, Schaubel DE. Semiparametric analysis of correlated recurrent and terminal events. Biometrics 2007; 63: 78-87. https://doi.org/10.1111/j.1541-0420.2006.00677.x DOI: https://doi.org/10.1111/j.1541-0420.2006.00677.x
Cook RJ, Lawless JF. Marginal analysis of recurrent events and a terminating event. Stat Med 1997; 16: 911-924. https://doi.org/10.1002/(SICI)1097-0258(19970430)16:8<911::AID-SIM544>3.0.CO;2-I DOI: https://doi.org/10.1002/(SICI)1097-0258(19970430)16:8<911::AID-SIM544>3.0.CO;2-I
Ghosh D, Lin DY. Marginal regression models for recurrent and terminal events. Statist Sinica 2002; 12: 663-668. https://www.jstor.org/stable/24306989
Cook RJ, Lawless JF, Lakhal CL, et al. Robust estimation of mean functions and treatment effects for recurrent events under event-dependent censoring and termination: Application to skeletal complications in cancer metastatic to bone. J Am Statist Assoc 2009; 104: 60-75. https://doi.org/10.1198/jasa.2009.0004 DOI: https://doi.org/10.1198/jasa.2009.0004
Cox DR. Regression models and life-tables, Journal of the Royal Statistical Society. Series B (Methodological) 1972; 34(2): 187-220. https://doi.org/10.1111/j.2517-6161.1972.tb00899.x DOI: https://doi.org/10.1111/j.2517-6161.1972.tb00899.x
Hougaard P. Analysis of multivariate survival data, Springer Verlag: New York 2000. DOI: https://doi.org/10.1007/978-1-4612-1304-8
Duchateau L, Janssen P. The frailty model, Springer: New York, 2008.
Che X, Angus J. A new joint model of recurrent event data with the additive hazards model for the terminal event time. Metrica 2016. https://doi.org/10.1007/s00184-016-0577-9 DOI: https://doi.org/10.1007/s00184-016-0577-9
Liu L, Wolfe RA, Huang X. Shared frailty models for recurrent events and a terminal event. Biometrics 2004; 60: 747-756. https://doi.org/10.1111/j.0006-341X.2004.00225.x DOI: https://doi.org/10.1111/j.0006-341X.2004.00225.x
Huang X, Liu L. A joint frailty model for survival and gap times between recurrent events. Biometrics 2007; 63(2): 747-756. https://doi.org/10.1111/j.1541-0420.2006.00719.x DOI: https://doi.org/10.1111/j.1541-0420.2006.00719.x
Joly P, Commenges D, Letenneur L. A penalized likelihood approach for arbitrarily censored and truncated data: application to age-specific incidence of dementia. Biometrics 1998; 54(1): 185-194. https://doi.org/10.2307/2534006 DOI: https://doi.org/10.2307/2534006
Rondeau V, Mathoulin-Pelissier S, Jacqmin-Gadda H, Brouste V, Soubeyran P. Joint frailty models for recurring events and death using maximum penalized likelihood estimation: application on cancer events. Biostatistics 2007; 8(4): 708-721. https://doi.org/10.1093/biostatistics/kxl043 DOI: https://doi.org/10.1093/biostatistics/kxl043
Marquardt D. An algorithm for least-squares estimation of nonlinear parameters. SIAM Journal on Applied Mathematics 1963; 11: 431-441. https://www.jstor.org/stable/2098941 DOI: https://doi.org/10.1137/0111030
Mazroui Y, Mathoulin-Pelissier S, Soubeyran P and Rondeau V. General joint frailty model for recurrent event data with a dependent terminal event: application to follicular lymphoma data. Statistics in Medicine 2012. https://doi.org/10.1002/sim.4479 DOI: https://doi.org/10.1002/sim.4479
Toenges G, Jahn-Eimermacher A. Computational issues in fitting joint frailty models for recurrent events with an associated terminal event. Computer Methods and Programs in Biomedicine 2020; 188: 1-13. https://doi.org/10.1016/j.cmpb.2019.105259 DOI: https://doi.org/10.1016/j.cmpb.2019.105259
Banerjee P, Goswami A, Bhunia S, Basu S. Determination of Causal Relationship Between Bilirubin and Other Liver Biomarker in Case of Hepatitis C. Biomed Stat Informatics 2021; 6(2): 23-31. https://doi.org/10.11648/j.bsi.20210602.11 DOI: https://doi.org/10.11648/j.bsi.20210602.11
Peng Y, Jiajia D, Jun Z. Joint analysis of recurrent event data with a dependent terminal event. J Syst Sci Complex 2017; 30: 1443-1458. https://doi.org/10.1007/s11424-017-6097-5 DOI: https://doi.org/10.1007/s11424-017-6097-5
González JR, Fernandez E, Moreno V, Ribes J, Peris M, Navarro M, Cambray M, Borrás JM. Sex differences in hospital readmission among colorectal cancer patients. Journal of Epidemiology and Community Health 2005; 59: 506-511. https://doi.org/10.1136/jech.2004.028902 DOI: https://doi.org/10.1136/jech.2004.028902
Fathoni M, Gunardi G, Adi-Kusumo F, Hutajulu SH, I Purwanto. Cox Proportional Hazard Regression Interaction Model and Its Application to Determine The Risk of Death in Breast Cancer Patients after Chemotherapy. Int J Stats Med Res 2022; 11: 105-113. https://doi.org/10.6000/1929-6029.2022.11.13 DOI: https://doi.org/10.6000/1929-6029.2022.11.13
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Policy for Journals/Articles with Open Access
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are permitted and encouraged to post links to their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work
Policy for Journals / Manuscript with Paid Access
Authors who publish with this journal agree to the following terms:
- Publisher retain copyright .
- Authors are permitted and encouraged to post links to their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work .
