Communications for Statistical Applications and Methods

  • 제24권6호
  • /
  • Pages.605-625
  • /
  • 2017
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

Cure rate proportional odds models with spatial frailties for interval-censored data

  • Yiqi, Bao (Departamento de Matematica Aplicada e Estatistica, Universidade de Sao Paulo) ;
  • Cancho, Vicente Garibay (Departamento de Matematica Aplicada e Estatistica, Universidade de Sao Paulo) ;
  • Louzada, Francisco (Departamento de Matematica Aplicada e Estatistica, Universidade de Sao Paulo) ;
  • Suzuki, Adriano Kamimura (Departamento de Matematica Aplicada e Estatistica, Universidade de Sao Paulo)
  • 투고 : 2017.07.08
  • 심사 : 2017.11.07
  • 발행 : 2017.11.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents proportional odds cure models to allow spatial correlations by including spatial frailty in the interval censored data setting. Parametric cure rate models with independent and dependent spatial frailties are proposed and compared. Our approach enables different underlying activation mechanisms that lead to the event of interest; in addition, the number of competing causes which may be responsible for the occurrence of the event of interest follows a Geometric distribution. Markov chain Monte Carlo method is used in a Bayesian framework for inferential purposes. For model comparison some Bayesian criteria were used. An influence diagnostic analysis was conducted to detect possible influential or extreme observations that may cause distortions on the results of the analysis. Finally, the proposed models are applied for the analysis of a real data set on smoking cessation. The results of the application show that the parametric cure model with frailties under the first activation scheme has better findings.

키워드

참고문헌

  1. Banerjee S and Carlin BP (2004). Parametric spatial cure rate models for interval-censored time-torelapse data, Biometrics, 60, 268-275. https://doi.org/10.1111/j.0006-341X.2004.00032.x
  2. Bennett S (1983). Analysis of survival data by the proportional odds model, Statistics in Medicine, 2, 273-277. https://doi.org/10.1002/sim.4780020223
  3. Berkson J and Gage RP (1952). Survival curve for cancer patients following treatment, Journal of the American Statistical Association, 47, 501-515. https://doi.org/10.1080/01621459.1952.10501187
  4. Besag J (1974). Spatial interaction and the statistical analysis of lattice systems, Journal of the Royal Statistical Society, Series B (Methodological), 36, 192-236. https://doi.org/10.1111/j.2517-6161.1974.tb00999.x
  5. Cancho VG, Ortega EMM, and Paula GA (2010). On estimation and influence diagnostics for log-Birnbaum-Saunders Student-t regression models: full Bayesian analysis, Journal of Statistical Planning and Inference, 140, 2486-2496. https://doi.org/10.1016/j.jspi.2010.02.017
  6. Carlin BP and Banerjee S (2003). Hierarchical multivariate CAR models for spatio-temporally correlated survival data, Bayesian Statistics, 7, 45-63.
  7. Chen MH, Ibrahim JG, and Sinha D (1999). A new Bayesian model for survival data with a surviving fraction, Journal of the American Statistical Association, 94, 909-919. https://doi.org/10.1080/01621459.1999.10474196
  8. Cook RD and Weisberg S (1982). Residuals and Influence in Regression, Chapman & Hall/CRC, FL.
  9. Collett D (1994). Modelling survival data. In D Collett (Ed), Modelling Survival Data in Medical Research (pp. 53-60), Springer, New York.
  10. Cooner F, Banerjee S, Carlin BP, and Sinha D (2007). Flexible cure rate modeling under latent activation schemes, Journal of the American Statistical Association, 102, 560-572. https://doi.org/10.1198/016214507000000112
  11. Dey DK and Birmiwal LR (1994). Robust Bayesian analysis using divergence measures, Statistics & Probability Letters, 20, 287-294. https://doi.org/10.1016/0167-7152(94)90016-7
  12. Finkelstein DM (1986). A proportional Hazards model for interval-censored failure time data, Biometrics, 42, 845-854. https://doi.org/10.2307/2530698
  13. Gamerman D and Lopes HF (2006). Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference (2nd ed.), Chapman & Hall/CRC, Boca Raton.
  14. Gelfand AE and Vounatsou P (2003). Proper multivariate conditional autoregressive models for spatial data analysis, Biostatistics, 4, 11-15. https://doi.org/10.1093/biostatistics/4.1.11
  15. Geweke J (1992). Evaluating the accuracy of sampling-based approaches to calculating posterior moments. In JM Bernardo, J Berger, AP Dawid, and JFM Smith (Eds), Bayesian Statistics 4 (pp. 169-193), Clarendon Press, Oxford.
  16. Gu Y, Sinha D, and Banerjee S (2011). Analysis of cure rate survival data under proportional odds model, Lifetime Data Analysis, 17, 123-134. https://doi.org/10.1007/s10985-010-9171-z
  17. Hu T and Xiang L (2013). Efficient estimation for semiparametric cure models with interval-censored data, Journal of Multivariate Analysis, 121, 139-151. https://doi.org/10.1016/j.jmva.2013.06.006
  18. Ibrahim JG, Chen MH, and Sinha D (2001). Bayesian Survival Analysis, Springer, New York.
  19. Lindsey JC and Ryan LM (1998). Methods for interval-censored data, Statistics in Medicine, 17, 219-238. https://doi.org/10.1002/(SICI)1097-0258(19980130)17:2<219::AID-SIM735>3.0.CO;2-O
  20. Ma X and Xiang L (2013). Testing for the presence of a cure fraction in clustered interval-censored survival data, Australian & New Zealand Journal of Statistics, 55, 173-190. https://doi.org/10.1111/anzs.12023
  21. Murray RP, Anthonisen NR, Connett JE, et al. (1998). Effects of multiple attempts to quit smoking and relapses to smoking on pulmonary function, Journal of Clinical Epidemiology, 51, 1317-1326. https://doi.org/10.1016/S0895-4356(98)00120-6
  22. Pan C, Cai B, Wang L, and Lin X (2014). Bayesian semiparametric model for spatially correlated interval-censored survival data, Computational Statistics & Data Analysis, 74, 198-208. https://doi.org/10.1016/j.csda.2013.11.016
  23. Peng F and Dey DK (1995). Bayesian analysis of outlier problems using divergence measures, Canadian Journal of Statistics, 23, 199-213. https://doi.org/10.2307/3315445
  24. Peto R (1973). Experimental survival curves for interval-censored data. Journal of the Royal Statistical Society Series C (Applied Statistics), 22, 86-91.
  25. Plummer M, Best N, Cowles K, and Vines K (2005). Output analysis and diagnostics for MCMC: R package version 0.10-3, Retrieved November 2, 2017, from: http://cran.rproject.org
  26. R Development Core Team (2010). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna.
  27. Rodrigues J, Cancho VG, de Castro M, and Louzada-Neto F (2009). On the unification of long-term survival models, Statistics & Probability Letters, 79, 753-759. https://doi.org/10.1016/j.spl.2008.10.029
  28. Rucker G and Messerer D (1988). Remission duration: an example of interval-censored observations, Statistics in Medicine, 7, 1139-1145. https://doi.org/10.1002/sim.4780071106
  29. Spiegelhalter DJ, Best NG, Carlin BP, and van der Linde A (2002). Bayesian measures of model complexity and fit, Journal of the Royal Statistical Society B (Statistical Methodology), 64, 583-639. https://doi.org/10.1111/1467-9868.00353
  30. Sun X and Chen C (2010). Comparison of Finkelstein's method with the conventional approach for interval-censored data analysis, Statistics in Biopharmaceutical Research, 2, 97-108. https://doi.org/10.1198/sbr.2010.09013
  31. Weiss R (1996). An approach to Bayesian sensitivity analysis, Journal of the Royal Statistical Society Series B (Methodological), 58, 739-750. https://doi.org/10.1111/j.2517-6161.1996.tb02112.x
  32. Xiang L, Ma X, and Yau KK (2011). Mixture cure model with random effects for clustered interval-censored survival data, Statistics in Medicine, 30, 995-1006.
  33. Yakovlev AY and Tsodikov AD (1996). Stochastic Models of Tumor Latency and Their Biostatistical Applications, World Scientific, Singapore.
  34. Yau KKW and Ng ASK (2001). Long-term survivor mixture model with random effects: application to a multi-centre clinical trial of carcinoma, Statistics in Medicine, 20, 1591-1607. https://doi.org/10.1002/sim.932
  35. Zeng D, Yin G, and Ibrahim JG (2006). Semiparametric transformation models for survival data with a cure fraction, Journal of the American Statistical Association, 101, 670-684. https://doi.org/10.1198/016214505000001122