Yaşam çözümlemesinde çok durumlu modellerin geçiş olasılıklarının tahmini ve bir uygulama

Yıl 2024, Cilt: 17 Sayı: 1, 14 - 29, 30.06.2024

Esra Çiftçi , Duru Karasoy

Öz

Yaşam çözümlemesinde, tanımlanan bir olay gerçekleşene kadar geçen süre incelenmektedir. Bireyin ya da incelenen birimin başlangıç noktasından son noktaya varıncaya kadar geçirdiği sürede başka durumların yaşanması ve durumlar arasında geçişlerin olması söz konusudur. Çok durumlu yaşam çözümlemesi modelleri iki durumlu klasik yaşam çözümlemesi modellerinin genişletilmiş biçimidir. Literatürde en çok kullanılan çok durumlu model, üç durumlu modeldir.
Bu çalışma ile üç durumlu model tanıtılmış ve iki durumlu modelde geçiş olasılığı ve standart hata tahminlerinde kullanılan tahmin edici yaklaşımı üç durumlu modele uyarlanmıştır. Geçiş olasılıklarının tahmin edilmesinde kullanılan Aalen-Johansen, ön düzgünleştirilmiş Aalen-Johansen, yaşam verisi analizi, Landmark, ön düzgünleştirilmiş Landmark, Landmark Aalen-Johansen ve ön düzgünleştirilmiş Landmark Aalen-Johansen tahmin edicilerine düzeltme yapılmış ve durumlar arası bütün geçişler için olasılık ve standart hata değerleri hesaplanmıştır. Yöntemlerin uygulanabilirliğini göstermek ve karşılaştırmak amacıyla R programında yer alan kolon kanseri verileri ile çalışılmıştır. Düzeltilmiş tahmin edicilerin standart hata değerleri daha düşük elde edilmiştir.

Anahtar Kelimeler

Çok durumlu model, geçiş olasılıkları, yaşam çözümlemesi

Etik Beyan

Etik beyan gerekmemektedir.

Estimation of the transition probabilities of multi-state models in survival analysis and an application

Öz

The time until an event occurs is examined in survival analysis. During the time from the starting point of an individual or a unit under study to the endpoint, other events may occur, and transitions between states are possible. Multi-state survival analysis models are an extension of the classical two-state survival analysis models. The most commonly used multi-state model in the literature is the three-state model. In this study, the three-state model structure is briefly presented and the predictive approach used for transition probabilities and standard error estimates in the two-state model is adapted to the three-state model. Adjustments are made to Aalen-Johansen, presmoothed Aalen-Johansen, lifetime data analysis, Landmark, presmoothed Landmark, Landmark Aalen-Johansen, and presmoothed Landmark Aalen-Johansen estimators used to estimate transition probabilities and probabilities and standard error values for all transitions between states are calculated.To demonstrate and compare the applicability of the methods, colon cancer data available in the R program Survidm package is used. Adjusted estimators have provided lower standard error values.

Anahtar Kelimeler

Multi-state model, transition probabilities, survival analysis

Kaynakça

• [1] J. D. Kalbeisch, R. L. Prentice, 1980, The Statistical Analysis of Failure Time Data, John Wiley & Sons., New York.
• [2] D.R. Cox, D. Oakes, 1984, Analysis of Survival Data, Chapman and Hall, New York.
• [3] A. Hamerle, 1989, Multiple-spell regression models for duration data, Applied Statistics, 38, 127-138.
• [4] J. P. Klein, M. L. Moeschberger, 1997, Survival Analysis Techniques for Censored and Truncated Data, Springer, New York.
• [5] P. Hougaard, 2000, Analysis of Multivariate Survival Data, Statistics for Biology and Health, Springer-Verlag, New York.
• [6] H. Putter, M. Fiocco, B. Geskus, 2007, Tutorial in biostatistics: Competing risks and multi-state models, Statistics in Medicine, 26, 2389-2430.
• [7] P.K. Andersen, Ø. Borgan, R.D. Gill, N. Keiding, 1993, Statistical Models Based on Counting Processes, Springer-Verlag, New York.
• [8] L. Meira-Machado, C. Cadarso Suarez, J. de Una Alvarez, P. Andersen, 2009, Multi-state models for the analysis of time to event data, Statistical Methods in Medical Research, 18 (2), 195-222.
• [9] D.R. Cox, 1972, Regression models and life-tables, Journal of Royal Statistical Sociaety, Series B 34, 187-220.
• [10] S.W. Lagakos, 1976, A stochastic model for censored-survival data in the presence of an auxiliary variable, Biometrics, 32, 551-559.
• [11] O.O. Aalen, 1978, Nonparametric inference for a family of counting processes, Annals of Statistics, 6, 701–726.
• [12] O.O. Aalen, S. Johansen, 1978, An emprical transition matrix for nonhomogeneous Markov chains based on censored observations, Scandinavian Journal of Statistics, 5, 141-150.
• [13] D. Courgeau, E. Lelievre, 1992, Event History Analysis in Demography, Clarendon Press, Oxford.
• [14] H.P. Blossfeld, G. Rohwer, 1995, Techniques of Event History Modeling, Lawrence Erlbaum Associates, New Jersey.
• [15] D. Commenges, 1999, Multi-state models inepidemiology, Lifetime Data Analysis, 5, 315–27.
• [16] P. Hougaard, 1999, Multi-state models: A review, Lifetime Data Analysis, 239–264.
• [17] P.K. Andersen, N. Keiding, 2002, Multi-state models for event history analysis, Statistical Methods in Medical Research, 11, 91–115.
• [18] A. Moreira, J. de Una-Alvarez, L. Machado, 2013, Presmoothing the Aalen-Johansen estimator in the illness-death model, Electronic Journal of Statistics, 7, 1491-1516.
• [19] J. Beyersmann, A. Allignol, M. Schumacher, 2012, Competing Risks and Multistate Models with R, Springer Science+Business Media, London.
• [20] D.G. Kleinbaum, M. Klein, 2010, Survival Analysis (Vol. 3), Springer, New York.
• [21] E. Kaplan, P. Meier, 1958, Nonparametric estimation from incomplete observations, Journal of the American Statistical Association, 53(282), 457-481.
• [22] D. Collett, 2003, Modeling Survival Data in Medical Research. 2nd Edition, Chapman & Hall., New York.
• [23] A. Moreira, 2014, Methods for Analysis of Multi-state Survival Data, Phd thesis, Universidade do Minho, Braga.
• [24] L. Meira-Machado, J. de Una-Alvarez, C. Cadarso-Suarez, 2006, Nonparametric estimation of transition probabilities in a non-Markov illness-death model, Lifetime Data Analysis, 12, 325–44.
• [25] J. de Una Alvarez, L. Meira-Machado, 2015, Nonparametric estimation of transition probabilities in the non-Markov illness-death model:a comparative study, Biometrics, 71, 364-375.
• [26] H.C. Van Houwelingen, 2007, Dynamic prediction by landmarking in event history analysis, Scandinavian Journal of Statistics, 34 (1), 70-85.
• [27] G. Soutinho, L. Meira-Machado, 2020, Estimations of the transition probabilities in multi-state survival data: New developments and practical recommendations, Wseas Transactions on Mathematics, 19, 353-366. [28] H. Putter, C. Spitoni, 2018, Nonparametric estimation of transition probabilities in non-Markov multistate models:” The Landmark Aalen-Johansen estimator, Statistical Methods in Medical Research, 27, 2081-2092.
• [29] G. Soutinho, L. Meira-Machado, P. Oliveira, 2022, A comparison of presmoothing methods in the estimation of transition probabilities, Communications in Statistics-Simulation and Computation, 51 (9), 5202-5221.
• [30] G. Dikta, 1998, On semiparametric random censorship models, Journal of Statistical Planning and Inference, 66, 253-279.
• [31] A. Amorim, J. de Una-Alvarez, L. Meira-Machado, 2011, Presmoothing the transition probabilities in illness-death model, Statistics and Probability Letters, 81 (7), 797-806.
• [32] Q. Zaman, M. Iqbal, S. Din, R. Fazl-e, H. Nawaz, 2012, Proposed shrunken variance estimator for survival function, Gomal University Journal of Research, 28 (2), 9-26.
• [33] C.B. Borkowf, 2005, A simple hybrid variance estimator for the Kaplan-Meier survival function, Statistics in Medicine, 24, 827-851.
• [34] C. G. Moertel, T. R. Fleming, J. S. Macdonald, D. G. Haller, J. A. Laurie, P. J. Goodman, J. S. Ungerleider, W. A. Emerson, D. C. Tormey, J. H. Glick,, M. H. Veeder, J. A. Mailliard, 1990, Levamisole and fluorouracil for adjuvant therapy of resected colon carcinoma, New England Journal of Medicine, 322 (6), 352–358.
• [35] E. Çiftçi, 2023, Çok durumlu modellerde geçiş olasılıklarının tahmini, Hacettepe Üniversitesi, Fen Bilimleri Enstitüsü, Ankara.