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Abstract
Dependent censoring often arises in biomedical studies when time to tumour progression (e.g., relapse of cancer) is censored by an informative terminal event (e.g., death). For meta-analysis combining existing studies, a joint survival model between tumour progression and death has been considered under semicompeting risks, which induces dependence through the study-specific frailty. Our paper here utilizes copulas to generalize the joint frailty model by introducing additional source of dependence arising from intra-subject association between tumour progression and death. The practical value of the new model is particularly evident for meta-analyses in which only a few covariates are consistently measured across studies and hence there exist residual dependence. The covariate effects are formulated through the Cox proportional hazards model, and the baseline hazards are nonparametrically modeled on a basis of splines. The estimator is then obtained by maximizing a penalized log-likelihood function. We also show that the present methodologies are easily modified for the competing risks or recurrent event data, and are generalized to accommodate left-truncation. Simulations are performed to examine the performance of the proposed estimator. The method is applied to a meta-analysis for assessing a recently suggested biomarker CXCL12 for survival in ovarian cancer patients. We implement our proposed methods in R joint.Cox package.
References
| 1. | Pazdur, R . Endpoints for assessing drug activity in clinical trials. Oncologist 2008; 13: 19–21. Google Scholar | Crossref | Medline | ISI |
| 2. | Shi, Q, Sargent, DJ. Meta-analysis for the evaluation of surrogate endpoints in cancer clinical trials. Int J Clin Oncol 2009; 14: 102–111. Google Scholar | Crossref | Medline | ISI |
| 3. | Michiels, S, Le Maître, A, Buyse, M Surrogate endpoints for overall survival in locally advanced head and neck cancer: meta-analyses of individual patient data. Lancet Oncol 2009; 10: 341–350. Google Scholar | Crossref | Medline | ISI |
| 4. | Buyse, M, Sargent, DJ, Saad, ED. Survival is not a good outcome for randomized trials with effective subsequent therapies. J Clin Oncol 2011; 29: 4719–4720. Google Scholar | Crossref | Medline | ISI |
| 5. | Sherrill, B, Amonker, M, Wu, Y Relationship between effects on time-to-disease progression and overall survival in studies of metastatic breast cancer. Br J Cancer 2008; 99: 1542–1548. Google Scholar | Crossref | ISI |
| 6. | Rondeau, V, Pignon, JP, Michiels, S. A joint model for dependence between clustered times to tumour progression and deaths: A meta-analysis of chemotherapy in head and neck cancer. Stat Meth Med Res 2015; 24: 711–729. Google Scholar | SAGE Journals | ISI |
| 7. | Cheema, PK, Burkes, RL. Overall survival should be the primary endpoint in clinical trials for advanced non-small cell lung cancer. Curr Oncol 2013; 20: e150–e160. Google Scholar | Crossref | Medline | ISI |
| 8. | Cox, DR . Regression models and life-tables (with discussion). J Royal Stat Soc Ser B 1972; 34: 187–220. Google Scholar |
| 9. | Burzykowski, T, Molenberghs, G, Buyse, M. The Evaluation of Surrogate Endpoints, New York: Springer, 2005. Google Scholar | Crossref |
| 10. | Emura, T, Chen, YH. Gene selection for survival data under dependent censoring, a copula-based approach. Stat Meth Med Res 2016; 25: 2840–2857. Google Scholar | SAGE Journals | ISI |
| 11. | Hougaard, P . Analysis of Multivariate Survival Data, New York: Springer, 2000. Google Scholar | Crossref |
| 12. | Duchateau, L, Janssen, P. The Frailty Model, New York: Springer, 2008. Google Scholar |
| 13. | Crowder, MJ . Multivariate Survival Analysis and Competing Risks, Boca Raton: CRC Press, 2012. Google Scholar | Crossref |
| 14. | Borenstein, M, Hedges, LV, Higgins, JPT Introduction to Meta-analysis, Wiley, 2009. Google Scholar | Crossref |
| 15. | Burzykowski, T, Molenberghs, G, Buyse, M Validation of surrogate end points in multiple randomized clinical trials with failure time end points. Appl Stat 2001; 50: 405–422. Google Scholar | Crossref | ISI |
| 16. | Fine, JP, Jiang, H, Chappell, R. On semi-competing risks data. Biometrika 2001; 88: 907–920. Google Scholar | Crossref | ISI |
| 17. | Emura, T . R joint.Cox: Penalized likelihood estimation under the joint Cox models between TTP and OS for meta-analysis. CRAN, R package version 2.0: 2015-06-18. CRAN: The Comprehensive R Archive Network. Google Scholar |
| 18. | Popple, A, Durrant, LG, Spendlove, I The chemokine, CXCL12, is an independent predictor of poor survival in ovarian cancer. Br J Cancer 2012; 106: 1306–1313. Google Scholar | Crossref | Medline | ISI |
| 19. | Ganzfried, BF, Riester, M, Haibe-Kains, B Curated ovarian data: clinically annotated data for the ovarian cancer transcriptome. Database 2013. Article ID bat013, DOI: 10.1093/database/bat013. Google Scholar | Crossref | Medline |
| 20. | Tsiatis, A . A nonidentifiability aspect of the problem of competing risks. Proc Natl Acad Sci USA 1975; 72: 20–22. Google Scholar | Crossref | Medline | ISI |
| 21. | Kryczek, I, Wei, S, Keller, E Stroma-derived factor (SDF-1/CXCL12) and human tumor pathogenesis. Am J Physiol-Cell Physiol 2007; 292: C987–C995. Google Scholar | Crossref | Medline | ISI |
| 22. | Rondeau, V, Gonzalez, JR, Mazroui, Y R frailtypack: general frailty models: shared, joint and nested frailty models with prediction. CRAN, R package version 2.7.5: 2015-03-06. CRAN: The Comprehensive R Archive Network. Google Scholar |
| 23. | Geerdens, C, Claeskens, G, Janssen, P. Goodness-of-fit tests for the frailty distribution in proportional hazards models with shared frailty. Biostatistics 2013; 14: 433–446. Google Scholar | Crossref | Medline | ISI |
| 24. | Rondeau, V, Mathoulin-Pelissier, S, Jacqmin-Gadda, H Joint frailty models for recurring events and death using maximum penalized likelihood estimation: Application on cancer events. Biostatistics 2007; 8: 708–721. Google Scholar | Crossref | Medline | ISI |
| 25. | Nelsen, RB . An introduction to Copulas, 2nd ed. New York: Springer Series in Statistics, Springer-Verlag, 2006. Google Scholar |
| 26. | O' Sullivan, F . Fast computation of fully automated log-density and log-hazard estimation. SIAM J Sci Stat Comput 1988; 9: 363–379. Google Scholar | Crossref | ISI |
| 27. | Joly, P, Commenges, D, Letenneur, L. A penalized likelihood approach for arbitrary censored and truncated data: application to age-specific incidence of dementia. Biometrics 1998; 54: 185–194. Google Scholar | Crossref | Medline | ISI |
| 28. | Rondeau, V, Commenges, D, Joly, P. Maximum penalized likelihood estimation in a gamma-frailty model. Lifetime Data Analysis 2003; 9: 139–153. Google Scholar | Crossref | Medline | ISI |
| 29. | Ramsay, J . Monotone regression spline in action. Statis Sci 1988; 3: 425–461. Google Scholar | Crossref |
| 30. | Sabatier, R, Finetti, P, Adelaide, J Down-regulation of ECRG4, a candidate tumor suppressor gene, in human breast cancer. PLoS One 2011; 6: e27656. Google Scholar | Crossref | Medline | ISI |
| 31. | Jenssen, TK, Kuo, WP, Stokke, T Association between gene expressions in breast cancer and patient survival. Human Genetics 2002; 111: 411–420. Google Scholar | Crossref | Medline | ISI |
| 32. | Matsui, S . Predicting survival outcomes using subsets of significant genes in prognostic marker studies with microarrays. BMC Bioinformatics 2006; 7: 156. Google Scholar | Crossref | Medline | ISI |
| 33. | Emura, T, Chen, YH, Chen, HY. Survival prediction based on compound covariate under Cox proportional hazard models. PLoS ONE 2012; 7: e47627. Google Scholar | Crossref | Medline | ISI |
| 34. | Clayton, DG . A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 1978; 65: 141–151. Google Scholar | Crossref | ISI |
| 35. | Mauguen, A, Rachet, B, Mathoulin-Pélissier, S Dynamic prediction of risk of death using history of cancer recurrences in joint frailty models. Stat Med 2013; 32: 5366–5380. Google Scholar | Crossref | Medline | ISI |
| 36. | Mauguen, A, Rachet, B, Mathoulin-Pélissier, S Validation of death prediction after breast cancer relapses using joint models. BMC Med Res Methodol 2015; 15: 27. Google Scholar | Crossref | Medline | ISI |
| 37. | Chen, YH . Maximum likelihood analysis of semicompeting risks data with semiparametric regression models. Lifetime Data Anal 2012; 18: 36–57. Google Scholar | Crossref | Medline | ISI |
| 38. | Hsieh, JJ, Wang, W, Ding, AA. Regression analysis based on semicompeting risks data. J Royal Stat Soc: Ser B (Statistical Methodology) 2008; 70: 3–20. Google Scholar | ISI |
| 39. | Rivest, LP, Wells, MT. A martingale approach to the copula-graphic estimator for the survival function under dependent censoring. J Mult Anal 2001; 79: 138–155. Google Scholar | Crossref | ISI |
| 40. | Braekers, R, Veraverbeke, N. A copula-graphic estimator for the conditional survival function under dependent censoring. Can J Stat 2005; 33: 429–447. Google Scholar | Crossref | ISI |
| 41. | Huang, X, Zhang, N. Regression survival analysis with an assumed copula for dependent censoring. Biometrics 2008; 64: 1090–1099. Google Scholar | Crossref | Medline | ISI |
| 42. | Chen, YH . Semiparametric marginal regression analysis for dependent competing risks under an assumed copula. J Royal Stat Soc Ser B 2010; 72: 235–251. Google Scholar | Crossref |
| 43. | Stapline, ND, Kimber, AC, Collett, D Dependent censoring in piecewise exponential survival models. Stat Meth Med Res 2015; 24: 325–341. Google Scholar | SAGE Journals | ISI |
| 44. | Escarela, G, Carriere, JF. Fitting competing risks with an assumed copula. Stat Meth Med Res 2003; 12: 333–349. Google Scholar | SAGE Journals | ISI |
| 45. | Fine, JP, Gray, RJ. A proportional hazards model for the subdistribution of a competing risk. J Am Stat Assoc 1999; 94: 548–560. Google Scholar | Crossref | ISI |
| 46. | Bakoyannis, G, Touloumi, G. Practical methods for competing risks data: a review. Stat Meth Med Res 2012; 21: 257–272. Google Scholar | SAGE Journals | ISI |
| 47. | Binder, H, Allignol, A, Schumacher, M Boosting for high-dimensional time-to-event data with competing risks. Bioinformatics 2009; 25: 890–896. Google Scholar | Crossref | Medline | ISI |
| 48. | Do Ha, I, Christian, NJ, Jeong, JH Analysis of clustered competing risks data using subdistribution hazard models with multivariate frailties. Stat Meth Med Res 2016; 25: 2488–2505. Google Scholar | SAGE Journals | ISI |
| 49. | González, JR, Fernandez, E, Moreno, V Sex differences in hospital readmission among colorectal cancer patients. J Epidemiol Commun Health 2005; 59: 506–511. Google Scholar | Crossref | Medline | ISI |
