فهرست و منابع پایان نامه مفاهیم بقا
فهرست:
تعاریف و مفاهیم اولیه 1
1-1 مقدمه ای در مفاهیم بقا 2
1-2 خلاصه ای از مقدمات 5
1-3 روش دلتا ، نتایج مهم و مثالها 6
1-4 فرآیندهای وینر و گوسی مربوطه 11
1-4-1 اطلاعی از فرآیند وینر 11
1-4-2 تعریف و وجود فرآیند وینر 12
1-4-3 پل براونی 12
فصل دوم : سانسور و برش 14
21 مقدمه 15
22 سانسور راست 17
2-2-1 سانسور نوع یک 17
2-2-2 سانسور پیشروی نوع یک 19
2-2-3 سانسور تعمیم یافته نوع یک 21
2-2-4 سانسور نوع دو 23
2-2-5 سانسور پیشروی نوع دو تعمیم 24
2-2-6 سانسور تصادفی 24
2-3 سانسور چپ و فاصله‌ای 26
2-3-1 سانسور چپ 26
2-3-2 سانسور فاصله‌ای 28
2-4 برش 29
برش راست 29
2-5 ساختار درستنمایی برای داده‌های سانسور شده و داده‌های بریده شده 30
نکات عملی 35
نکات تئوری 35
2-6 برآورد ناپارامتری کمیتهای اصلی برای داده‌های از راست سانسور و بریده شده از چپ 37
2-6-2 برآوردگرهای توابع بقا و بخت تجمعی برای داده‌های از راست سانسور 38
فصل سوم: برآورد ناپارامتری از داده های بقای مقطعی 42
3-1 مقدمه 43
3-2 برآورد حد- حاصلضربی در مقابل برآورد واردی 51
3-2-1 یک حالت خاص 52
3-2-2 حالت کلی 54
3-3 برآورد ناپارامتری 58
3-4 خاصیت های مجانبی 63
3-5 کوواریانس های مجانبی توأم، برآورد ناپارامتری 81
3-6 برآورد ناپارامتری 85
3-6-1 NPMLEی 87
3-6-2 اعتبار 88
3-6-3 بوت استرپ بدیهی تعمیم یافته 89
فصل چهارم : بررسی خواص مجانبی MLE ی تابع بقا درنمونهگیری در طول- اُریب همراه با سانسور راست : رویکردی غیرشرطی 92
4-1 مقدمه 93
4- 2 مدل های شرطی در مقایسه با مدلهای غیرشرطی 96
4-3 علامتگذاری و موارد مقدماتی 97
4-4 برآورد و مجانب ها 100
4-5 کاربرد برای بقای همراه با دمانس 121
4-6 تفسیرهای آخر 122
کتابنامه 123
منبع:
Aalen, O. O., (1978b), "NonParametric Inference for a Family of Counting Processes, "The Annals of statistics, 6, 701-726.
Andersen. P. K., Borgan, Q., Gill, R. D. and Keiding, N. (1993), Statistical Models Based on Counting Processes, New York: Springer – verlag.
Asgharian, M., and Wolfson, D. B. (2001), "Asymptotic Behaviour of the MPMLE of the Survivor Function When the Data are Length-Biased and Subject to Right Censoring," Technical Report, McGill university, Dept. of Mathematics and Statistics.
Bilker, W. B., and Wang, M.-C. (1997), "Bootstrapping Left-Truncated and Right-Censored Data," Commumications in Statistics. Simulation and Computation, 26, 141-171.
Billingsley, P. (1968), Convergence of Probability Measures, New York: John Wiley.
Blumenthal, S. (1967), "Proportional Sampling in Life Length Studies, " Technometrics, 9, 205-218.
Brookmeyer, R., and Gail, M. H. (1987), "Biases in Prevalent Cohorts," Biometrics, 43, 739-749.
Brookmeyer, R., Gail, M. H., and Polk, B. F. (1987), "The Prevalent Cohort Study and the AIDS," American Journal of Epidemiology, 126, 14-24.
Chao, M. - T. (1987), "Influence Curves for Randomly Truncated Data," Biometrika, 74, 426-429.
Cox, D. R. (1969), "Some Sampling Problems in Technology," in New Developments in Survey Sampling. eds. Johnson and Smith. New York: Wiley.
Cox, D. R., and Oakes, D. (1984), Analysis of Survival Data, London: Chapmian & Hall.
Csorgo, M., and Revesz, P. (1981), Strong Approximations in probability and Statistics.
David, H. A., and Moeschberger, M. L., (1978) The Theory of Competing Risks. London: Charles Griffin.
Efron, B. (1981), "Censored Data and the Bootstrap," Journal of the American Statistical Association, 76, 312-321.
Gilbert, P. B., Lele, S. R., and Vardi, Y. (1999), "Maximum Likelihood Estimation in Semiparametric Selection Bias Models With Application to an AIDS Vaccine," Biometrika, 86,27-43.
Gill, R. D., Vardi, Y., and Wellner, J. A. (1988), "Large-Sample Theory of Empirical Distributions in Biased Sampling Models," The Annals of Statistics, 16, 1069-1112.
Gross, S., and Lai, T. I., (1996), "Bootstrap Methods for Truncated and Censored Data," Statistica Sinica, 65,09-530.
Huang. Y., and Wang. M.-C. (1995), "Estimating the Occurrence Rate for Prevalent Survival Data in Competing Risks Models," Journal of the American Statistical Association, 90, 1406-1415.
Hyde, J, (1977), "Testing survival Under Right Censoring and Left Truncation," Biometrika, 64, 225-230.
Kalbfleisch, J. D., and Lawless, J. F. (1988), "Inferences Based on Retrospective Ascertainment: An Analysis of the Data on Transfusion Related AIDS," Journal of the American Statistical Association, 84 , 360 – 372.
Kaplan, E. L., and Meier, P. (1958), "Nonparametric Estimation From Incomplete Observations," Journal of the American Statistical Association, 53, 457-481.
Keiding, N., and Gill, R. D. (1990), "Random Truncation Models and Markov Proccess," The Annals of Statistics, 18, 582 – 602.
Lagakos, S. W., Barraj, L. M., and De Gruttola, V. (1988), "Nonparametric Analysis of Truncated Survival Data With Application to AIDS," Biometrika, 75, 515- 524.
McFadden. J. A. (1962), "On the Lengths of intervals in a Stationary Point Process," Journal of the Royal Statistical Society, Ser. B, 24.364-382.
Nelson, W.,(1972), "Theory and Applications of Hazard plotting for Censored Failure Data," Technometrics, 14, 945-965.
Pan, W., and Chappell, R. (1998), "A Nonparametric Estimator of Survival Functions for Arbitrarily Truncated and Censored Data." Lifetime Data Analysis, 4,187-202.
Ross, S. M. (1983), Stochastic Processes, New York: John Wiley.
Stern, Y., Tang, M., Albert, M. S., Brandt, J., Jacobs, D. M., Bell, K., Marder, K., Sano, M., Devanand, D., Albert, S. M., and Tsai, W., (1997), "Predicting Time to Nursing Home Care and Death in Individuals With Alzheimer Disease," Journal of the American Medical Association, 277, 806-812.
Tsai, W.-Y., Jewell, N. P., and Wang, M.-C. (1987), "A Note on the Product-Limit Estimator Under Right Censoring and Left Truncation," Biometrika, 74, 883-886.
Tsodikov, A. (1998), " A Proportional Hazards Model Taking Acceunt of Long – Term Survivors," Biometrics, 54, 1508-1516.
Turnbull, B. W., (1974), "Nonparametric Estimation of a Survivorship Function with Doubly Censored Data," Journal of the American Statistical Association, 69, 169-173.
Turnbull, B. W. (1976), " The Empirical Distribution Function With Arbitrarily Grouped, Censored, and Truncated Data," Journal of the Royal Statistical Society, Ser. B, 38, 290-295.
Van der Laan, M. J., and Hubbard, A. E. (1998). "Locally Efficient Estimation of the Survival Distribution With Right-Censored Data and Convariates When Collection of Data is Delayed," Biometrika, 85, 771-783.
Vander Vaart, A. W. ( ), Mathematische statistiek.
Vardi, Y. (1982), "Nonparametric Estimation in the Presence of Length Bias," The Annals of Statistics, 10, 616-620.
____ (1985), "Empirical Distributions in Selection Bias Models," The Annals of Statistics, 13, 178-205.
____ (1989), "Multiplicative Censoring, Renewal Processes, Deconvolution and Decreasing Density," Biometrika, 76, 751-761.
Vardi, Y., and zhang, C.-H. (1992), "Large Sample Study of Empirical Distributions in a Random – Multiplitcative Censoring Model," The Annals of Statistics, 25, 1022-1039.
Wang, M.-C. (1987), "Product-Limit Estimates: A Generalized Maximum Likelihood Study," Communication in Statistics, Part A __ Theory and Methods, 6, 3117-3132.
___ (1989), "A Semiparametric Model for Randomly Truncated Data," Journal of the American Statistical Association, 84, 742-748.
___ (1991), "Nonparametric Estimation From Cross-Sectional Survival Data," Journal of the American Statistical Association, 86, 130-143.
____ (1996), "Hazards Regression Analysis for length-biased Data," Biometrika, 83, 343-354.
Wang, M.-C., Brookmeyer, R., and Jewell, N. P. (1993), "Statistical Models for Prevalent Cohort Data," Biometrics, 49, 1-11.
Wang, M.-C., Jewll, N. P., and Tsai, W.-Y. (1986), "Asymptotic Properties of the Product Limit Estimate Under Random Truncation," The Annals of Statistics, 14, 1597 – 1605.
Winter, B. B., and Foldes, A. (in press), " Product-limit Estimators for Use With Length-Biased Data," Canadian Journal of Statistics.
Wolfson. C., Wolfson, D., Asgharian, M., M'Lan, C. F., Qstbye, T, Rochwood, K., and Hogan, M., for the Clinical Progression of Dementia Study Group (2001), "A Re-Evaluation of the Duration of Survival After the Onset of Dementia," The New England Journal of Medicine. 344, 1111-1116.
Woodroofe, M. (1985), "Estimating a Distribution Function With Truncated Data, " The Annals of Statistics, 13, 163-177.