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Aralıklı Sansürlü Veriler için Sağkalım Modelleri

Yıl 2020, , 267 - 280, 26.08.2020
https://doi.org/10.19113/sdufenbed.652776

Öz

Sansürleme, sağkalım analizi diğer istatistiksel yöntemlerden ayıran en önemli özelliktir. Sansürleme türleri ise sağdan, soldan ve aralıklı sansürleme olarak sınıflandırılmaktadır. Sağkalım analizinde kullanılan modellerin çoğu gözlemlerin sağdan sansürlü olduğu veri kümeleri için geliştirilmiştir. Aralıklı sansürlü veriler ile ilgili çalışmalar da son yıllarda hız kazanmıştır. Birimin başarısızlık süresi belli bir aralıkta gerçekleşiyorsa aralıklı sansürlü gözlemler söz konusudur. Bu veriler genellikle, ilgilenilen gözlemlerin sürekli izlenemediği durumda oluşur. Sadece ilgilenilen olayın iki gözlem periyodu arasında meydana geldiği bilinmektedir. sağkalım çözümlemesinde yaygın olarak kullanılan Cox regresyon modeli ve parametrik sağkalım modelleri aralıklı sansürlü veriler için de geliştirilmiştir. Bu çalışmada aralıklı sansürlü veriler için sağkalım modelleri incelenmiş ve literatürde yer alan Primer Biliyer Siroz verisi hem aralıklı sansürlü hem de sağdan sansürlü olarak ele alınarak analiz edilmiştir.

Kaynakça

  • [1] Barlow, R. E., Proschan, F. 1975. Importance of System Components and Fault Tree Events. Stochastic Processes and their Applications, 3(2), 153-173.
  • [2] Cox, D. R. 1972. Regression Models and Life-Tables. Journal of the Royal Statistical Society, Series B, 34(2), 187-220.
  • [3] Finkelstein, D. M., Wolfe, R. A. 1985. A Semiparametric Model for Regression Analysis of Interval-Censored Failure Time Data. Biometrics, 41(4), 993-945.
  • [4] Finkelstein, D. M. 1986. A Proportional Hazards Model for Interval-Censored Failure Time Data. Biometrics, 42(4), 845-854.
  • [5] Huang, J., Wellner, J. A. 1995. Asymptotic Normality of The NPMLE of Linear Functionals for Interval Censored Data, Case 1. Statistica Neerlandica, 49(2), 153-163.
  • [6] Huang, J. 1996. Efficient Estimation for the Proportional Hazards Model with Interval Censoring. The Annals of Statistics, 24(2), 540-568.
  • [7] Satten, G. A. 1996. Rank-based Inference in the Proportional Hazards Model for Interval Censored Data. Biometrika, 83(2), 355-370.
  • [8] Younes, N., Lachin, J. 1997. Linked-based Models for Survival Data with Interval and Continuous Time Censoring. Biometrics, 53(4), 1199-1211.
  • [9] Huang, J., Rossini, A. J. 1997. Sieve Estimation for The Proportional Odds Failure-Time Regression Model With İnterval Censoring. Journal of the American Statistical Association, 92:439, 960-967.
  • [10] Goggins, W. B., Finkelstein, D. M., Schoenfeld, D. A., Zaslavsky, A. M. 1998. A Markov Chain Monte Carlo EM Algorithm for Analyzing İnterval Censored Data Under The Cox Proportional Hazards Model. Biometrics, 54(4),1498-507.
  • [11] Geskus, R., Groeneboom, P. 1999. Asymptotically Optimal Estimation of Smooth Functionals for Interval Censoring, Case 2. The Annals of Statistics, 27(2), 627-674.
  • [12] Pan, W. 2000. A Multiple Imputation Approach to Cox Regression with Interval-Censored Data. Biometrics, 56(1), 199-203.
  • [13] Xue, H., Lam, K. F., Cowling, B. J., de Wolf, F. 2006. Semi-parametric Accelerated Failure Time Regression Analysis with Application to Interval-Censored HIV/AIDS data. Statistics in Medicine, 25(22), 3850-3863.
  • [14] Zeng, D., Cai, J., Shen, Y. 2006. Semiparametric Additive Risks Model for Interval-Censored Data. Statistica Sinica, 16, 287-302.
  • [15] Banerjee, M., Sen, B. 2007. A Pseudolikelihood Method for Analyzing Interval Censored data. Biometrika, 94(1), 71-86.
  • [16] Heller, G. 2011. Proportional Hazards Regression with Interval Censored Data Using An Inverse Probability Weight. Lifetime Data Analysis, 17(3), 373-85.
  • [17] Rabinowitz, D., Tsiatis, A. A., Aragon, J. 1995. Regression with Interval-Censored Data. Biometrika, 82(3), 501-513.
  • [18] Betensky, R. A., Rabinowitz, D., Tsiatis, A. A. 2001. Computationally Simple Accelerated Failure Time Regression for Interval Censored Data. Biometrika, 88(3), 703-711.
  • [19] Oller, R., Gómez, G., Calle, M. L. 2004. Interval Censoring: Model Characterizations for The Validity of The Simplified Likelihood. The Canadian Journal of Statistics, 32(3), 315-326.
  • [20] Zhang, Z., Sun, L., Zhao, X., Sun, J. 2005. Regression Analysis of Interval Censored Failure Time Data with Linear Transformation Models. The Canadian Journal of Statistics, 33(1), 61-70.
  • [21] Lawless, J. F., Babineau, D. 2006. Models for Interval Censoring and Simulation-Based Inference for Lifetime Distributions. Biometrika, 93(3), 671-686.
  • [22] Tian, L., Cai, T. 2006. On The Accelerated Failure Time Model for Current Status and Interval Censored Data. Biometrika, 93(2), 329-342.
  • [23] Zhang, Z., Sun, L., Sun, J., Finkelstein, D. M. 2007. Regression Analysis of Failure Time Data with Informative Interval Censoring. Statistics in Medicine, 26(12), 2533-46.
  • [24] Zhu, L., Tong, X., Sun, J. 2008. A Transformation Approach for The Analysis of Interval-Censored Failure Time Data. Lifetime Data Analysis, 14(2), 167-78.
  • [25] Radhey, S. S., Totawattage, D.P. 2013. The Statistical Analysis of Interval-Censored Failure Time Data with Applications. Journal of Statistics, 3, 155-166.
  • [26] Gomez, G., Calle, M. L., Oller, R., Langohr, K. 2009. Tutorial on Methods for Interval-Censored Data and Their Implementation in R. Statistical Modelling, 9(4), 259-297.
  • [27] Fay, M. P. 2014. interval: Weighted logrank tests and NPMLE for interval-censored data [Computer software manual]. Retrieved from https://CRAN.R project.org/package=interval (R package version 1.1-0.1), 2014.
  • [28] Anderson-Bergman, C. 2017. icenReg: Regression Models for Interval Censored Data in R. Journal of Statistical Software, 81(12), 1-23.
  • [29] Delord, M. 2017. MIICD: Data Augmentation and Multiple Imputation for Interval Censored Data [Computer software manual]. Retrieved from http://CRAN.R-project.org/package=MIICD (R package version 2.4).
  • [30] Bogaerts, K., Komàrek, A., Lesaffre, E. 2018. Survival analysis with interval-censored data. A practical approach with examples in R, SAS, and BUGS. 1st edition. CRC Press by Taylor and Francis Group, 584s.
  • [31] So, Y., Johnston, G., Kim, S. 2010. H. Analyzing Interval Censored Survival Data. SAS Global Forum Paper 257.
  • [32] Guo, C., So, Y., Johnston, G. 2014. Analyzing Interval-Censored Data with The ICLIFETEST Procedure. Paper SAS279-2014.
  • [33] Yang, X. 2017. Analyzing interval-censored surival-time data in Stata. https://www.stata.com/meeting/baltimore17/slides/Baltimore17_Yang.pdf. (Erişim Tarihi: 10.03.2018)
  • [34] Murtaugh, P., Dickson, E. R., Dam, G. V., Malinchoc, M., Grambsch, P. M., Langworthayn A. and Gips, C. H. 1994. Primary Biliary Cirrhosis: Prediction of Short-term Survival Based on Repeated Patient Visits. Hepatology, 20, 126-134.
  • [35] Turnbull, B. W. 1976. The Empirical Distribution with Arbitrarily Grouped Censored and Truncated Data. Journal of the Royal Statistical Society: Series B, 38(3), 290-295.
  • [36] Hoel, D. G., Walburg, H. E. 1972. Statistical Analysis of Survival Experiments. Journal of National Cancer Institute, 49, 361-372.
  • [37] Carvalho, J. C., Ekstrand, K. R., Thylstrup, A. 1989. Dental Plaque and Caries on Occlusal Surfaces of First Permanent Molars in Relation to Stage of Eruption. Journal of Dental Research, 68(5), 773-779.
  • [38] Kim, M. Y., De Gruttola, V. G., Lagakos, S. W. 1993. Analyzing Doubly Censored Data with Covariates, with Application to AIDS. Biometrics, 49(1), 13-22.
  • [39] Betensky, R. A., Finkelstein, D. M. 1999. A Non-Parametric Maximum Likelihood Estimator for Bivariate Interval Censored Data. Statistics in Medicine, 18(22), 3089-3100.
  • [40] Goggins, W. B., Finkelstein, D. M. 2000. A Proportional Hazards Model for Multivariate Interval-Censored Failure Time Data. Biometrics, 56, 940-943.
  • [41] Meyns, B., Jashari, R., Gewillig, M., Mertens, L., Komàrek, A., Lesaffre, E., Budts, W, Daenen, W. 2005. Factors Influencing The Survival of Cryopreserved Homografts. The Second Homograft Performs as Well as the First. European Journal of Cardio-thoracic Surgery, 28(2), 211-216.
  • [42] Goethals, K., Ampe, B., Berkvens, D., Laevens, H., Janssen, P., Duchateau, L. 2009. Modeling Interval-Censored, Clustered Cow Udder Quarter Infection Times through the Shared Gamma Frailty Model. Journal of Agricultural, Biological, and Environmental Statistics, 14(1), 1-14.
  • [43] Hough, G. 2010. Sensory shelf life estimation of food products. 1st edition. Boca Raton: CRC Press, 264s.
  • [44] Karvanen, J., Rantanen, A., Luoma, L. 2014. Survey Data and Bayesian Analysis: A Cost-Efficient Way to Estimate Customer Equity. Quantitative Marketing and Economics, 12(3), 305-329.
  • [45] Groeneboom, P., Wellner, J. A. 1992. Information bounds and nonparametric maximum likelihood estimation. Basel: Birkhäuser-Verlag, 130s.
  • [46] Huang, J., Wellner, J. A. 1997. Interval Censored Survival Data: A Review of Recent Progress. Proceedings of the First Seattle Symposium in Biostatistics: Survival Analysis, eds. Lin, D. and Fleming, T. Springer-Verlag, New York, 123-169.
  • [47] Sun, J. 1998. Interval Censoring. Encyclopedia of Biostatistics, John Wiley, 1st Edition, 2090-2095.
  • [48] Sun, J., Zhao, Q., Zhao, X. 2005. Generalized Log Rank Tests for Interval-Censored Failure Time Data. Scandinavian Journal of Statistics, 32(1), 49-57.
  • [49] Yu, Q., Li, L., Wong, G.. 2000. On Consistency of Self-Consistent Estimator of Survival Functions with Interval-Censored Data. Scandinavian Journal of Statistics, 27(1), 35-44.
  • [50] Schick, A., Yu, Q. 2000. Consistency of the GMLE with Mixed Case Interval-Censored Data. Scandinavian Journal of Statistics, 27(1), 45-55.
  • [51] Wellner, J. A. 1995. Interval censoring case 2: alternative hypotheses. Analysis of Censored Data (Pune, 1994/1995), eds. H. L. Koul and J. V. Deshoande, IMS Lecture Notes, Monograph Series 27, 271-219.
  • [52] Dinse, G. E., Lagakos, S. W. 1983. Regression Analysis of Tumor Prevalence Data. Applied Statistics, 32, 236-248.
  • [53] Keiding, N. 1991. Age-specific Incidence and Prevalence: A Statistical Perspective (with discussion). Journal of the Royal Statistical Society, Series A, 154, 371-412.
  • [54] Keiding, N., Begtrup, K., Scheike, T. H., Hasibeder, G. 1996. Estimation from Current Status Data in Continuous Time. Lifetime Data Analysis, 2, 119-129.
  • [55] Shiboski, S. C., Jewell, N. P. 1992. Statistical Analysis of the Time Dependence of HIV Infectivity Based on Partner Study Data. Journal of the American Statistical Association, 87, 360-372.
  • [56] Diamond, I. D., McDonald, J. W., Shah, I. H. 1986. Proportional Hazards Models for Current Status Data: Application to the Study of Differentials in Age at Weaning in Pakistan. Demography, 23, 607-620.
  • [57] Diamond, I. D., McDonald, J. W. 1991. The analysis of current status data. Demographic Applications of Event History Analysis, eds. Trussel, J., Hankinson, R. and Tilton, J. Oxford University Press: Oxford, U.K.
  • [58] Sun, J. 2006. The statistical analysis of interval-censored failure time data. Statistics for Biology and Health, Springer, New York, 304s.
  • [59] Dil, E. 2019. Boylamsal ve yaşam verilerinin parametrik bileşik modellemesi. Hacettepe Üniversitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi, 64s.

Survival Models with Interval Censored Data

Yıl 2020, , 267 - 280, 26.08.2020
https://doi.org/10.19113/sdufenbed.652776

Öz

Censoring is the most important feature that distinguishes survival analysis from other statistical methods. The types of censoring are classified as right, left and interval censoring. Most of the models used in survival analysis were developed for data sets in which observations were right censored. Studies on interval censoring gains speed in recent years. If the failure time of the unit occurs within a certain range, there are interval censored observations. These data usually occur when observations of interest are not constantly monitored. It is only known that the event of interest takes place between two observation periods. Cox regression model and parametric survival models used commonly in survival analysis have been developed for interval censored data. In this study, survival models for interval censored data are examined and primary biliary cirrhosis data is analyzed both for right censored and interval censored data structure.

Kaynakça

  • [1] Barlow, R. E., Proschan, F. 1975. Importance of System Components and Fault Tree Events. Stochastic Processes and their Applications, 3(2), 153-173.
  • [2] Cox, D. R. 1972. Regression Models and Life-Tables. Journal of the Royal Statistical Society, Series B, 34(2), 187-220.
  • [3] Finkelstein, D. M., Wolfe, R. A. 1985. A Semiparametric Model for Regression Analysis of Interval-Censored Failure Time Data. Biometrics, 41(4), 993-945.
  • [4] Finkelstein, D. M. 1986. A Proportional Hazards Model for Interval-Censored Failure Time Data. Biometrics, 42(4), 845-854.
  • [5] Huang, J., Wellner, J. A. 1995. Asymptotic Normality of The NPMLE of Linear Functionals for Interval Censored Data, Case 1. Statistica Neerlandica, 49(2), 153-163.
  • [6] Huang, J. 1996. Efficient Estimation for the Proportional Hazards Model with Interval Censoring. The Annals of Statistics, 24(2), 540-568.
  • [7] Satten, G. A. 1996. Rank-based Inference in the Proportional Hazards Model for Interval Censored Data. Biometrika, 83(2), 355-370.
  • [8] Younes, N., Lachin, J. 1997. Linked-based Models for Survival Data with Interval and Continuous Time Censoring. Biometrics, 53(4), 1199-1211.
  • [9] Huang, J., Rossini, A. J. 1997. Sieve Estimation for The Proportional Odds Failure-Time Regression Model With İnterval Censoring. Journal of the American Statistical Association, 92:439, 960-967.
  • [10] Goggins, W. B., Finkelstein, D. M., Schoenfeld, D. A., Zaslavsky, A. M. 1998. A Markov Chain Monte Carlo EM Algorithm for Analyzing İnterval Censored Data Under The Cox Proportional Hazards Model. Biometrics, 54(4),1498-507.
  • [11] Geskus, R., Groeneboom, P. 1999. Asymptotically Optimal Estimation of Smooth Functionals for Interval Censoring, Case 2. The Annals of Statistics, 27(2), 627-674.
  • [12] Pan, W. 2000. A Multiple Imputation Approach to Cox Regression with Interval-Censored Data. Biometrics, 56(1), 199-203.
  • [13] Xue, H., Lam, K. F., Cowling, B. J., de Wolf, F. 2006. Semi-parametric Accelerated Failure Time Regression Analysis with Application to Interval-Censored HIV/AIDS data. Statistics in Medicine, 25(22), 3850-3863.
  • [14] Zeng, D., Cai, J., Shen, Y. 2006. Semiparametric Additive Risks Model for Interval-Censored Data. Statistica Sinica, 16, 287-302.
  • [15] Banerjee, M., Sen, B. 2007. A Pseudolikelihood Method for Analyzing Interval Censored data. Biometrika, 94(1), 71-86.
  • [16] Heller, G. 2011. Proportional Hazards Regression with Interval Censored Data Using An Inverse Probability Weight. Lifetime Data Analysis, 17(3), 373-85.
  • [17] Rabinowitz, D., Tsiatis, A. A., Aragon, J. 1995. Regression with Interval-Censored Data. Biometrika, 82(3), 501-513.
  • [18] Betensky, R. A., Rabinowitz, D., Tsiatis, A. A. 2001. Computationally Simple Accelerated Failure Time Regression for Interval Censored Data. Biometrika, 88(3), 703-711.
  • [19] Oller, R., Gómez, G., Calle, M. L. 2004. Interval Censoring: Model Characterizations for The Validity of The Simplified Likelihood. The Canadian Journal of Statistics, 32(3), 315-326.
  • [20] Zhang, Z., Sun, L., Zhao, X., Sun, J. 2005. Regression Analysis of Interval Censored Failure Time Data with Linear Transformation Models. The Canadian Journal of Statistics, 33(1), 61-70.
  • [21] Lawless, J. F., Babineau, D. 2006. Models for Interval Censoring and Simulation-Based Inference for Lifetime Distributions. Biometrika, 93(3), 671-686.
  • [22] Tian, L., Cai, T. 2006. On The Accelerated Failure Time Model for Current Status and Interval Censored Data. Biometrika, 93(2), 329-342.
  • [23] Zhang, Z., Sun, L., Sun, J., Finkelstein, D. M. 2007. Regression Analysis of Failure Time Data with Informative Interval Censoring. Statistics in Medicine, 26(12), 2533-46.
  • [24] Zhu, L., Tong, X., Sun, J. 2008. A Transformation Approach for The Analysis of Interval-Censored Failure Time Data. Lifetime Data Analysis, 14(2), 167-78.
  • [25] Radhey, S. S., Totawattage, D.P. 2013. The Statistical Analysis of Interval-Censored Failure Time Data with Applications. Journal of Statistics, 3, 155-166.
  • [26] Gomez, G., Calle, M. L., Oller, R., Langohr, K. 2009. Tutorial on Methods for Interval-Censored Data and Their Implementation in R. Statistical Modelling, 9(4), 259-297.
  • [27] Fay, M. P. 2014. interval: Weighted logrank tests and NPMLE for interval-censored data [Computer software manual]. Retrieved from https://CRAN.R project.org/package=interval (R package version 1.1-0.1), 2014.
  • [28] Anderson-Bergman, C. 2017. icenReg: Regression Models for Interval Censored Data in R. Journal of Statistical Software, 81(12), 1-23.
  • [29] Delord, M. 2017. MIICD: Data Augmentation and Multiple Imputation for Interval Censored Data [Computer software manual]. Retrieved from http://CRAN.R-project.org/package=MIICD (R package version 2.4).
  • [30] Bogaerts, K., Komàrek, A., Lesaffre, E. 2018. Survival analysis with interval-censored data. A practical approach with examples in R, SAS, and BUGS. 1st edition. CRC Press by Taylor and Francis Group, 584s.
  • [31] So, Y., Johnston, G., Kim, S. 2010. H. Analyzing Interval Censored Survival Data. SAS Global Forum Paper 257.
  • [32] Guo, C., So, Y., Johnston, G. 2014. Analyzing Interval-Censored Data with The ICLIFETEST Procedure. Paper SAS279-2014.
  • [33] Yang, X. 2017. Analyzing interval-censored surival-time data in Stata. https://www.stata.com/meeting/baltimore17/slides/Baltimore17_Yang.pdf. (Erişim Tarihi: 10.03.2018)
  • [34] Murtaugh, P., Dickson, E. R., Dam, G. V., Malinchoc, M., Grambsch, P. M., Langworthayn A. and Gips, C. H. 1994. Primary Biliary Cirrhosis: Prediction of Short-term Survival Based on Repeated Patient Visits. Hepatology, 20, 126-134.
  • [35] Turnbull, B. W. 1976. The Empirical Distribution with Arbitrarily Grouped Censored and Truncated Data. Journal of the Royal Statistical Society: Series B, 38(3), 290-295.
  • [36] Hoel, D. G., Walburg, H. E. 1972. Statistical Analysis of Survival Experiments. Journal of National Cancer Institute, 49, 361-372.
  • [37] Carvalho, J. C., Ekstrand, K. R., Thylstrup, A. 1989. Dental Plaque and Caries on Occlusal Surfaces of First Permanent Molars in Relation to Stage of Eruption. Journal of Dental Research, 68(5), 773-779.
  • [38] Kim, M. Y., De Gruttola, V. G., Lagakos, S. W. 1993. Analyzing Doubly Censored Data with Covariates, with Application to AIDS. Biometrics, 49(1), 13-22.
  • [39] Betensky, R. A., Finkelstein, D. M. 1999. A Non-Parametric Maximum Likelihood Estimator for Bivariate Interval Censored Data. Statistics in Medicine, 18(22), 3089-3100.
  • [40] Goggins, W. B., Finkelstein, D. M. 2000. A Proportional Hazards Model for Multivariate Interval-Censored Failure Time Data. Biometrics, 56, 940-943.
  • [41] Meyns, B., Jashari, R., Gewillig, M., Mertens, L., Komàrek, A., Lesaffre, E., Budts, W, Daenen, W. 2005. Factors Influencing The Survival of Cryopreserved Homografts. The Second Homograft Performs as Well as the First. European Journal of Cardio-thoracic Surgery, 28(2), 211-216.
  • [42] Goethals, K., Ampe, B., Berkvens, D., Laevens, H., Janssen, P., Duchateau, L. 2009. Modeling Interval-Censored, Clustered Cow Udder Quarter Infection Times through the Shared Gamma Frailty Model. Journal of Agricultural, Biological, and Environmental Statistics, 14(1), 1-14.
  • [43] Hough, G. 2010. Sensory shelf life estimation of food products. 1st edition. Boca Raton: CRC Press, 264s.
  • [44] Karvanen, J., Rantanen, A., Luoma, L. 2014. Survey Data and Bayesian Analysis: A Cost-Efficient Way to Estimate Customer Equity. Quantitative Marketing and Economics, 12(3), 305-329.
  • [45] Groeneboom, P., Wellner, J. A. 1992. Information bounds and nonparametric maximum likelihood estimation. Basel: Birkhäuser-Verlag, 130s.
  • [46] Huang, J., Wellner, J. A. 1997. Interval Censored Survival Data: A Review of Recent Progress. Proceedings of the First Seattle Symposium in Biostatistics: Survival Analysis, eds. Lin, D. and Fleming, T. Springer-Verlag, New York, 123-169.
  • [47] Sun, J. 1998. Interval Censoring. Encyclopedia of Biostatistics, John Wiley, 1st Edition, 2090-2095.
  • [48] Sun, J., Zhao, Q., Zhao, X. 2005. Generalized Log Rank Tests for Interval-Censored Failure Time Data. Scandinavian Journal of Statistics, 32(1), 49-57.
  • [49] Yu, Q., Li, L., Wong, G.. 2000. On Consistency of Self-Consistent Estimator of Survival Functions with Interval-Censored Data. Scandinavian Journal of Statistics, 27(1), 35-44.
  • [50] Schick, A., Yu, Q. 2000. Consistency of the GMLE with Mixed Case Interval-Censored Data. Scandinavian Journal of Statistics, 27(1), 45-55.
  • [51] Wellner, J. A. 1995. Interval censoring case 2: alternative hypotheses. Analysis of Censored Data (Pune, 1994/1995), eds. H. L. Koul and J. V. Deshoande, IMS Lecture Notes, Monograph Series 27, 271-219.
  • [52] Dinse, G. E., Lagakos, S. W. 1983. Regression Analysis of Tumor Prevalence Data. Applied Statistics, 32, 236-248.
  • [53] Keiding, N. 1991. Age-specific Incidence and Prevalence: A Statistical Perspective (with discussion). Journal of the Royal Statistical Society, Series A, 154, 371-412.
  • [54] Keiding, N., Begtrup, K., Scheike, T. H., Hasibeder, G. 1996. Estimation from Current Status Data in Continuous Time. Lifetime Data Analysis, 2, 119-129.
  • [55] Shiboski, S. C., Jewell, N. P. 1992. Statistical Analysis of the Time Dependence of HIV Infectivity Based on Partner Study Data. Journal of the American Statistical Association, 87, 360-372.
  • [56] Diamond, I. D., McDonald, J. W., Shah, I. H. 1986. Proportional Hazards Models for Current Status Data: Application to the Study of Differentials in Age at Weaning in Pakistan. Demography, 23, 607-620.
  • [57] Diamond, I. D., McDonald, J. W. 1991. The analysis of current status data. Demographic Applications of Event History Analysis, eds. Trussel, J., Hankinson, R. and Tilton, J. Oxford University Press: Oxford, U.K.
  • [58] Sun, J. 2006. The statistical analysis of interval-censored failure time data. Statistics for Biology and Health, Springer, New York, 304s.
  • [59] Dil, E. 2019. Boylamsal ve yaşam verilerinin parametrik bileşik modellemesi. Hacettepe Üniversitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi, 64s.
Toplam 59 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

İlknur Eröz 0000-0002-2563-411X

Nihal Ata 0000-0001-5204-680X

Yayımlanma Tarihi 26 Ağustos 2020
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

APA Eröz, İ., & Ata, N. (2020). Aralıklı Sansürlü Veriler için Sağkalım Modelleri. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 24(2), 267-280. https://doi.org/10.19113/sdufenbed.652776
AMA Eröz İ, Ata N. Aralıklı Sansürlü Veriler için Sağkalım Modelleri. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. Ağustos 2020;24(2):267-280. doi:10.19113/sdufenbed.652776
Chicago Eröz, İlknur, ve Nihal Ata. “Aralıklı Sansürlü Veriler için Sağkalım Modelleri”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 24, sy. 2 (Ağustos 2020): 267-80. https://doi.org/10.19113/sdufenbed.652776.
EndNote Eröz İ, Ata N (01 Ağustos 2020) Aralıklı Sansürlü Veriler için Sağkalım Modelleri. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 24 2 267–280.
IEEE İ. Eröz ve N. Ata, “Aralıklı Sansürlü Veriler için Sağkalım Modelleri”, Süleyman Demirel Üniv. Fen Bilim. Enst. Derg., c. 24, sy. 2, ss. 267–280, 2020, doi: 10.19113/sdufenbed.652776.
ISNAD Eröz, İlknur - Ata, Nihal. “Aralıklı Sansürlü Veriler için Sağkalım Modelleri”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 24/2 (Ağustos 2020), 267-280. https://doi.org/10.19113/sdufenbed.652776.
JAMA Eröz İ, Ata N. Aralıklı Sansürlü Veriler için Sağkalım Modelleri. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2020;24:267–280.
MLA Eröz, İlknur ve Nihal Ata. “Aralıklı Sansürlü Veriler için Sağkalım Modelleri”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 24, sy. 2, 2020, ss. 267-80, doi:10.19113/sdufenbed.652776.
Vancouver Eröz İ, Ata N. Aralıklı Sansürlü Veriler için Sağkalım Modelleri. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2020;24(2):267-80.

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