Flexible Regression Models for Carcinogenesis Studies

M. Nikulin   ; Hong-Dar Isaac Wu

Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 10, Tome 339 (2006), pp. 78-101

Résumé

Dynamic or flexible regression models are used more and more often in carcinogenesis studies to relate lifetime distribution to the time-depending explanatory variables. In addition to the classical regression models such as Cox model, AFT model, Linear transformation model, Frailty model, etc. In the paper exposed the so-called flexible regression models which well adapted to study the cross-effects of survival functions, which are sometimes observed in clinical trials. A classical example is the well-known data concerning effects of chemotherapy (CH) and chemotherapy plus radiotherapy (CH+R) on the survival times of gastric cancers patients, see Stablein and Koutrouvelis (1985), Kleinbaum (1996), Klei and Moeschberger (1997), Wu, Hsieh and Chen (2002), Bagdonavicius, Hafdi and Nikulin (2004), etc. In this paper we give examples to illustrate possible applications of the Hsieh model (2001) and the SCE model, proposed by Bagdonavicius and Nikulin (2005), adapted to treat survival data with one crossing point. We do the comparison of both models.

Bibliographie

[1] O. Aalen, “A model for nonparametric regression analysis of counting processes”, Lect. Notes Statists, 2, eds. W. Klonecki, A. Kozek and J. Rosinski, Springer Verlag, New York, 1980, 1–25 | MR

[2] V. Bagdonavičius and M. Nikulin, Stochastic models of accelerated life, Advanced Topics in Stochastic Modelling, eds. J. Gutienez, M. Valderrama, World Scient., Singapore, 1994 | MR

[3] V. Bagdonavičius and M. Nikulin, Additive and Multiplicative Semiparametric Models in Accelerated Life Testing and Survival Analysis, Queen's Papers in Pure and Applied Mathematics, 108, Queen's Univ., Kingston, Ontarioo, 1998 | MR | Zbl

[4] V. Bagdonavičius and M. Nikulin, “Generalized proportional hazards model based on modified partial likelihood”, Lifetime Data Analysis, 5 (1999), 329–350 | DOI | MR | Zbl

[5] V. Bagdonavičius, M. Hafdi, and M. Nikulin, “The Generalized Proportional Hazards Model and its Application for Statistical Analysis of the Hsieh Model”, Proceedings of The Second Euro-Japanese Workshop on Stochastic Risk Modelling for Finance, Insurance, Production and Reliability (September 18–20, Chamonix, France), eds. T. Dohi, N. Limnios, S. Osaki, 2002, 42–53

[6] V. Bagdonavičius, M. Hafdi, K. El Himdi, and M. Nikulin, Analyse du modèle des hazards proportionnels généralisé. Application sur les donnés du cancer des poumons, Preprint 0201, I.F.R. “Santé Publique”, 2002

[7] V. Bagdonavičius, M. Hafdi, K. El Himdi, and M. Nikulin, Analysis of Survival Data with Cross-Effects of Survival Functions. Applications for Chemo and Radiotherapy Data, Preprint 0202, I.F.R. “Santé Publique”, 2002

[8] V. Bagdonavičius and M. Nikulin, Accelerated Life Models: Modeling and Statistical Analysis, Chapman and Hall/CRC, Boca Raton, 2002

[9] V. Bagdonavičius and M. Nikulin,, “Statistical analysis of survival and reliability data with multiple crossings of survival functions”, Comptes Rendus de l'Academie des Sciences de Paris, Ser. I, 340 (2005), 377–382 | MR | Zbl

[10] V. Bagdonavičius and M. Nikulin, “Analysis of survival data with non-proportional hazards and crossings of survival functions”, Quantitative Methods in Cancer and Humain Risk Assesment, eds. L. Edler, Ch. Kitsos, J. Wiley and Sons, NY, 2005, 193–209

[11] S. Bennett, “Analysis of survival data by the proportional odds model”, Statistics in Medicine, 2 (1983), 273–277 | DOI

[12] D. R. Cox, “Regression models and life tables”, J. R. Statist. Soc. B, 34 (1972), 187–220 | MR | Zbl

[13] R. Cox, “Partial likelihood”, Biometrika, 62 (1975), 269–276 | DOI | MR | Zbl

[14] D. R. Cox and D. Oakes,, Analysis of Suvival Data, Chapman and Hall, New York, 1984 | MR

[15] D. M. Dabrowska and K. A. Doksum, “Partial likelihood in Transformations Models with Censored Data”, Scand. J. Statist., 15 (1988), 1–23 | MR | Zbl

[16] D. Dabrowska, “Quantile regression in transformation models”, Sankhya, 67 (2005), 153–187 | MR

[17] D. Dabrowska, Information bounds and efficient estimation in a class of censored transformation models, arXiv: /math.ST/0608088 | MR

[18] D. Dabrowska, “Estimation in a class of semi-parametric transformation models”, Optimality, Second Eric L. Lehmann Symposium, Lecture Notes and Monograph Series, 49, ed. J. Rojo, Institute of Math. Statistics, 2006, 166–216 | MR

[19] P. Greenwood and M. Nikulin, A Guide to Chi-Squared Testing, John Wiley and Sons, New York, 1996 | MR

[20] P. Hougaard, “Survival models for heterogeneous populations derived from stable distributions”, Biometrika, 73:3 (1986), 387–396 | DOI | MR | Zbl

[21] F. Hsieh, “On heteroscedastic hazards regression models: theory and application”, Journal of the Royal Statistical Society, Series B, 63 (2001), 63–79 | DOI | MR | Zbl

[22] S. Johansen, “An extension of Cox's regression model”, Internat. Statist. Rev., 51 (1983), 165–174 | DOI | MR | Zbl

[23] K. Chen, Z. Jin, Z. Ying, “Semiparametric analysis of transformation models with censored data”, Biometrika, 89:3 (2002), 639–668 | DOI | MR

[24] D. Kleinbaum, Survival Analysis: A Self-Learning text, Springer-Verlag, New York, 1996 | Zbl

[25] J. P. Klein and M. L. Moeschberger, Survival Analysis, Springer, New York, 1997

[26] J. F. Lawless, Statistical Models and Methods for Lifetime Data, J. Wiley, New York, 1982 | MR | Zbl

[27] D. Y. Lin and C. J. Geyer, “Computational methods for semiparametric linear regression with censored data”, J. Comput. Graph. Statist., 1 (1992), 77–90 | DOI

[28] D. Y. Lin and Z. Ying, “Semiparametric analysis of the general additive-multiplicative hazard models for counting processes”, The Annals of Statistics, 23:5 (1996), 1712–1734 | DOI | MR

[29] T. Martinussen and T. Scheike, Dynamic regression models for survival analysis, Springer, New York, 2006 | MR | Zbl

[30] I. W. McKeague and P. D. Sasieni, “A partly parametric additive risk model”, Biometrika, 81:3 (1994), 501–514 | DOI | MR | Zbl

[31] S. A. Murphy and A. W. van der Vaart, “MLE in the proportional odds model”, Journal of the American Statistical Association, 92 (1997), 968–976 | DOI | MR | Zbl

[32] S. Piantadosi, Clinical Trials, J. Wiley and Sons, New York, 1997 | MR

[33] N. M. Sedyakin, “On one physical principle in reliability theory”, Techn. Cybernetics, 3 (1966), 80–87

[34] D. M. Stablein and I. A. Koutrouvelis, “A two sample test sensitive to crossing hazards in uncensored and singly censored data”, Biometrics, 41 (1985), 643–652 | DOI | MR | Zbl

[35] D. I. Wu, “Effect of Ignoring Heterogeneity in Hazards Regression”, Parametric and Semipametric Models with Applicatiions to Reliability, Survival Analysis, and Quality of Life, eds. M. Nikulin, N. Balakrishnan, M. Mesbah, N. Limnios, Birkhauser, Boston, 2004, 239–250 | MR

[36] H-D. I. Wu, “Statistical Inference for two-sample and regression models with heterogeneity effects: a collected-sample perspective”, Probability, Statistics and Modelling in Public Health, eds. M. Nikulin, D. Commenges, C. Huber, Springer, New York, 2006, 452–465 | MR

[37] H-D. I. Wu, “A Partial score test for difference among heterogeneous populations”, Journal of Statistical Planning and Inference, 137 (2007), 527–537 | DOI | MR | Zbl

[38] H-D. I. Wu and F. Hsieh, Heterogeneity and varying effect in hazards regression, Preprint. Schoool of Public Health, China Medical University, Taichung, Taiwan, 2002 | MR

[39] H-D. I. Wu, F. Hsieh, and C.-H. Chen, “Validation of a heteroscedastic hazards regression model”, Lifetime Data Analysis, 8 (2002), 21–34 | DOI | MR | Zbl

[40] S. Yang and R. L. Prentice, “Semiparametric inference in the Proportional odds regression model”, Journal of the American Statistical Association, 94 (1999), 125–136 | DOI | MR | Zbl