Lectures on survival analysis

  • Richard D. Gill
Part of the Lecture Notes in Mathematics book series (LNM, volume 1581)


Point Process Empirical Process Supremum Norm Martingale Property Integrable Martingale 
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  1. O.O. Aalen (1972), Estimering av Risikorater for Prevensjonsmidlet 'spiralen' (in Norwegian), Master's thesis, Inst. Math., Univ. Oslo.Google Scholar
  2. O.O. Aalen (1975), Statistical Inference for a Family of Counting Processes, PhD thesis, Univ. California, Berkeley.zbMATHGoogle Scholar
  3. O.O. Aalen (1976), Nonparametric inference in connection with multiple decrement models, Scand. J. Statist. 3, 15–27.MathSciNetzbMATHGoogle Scholar
  4. O.O. Aalen (1978), Nonparametric inference for a family of counting processes, Ann. Statist. 6, 701–726.MathSciNetCrossRefzbMATHGoogle Scholar
  5. O.O. Aalen and S. Johansen (1978), An empirical transition matrix for nonhomogeneous Markov chains based on censored observations, Scand. J. Statist. 5, 141–150.MathSciNetzbMATHGoogle Scholar
  6. M.G. Akritas (1986), Bootstrapping the Kaplan-Meier estimator, J. Amer. Statist. Assoc. 81, 1032–1038.MathSciNetzbMATHGoogle Scholar
  7. W. Alexi, B. Chor, O. Goldreich, and C.P. Schnorr (1988), RSA and Rabin functions: certain parts are as hard as the whole, SIAM J. Comp. 17, 194–209.MathSciNetCrossRefzbMATHGoogle Scholar
  8. B. Altshuler (1970), Theory for the measurement of competing risks in animal experiments, Math. Biosci. 6, 1–11.MathSciNetCrossRefzbMATHGoogle Scholar
  9. P.K. Anderson, Ø. Borgan, R.D. Gill, and N. Keiding, (1982), Linear nonparametric tests for comparison of counting processes, with application to censored survival data (with discussion), Int. Statist. Rev. 50, 219–258; Amendment, 52, 225 (1984).CrossRefzbMATHGoogle Scholar
  10. P.K. Andersen, Ø. Borgan, R.D. Gill, and N. Keiding (1993), Statistical Models Based on Counting Processes, Springer, New York.CrossRefzbMATHGoogle Scholar
  11. A.J. Baddeley (1987), Integrals on a moving manifold and geometrical probability, Adv. Appl. Probab. 9, 588–603.MathSciNetCrossRefzbMATHGoogle Scholar
  12. A.J. Baddeley and R.D. Gill (1992), Kaplan-Meier estimators for interpoint distance distributions of spatial point processes, Preprint 718, Dept. Math., Univ. Utrecht; revised version (1993), submitted to Ann. Statist. Google Scholar
  13. A.J. Baddeley, R.A. Moyeed, C.V. Howard, S. Reid, and A. Boyde (1993), Analysis of a three-dimensional point pattern with replication, Appl. Statist. 42, to appear.Google Scholar
  14. L.G. Barendregt and M.J. Rottschäfer (1991), A statistical analysis of spatial point patterns: a case study, Statistica Neerlandica 45, 345–363.CrossRefGoogle Scholar
  15. M. Ben-Or, B. Chor, and A. Shamir (1983), On the cryptographic security of single RSA bits, Proc. 15th ACM Symp. Theor. Comp., 421–430.Google Scholar
  16. P.J. Bickel, C.A.J. Klaassen, Y. Ritov, and J.A. Wellner (1993), Efficient and Adaptive Inference for Semiparametric Models, Johns Hopkins University Press, Baltimore (in press).zbMATHGoogle Scholar
  17. M. Blum and S. Micali (1984), How to generate cryptographically strong sequences of pseudo-random bits, SIAM J. Comp. 13, 850–864.MathSciNetCrossRefzbMATHGoogle Scholar
  18. P.E. Böhmer (1912), Theorie der unabhängigen Wahrscheinlichkeiten, Rapports, Mém. et Procés-verbaux 7 e Congrès Int. Act. Amsterdam 2, 327–343.Google Scholar
  19. S.J. Brands (1991), The Cryptographic Approach to Pseudo-random Bit Generation, Master's thesis, Dept. Math. Univ. Utrecht.Google Scholar
  20. N.E. Breslow and J.J. Crowley (1974), A large sample study of the life table and product limit estimates under random censorship, Ann. Statist. 2, 437–453.MathSciNetCrossRefzbMATHGoogle Scholar
  21. C.F. Chung (1989a), Confidence bands for percentile residual lifetime under random censorship model, J. Multiv. Anal. 29, 94–126.MathSciNetCrossRefzbMATHGoogle Scholar
  22. C.F. Chung (1989b), Confidence bands for quantile function under random censorship, Ann. Inst. Statist. Math. 42, 21–36.MathSciNetCrossRefzbMATHGoogle Scholar
  23. P. Courrège and P. Priouret (1965), Temps d'arrêt d'un fonction aléatoire, Publ. Inst. Stat. Univ. Paris 14, 245–274.zbMATHGoogle Scholar
  24. D.R. Cox (1972), Regression models and life-tables (with discussion), J. Roy. Statist. Soc. (B) 34, 187–220.zbMATHGoogle Scholar
  25. D.R. Cox (1975), Partial likelihood, Biometrika 62, 269–276.MathSciNetCrossRefzbMATHGoogle Scholar
  26. M.W. Crofton (1869), Sur quelques théorèmes du calcul intégral, Comptes Rendus de l'Académie des Sciences de Paris 68, 1469–1470.zbMATHGoogle Scholar
  27. D.M. Dabrowska (1988), Kaplan-Meier estimate on the plane, Ann. Statist 16, 1475–1489.MathSciNetCrossRefzbMATHGoogle Scholar
  28. D.M. Dabrowska (1993), Product integrals and measures of dependence, Preprint, Dept. Biostatistics, Univ. Calif., Los Angeles.Google Scholar
  29. B. van Dalen (1993), Ancient and Mediaeval Astronomical Tables: Mathematical Structure and Parameter Values, Ph.D. Thesis, Dept. Math., Univ. Utrecht.Google Scholar
  30. A.P. Dempster, N.M. Laird, and D.R. Rubin (1977), Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion), J. Roy. Statist. Soc. (B) 39, 1–38.MathSciNetzbMATHGoogle Scholar
  31. P.J. Diggle (1983), Statistical Analysis of Spatial Point Patterns, Academic Press, London.zbMATHGoogle Scholar
  32. R.L. Dobrushin (1953), Generalization of Kolmogorov's equations for a Markov process with a finite number of possible states, Mat. Sb. (N.S.) 33, 567–596 (in Russian).Google Scholar
  33. R.L. Dobrushin (1954), Study of regularity of Markov processes with a finite number of possible states, Mat. Sb. (N.S.) 34, 542–596 (in Russian).Google Scholar
  34. S.I. Doguwa (1990), On edge-corrected kernel-based pair correlation function estimators for point processes. Biom. J. 32, 95–106.CrossRefGoogle Scholar
  35. S.I. Doguwa and G.J.G. Upton (1990), On the estimation of the nearest neighbour distribution, G(t), for point processes, Biom. J. 32, 863–876.CrossRefGoogle Scholar
  36. J.D. Dollard and C.N. Friedman (1979), Product Integration with Applications to Differential Equations (with an appendix by P. R. Masani), Addison-Wesley, Reading, Massachusetts.zbMATHGoogle Scholar
  37. H. Doss and R.D. Gill (1992), A method for obtaining weak convergence results for quantile processes, with applications to censored survival data, J. Amer. Statist. Assoc. 87, 869–877.MathSciNetCrossRefzbMATHGoogle Scholar
  38. R.M. Dudley (1966), Weak convergence of probabilities on nonseparable metric spaces and empirical measures on Euclidean spaces, Illinois J. Math. 10, 109–126.MathSciNetzbMATHGoogle Scholar
  39. R.M. Dudley (1992), Empirical processes: p-variation for p≤2 and the quantile-quantile and f FdG operators, Preprint, Dept. Math., Mass. Inst. Tech.Google Scholar
  40. B. Efron (1967), The two sample problem with censored data, Proc. 5th Berkeley Symp. Math. Statist. Probab. 4, 851–853.Google Scholar
  41. B. Efron (1979), Bootstrap methods: Another look at the jackknife, Ann. Statist. 7, 1–26.MathSciNetCrossRefzbMATHGoogle Scholar
  42. B. Efron (1981), Censored data and the bootstrap, J. Amer. Statist. Assoc. 76, 312–319.MathSciNetCrossRefzbMATHGoogle Scholar
  43. B. Efron and I.M. Johnstone (1990), Fisher's information in terms of the hazard rate, Ann. Statist. 18, 38–62.MathSciNetCrossRefzbMATHGoogle Scholar
  44. E.M.R.A. Engel (1992), A Road to Randomness in Physical Systems, Springer Lecture Notes in Statistics 71.Google Scholar
  45. H. Federer (1969), Geometric Measure Theory, Springer Verlag, Heidelberg.zbMATHGoogle Scholar
  46. A.M. Ferrenberg, D.P. Landau, and Y.J. Wong (1992), Monte Carlo simulations: hidden errors from ‘good’ random number generators, Phys. Rev. Letters 69, 3382–3384.CrossRefGoogle Scholar
  47. T.R. Fleming and D.P. Harrington (1991), Counting Processes and Survival Analysis, Wiley, New York.zbMATHGoogle Scholar
  48. M.A. Freedman (1983), Operators of p-variation and the evolution representation theorem, Trans. Amer. Math. Soc. 279, 95–112.MathSciNetzbMATHGoogle Scholar
  49. R.D. Gill (1980), Censoring and Stochastic Integrals, Mathematical Centre Tracts 124, Mathematisch Centrum, Amsterdam.zbMATHGoogle Scholar
  50. R.D. Gill (1980b), Nonparametric estimation based on censored observations of a Markov renewal process, Z. Wahrsch. verw. Geb. 53, 97–116.MathSciNetCrossRefzbMATHGoogle Scholar
  51. R.D. Gill (1981), Testing with replacement and the product limit estimator, Ann. Statist. 9, 853–860.MathSciNetCrossRefzbMATHGoogle Scholar
  52. R.D. Gill (1983), Large sample behavior of the product-limit estimator on the whole line, Ann. Statist. 11, 49–58.MathSciNetCrossRefzbMATHGoogle Scholar
  53. R.D. Gill (1986), On estimating transition intensities of a Markov process with aggregated data of a certain type: ‘Occurrences but no exposures', Scand. J. Statist. 13, 113–134.MathSciNetzbMATHGoogle Scholar
  54. R.D. Gill (1989), Non-and semi-parametric maximum likelihood estimators and the von Mises method (Part 1), Scand. J. Statist. 16, 97–128.MathSciNetzbMATHGoogle Scholar
  55. R.D. Gill (1992), Multivariate survival analysis, Theory Prob. Appl. 37 (English translation), 18–31 and 284–301.MathSciNetCrossRefzbMATHGoogle Scholar
  56. R.D. Gill and S. Johansen (1990), A survey of product-integration with a view towards application in survival analysis, Ann. Statist. 18, 1501–1555.MathSciNetCrossRefzbMATHGoogle Scholar
  57. R.D. Gill and B.Ya. Levit (1992), Applications of the van Trees inequality: a Bayesian Cramér-Rao bound, Preprint 733, Dept. Math., Univ. Utrecht.Google Scholar
  58. R.D. Gill, M.J. van der Laan, and J.A. Wellner (1993), Inefficient estimators of the bivariate survival function for three multivariate models, Preprint 767, Dept. Math., Univ. Utrecht.Google Scholar
  59. R.D. Gill and A.W. van der Vaart (1993), Non-and semi-parametric maximum likelihood estimators and the von Mises Method (Part 2), Scand. J. Statist. 20.Google Scholar
  60. M.J. Gillespie and L. Fisher (1979), Confidence bands for the Kaplan-Meier survival curve estimates, Ann. Statist. 7, 920–924.MathSciNetCrossRefzbMATHGoogle Scholar
  61. M. Greenwood (1926), The natural duration of cancer, Reports on Public Health and Medical Subjects 33, 1–26, His Majesty's Stationery Office, London.Google Scholar
  62. P. Groeneboom and J.A. Wellner (1992), Information Bounds and Nonparametric Maximum Likelihood Estimation, Birkhäuser Verlag, Basel.CrossRefzbMATHGoogle Scholar
  63. H.J. Hall and J.A. Wellner (1980), Confidence bands for a survival curve from censored data, Biometrika 67, 133–143.MathSciNetCrossRefzbMATHGoogle Scholar
  64. N.L. Hjort (1985a), Bootstrapping Cox's regression model, Tech. Rept. 241, Department of Statistics, Stanford University, California.Google Scholar
  65. N.L. Hjort (1985b), Discussion of the paper by P.K. andersen and Ø. Borgan, Scand. J. Statist. 12, 141–150.Google Scholar
  66. J. Jacod (1975), Multivariate point processes: Predictable projection, Radon-Nikodym derivatives, representation of martingales, Z. Wahrsch. verw. Geb. 31, 235–253.MathSciNetCrossRefzbMATHGoogle Scholar
  67. J. Jacod and A.N. Shiryaev (1987), Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin.CrossRefzbMATHGoogle Scholar
  68. N. Jewell (1982), Mixtures of exponential distributions, Ann. Statist. 10, 479–484.MathSciNetCrossRefzbMATHGoogle Scholar
  69. E.L. Kaplan and P. Meier (1958), Non-parametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53, 457–481, 562–563.MathSciNetCrossRefzbMATHGoogle Scholar
  70. R.L. Karandikar (1983), Multiplicative stochastic integration, pp. 191–199 in: V. Mandrekar and H. Salehi (eds), Prediction Theory and Harmonic Analysis, North-Holland, Amsterdam.Google Scholar
  71. N. Keiding and R.D. Gill (1990), Random truncation models and Markov processes, Ann. Statist. 18, 582–602.MathSciNetCrossRefzbMATHGoogle Scholar
  72. J. Kiefer and J. Wolfowitz (1956), Consistency of the maximum likelihood estimator in the presence of infinitely many nuisance parameters, Ann. Math. Statist. 27, 887–906.MathSciNetCrossRefzbMATHGoogle Scholar
  73. D.E. Knuth (1981), The Art of Computer Programming, vol. 2: Seminumerical Algorithms, Addison-Wesley.Google Scholar
  74. M.J. van der Laan (1993a), General identity for linear parameters in convex models with applications to efficiency of the (NP)MLE, Preprint 765, Dept. Math., Univ. Utrecht.Google Scholar
  75. M.J. van der Laan (1993b), Efficiency of the NPMLE in the line segment problem, Preprint 773, Math. Inst., Univ. Utrecht.Google Scholar
  76. M.J. van der Laan (1993c), Repairing the NPMLE with application to the bivariate censoring model, Preprint, Dept. Math., Univ. Utrecht.Google Scholar
  77. G.M. Laslett (1982a), The survival curve under monotone density constraints with application to two-dimensional line segment processes, Biometrika 69, 153–160.MathSciNetGoogle Scholar
  78. G.M. Laslett (1982b), Censoring and edge effects in areal and line transect sampling of rock joint traces, Math. Geol. 14, 125–140.CrossRefGoogle Scholar
  79. B.Ya. Levit (1990), Approximately integrable linear statistical models in non-parametric estimation, Tech. Rep. 90-37C, Dept. Statist., Purdue Univ.Google Scholar
  80. M. Luby (1993), Pseudo-Randomness and Applications, Princeton Univ. Press.Google Scholar
  81. J.S. MacNerney (1963), Integral equations and semigroups, Illinois J. Math. 7, 148–173.MathSciNetzbMATHGoogle Scholar
  82. P.R. Masani (1981), Multiplicative partial integration and the Trotter product formula, Adv. Math. 40, 1–9.MathSciNetCrossRefzbMATHGoogle Scholar
  83. D. Mauro (1985), A combinatoric approach to the Kaplan-Meier estimator, Ann. Statist. 13, 142–149.MathSciNetCrossRefzbMATHGoogle Scholar
  84. P. Meier (1975), Estimation of a distribution function from incomplete observations, pp. 67–87 in: J. Gani (ed.), Perspectives in Probability and Statistics, Applied Probability Trust, Sheffield.Google Scholar
  85. R.E. Miles (1974), On the elimination of edge-effects in planar sampling, pp. 228–247 in: E.F. Harding and D.G. Kendall (eds.), Stochastic Geometry (a tribute to the memory of Rollo Davidson), Wiley, New York.Google Scholar
  86. S.A. Murphy (1993), Consistency in a proportional hazards model incorporating a random effect, Ann. Statist. 21, to appear.Google Scholar
  87. V.N. Nair (1981), Plots and tests for goodness of fit with randomly censored data, Biometrika 68, 99–103.MathSciNetCrossRefGoogle Scholar
  88. V.N. Nair (1984), Confidence bands for survival functions with censored data: a comparative study, Technometrics 14, 265–275.CrossRefGoogle Scholar
  89. G. Marsaglia and A. Zaman (1991), A new class of random number generators, Ann. Appl. Probab. 1, 462–480.MathSciNetCrossRefzbMATHGoogle Scholar
  90. W. Nelson (1969), Hazard plotting for incomplete failure data, J. Qual. Technol. 1, 27–52.Google Scholar
  91. G. Neuhaus (1992), Conditional rank tests for the two-sample problem under random censorship: treatment of ties, in: Vilaplana (ed.), V Proceedings Statistics in the Basque Country.Google Scholar
  92. G. Neuhaus (1993), Conditional rank tests for the two-sample problem under random censorship, Ann. Statist. (to appear).Google Scholar
  93. G.G. Nielsen, R.D. Gill, P.K. Andersen, and T.I.A. Sørensen (1992), A counting process approach to maximum likelihood estimation in fraily models, Scand. J. Statist. 19, 25–43.MathSciNetzbMATHGoogle Scholar
  94. G. Peano (1888), Intégration par séries des équations différentielles linéaires, Math. Ann. 32, 450–456.MathSciNetCrossRefzbMATHGoogle Scholar
  95. J. Pfanzagl (1988), Consistency of maximum likelihood estimators for certain nonparametric families, in particular: mixtures, J. Statist. Planning and Inference 19, 137–158.MathSciNetCrossRefzbMATHGoogle Scholar
  96. D. Pollard (1984), Convergence of Stochastic Processes, Springer-Verlag, New York.CrossRefzbMATHGoogle Scholar
  97. D. Pollard (1990), Empirical processes: Theory and Applications, Regional conference series in probability and statistics 2, Inst. Math. Statist., Hayward, California.zbMATHGoogle Scholar
  98. R.L. Prentice and J. Cai (1992a), Covariance and survivor function estimation using censored multivariate failure time data, Biometrika 79, 495–512.MathSciNetCrossRefzbMATHGoogle Scholar
  99. R.L. Prentice and J. Cai (1992b), Marginal and conditional models for the analysis of multivariate failure time data, pp. 393–406 in: J.P. Klein and P.K. Goel (eds), Survival Analysis: State of the Art, Kluwer, Dordrecht.CrossRefGoogle Scholar
  100. P. Protter (1990), Stochastic Integration and Differential Equations (a New Approach), Springer.Google Scholar
  101. M. Rabin (1979), Digitalized signatures and public key functions as intractable as factorization, Tech. Rep. 212, Lab. Comp. Sci., Mass. Inst. Tech.Google Scholar
  102. R. Rebolledo (1980), Central limit theorems for local martingales, Z. Wahrsch. verw. Geb. 51, 269–286.MathSciNetCrossRefzbMATHGoogle Scholar
  103. J.A. Reeds (1976), On the Definition of von Mises Functionals, PhD thesis, Research Rept. S-44, Dept. Statist., Harvard Univ.Google Scholar
  104. N. Reid (1981), Influence functions for censored data, Ann. Statist. 9, 78–92.MathSciNetCrossRefzbMATHGoogle Scholar
  105. A. Rényi (1953), On the theory of order statistics, Acta Math. Acad. Sci. Hungar. 4, 191–231.MathSciNetCrossRefzbMATHGoogle Scholar
  106. B.D. Ripley (1981), Spatial Statistics, Wiley, New York.CrossRefzbMATHGoogle Scholar
  107. B.D. Ripley (1988), Statistical Inference for Spatial Processes, Cambridge Univ. Press. *** DIRECT SUPPORT *** A00I6B38 00003Google Scholar

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© Springer-Verlag 1994

Authors and Affiliations

  • Richard D. Gill
    • 1
  1. 1.Mathematical InstituteUniversity UtrechtUtrechtNetherlands

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