Multivariate survival analysis and competing risks

Multivariate Survival Analysis and Competing Risks

Volumn , Issue , 2012, Pages 1-377

  Crowder, Martin ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85055391829     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1201/b11893     Document Type: Book

References (427)

1. Andersen, P.K., Borgan, O., Gill, R.D., and Keiding, N. (1993) Statistical Models Based on Counting Processes. Springer-Verlag, New York.
2. Bedford, T., and Cooke, R.M. (2001) Probabilistic Risk Analysis: Foundations and Methods. Cambridge University Press, Cambridge.
3. Chiang, C.L. (1968) Introduction to Stochastic Processes in Biostatics. Wiley, New York.
4. Collett, D. (2003) Modelling Survival Data in Medical Research, Second Edition. Chapman & Hall/CRC Press, Boca Raton, FL.
5. Cook, R.J., and Lawless, J.F. (2007) The Statistical Analysis of Recurrent Events. Springer, New York.
6. Cox, D.R. (1962) Renewal Theory. Methuen, London.
7. Cox, D.R., and Oakes, D. (1984) Analysis of Survival Data. Chapman & Hall, London.
8. Crowder, M.J., Kimber, A.C., Smith, R.L., and Sweeting, T.J. (1991) Statistical Analysis of Reliability Data. Chapman & Hall, London.
9. David, H.A., and Moeschberger, M.L. (1978) The Theory of Competing Risks. Griffin, London.
10. Elandt-Johnson, R.C., and Johnson, N.L. (1980) Survival Models and Data Analysis. Wiley, New York.
11. Fleming, T.R., and Harrington, D.P. (1991) Counting Processes and Survival Models. Wiley, New York.
12. Groenboom, P., and Wellner, J.A. (1992) Nonparametric Maximum Likelihood Estimators for Interval Censoring and Deconvolution. Birkhauser, Boston.
13. Hougaard, P. (2000) Analysis of Multivariate Survival Data. Springer-Verlag, New York.
14. Kalbfleisch, J.D., and Prentice, R.L. (1980) The Statistical Analysis of Failure Time Data. Wiley, New York.
15. Kalbfleisch, J.D., and Prentice, R.L. (2002) The Statistical Analysis of Failure Time Data, Second Edition.Wiley, New York.
16. Kemeny, J.G., and Snell, J.L. (1960) Finite Markov Chains. Van Nostrand, Princeton, NJ.
17. King, J.R. (1971) Probability Charts for Decision Making. Industrial Press, New York.
18. Lawless, J.F. (1982) Statistical Models and Methods for Lifetime Data. Wiley, New York.
19. Lawless, J.F. (2003) Statistical Models and Methods for Lifetime Data, Second Edition. Wiley, New York.
20. Martz, H.F. and Waller, R.A. (1982) Bayesian Reliability Analysis. Wiley, New York.
21. McCullagh, P., and Nelder, J.A. (1989) Generalized Linear Models, Second Edition. Chapman & Hall/CRC Press, Boca Raton, FL.
22. Nelson, W.B. (1982) Applied Life Data Analysis. Wiley, New York.
23. Nelson, W.B. (1990) Accelerated Testing: Statistical Models, Test Plans and Data Analysis. Wiley, New York.
24. Sobczyk, K., and Spencer, Jr., B.F. (1992) Random Fatigue: From Data to Theory. Academic Press, New York.
25. Therneau, T.M., and Grambsch, P.M. (2000) Modelling Survival Data: Extending the Cox Model. Springer-Verlag, New York.
26. Williams, D. (1991) Probability with Martingales. Cambridge University Press, Cambridge.
27. Wolstenholme, L. (1998) Reliability Modelling: a Statistical Approach. Chapman & Hall/CRC Press, Boca Raton, FL.
28. Aalen, O.O. (1975) Statistical Inference for a Family of Counting Processes. Ph.D. Thesis, University of California, Berkeley.
29. Aalen, O.O. (1995) Phase type distributions in survival analysis. Scand. J. Statist. 22, 447-463.
30. Albert, J.R.G., and Baxter, L.A. (1995) Applications of theEMalgorithm to the analysis of life length data. Appl. Statist. 44, 323-348.
31. Allen, W.R. (1963) A note on the conditional probability of failure when hazards are proportional. Operations Res. 11, 658-659.
32. Armitage, P. (1959) The comparison of survival curves. J. Roy. Statist. Soc. A 122, 279-300.
33. Barlow, W.E., and Prentice, R.L. (1988) Residuals for relative risk regression. Biometrika 75, 65-74.
34. Boardman T.J., and Kendell, P.J. (1970) Estimation in compound exponential failure models. Technometrics 12, 891-900.
35. Breslow, N., and Crowley, J. (1974) A large sample study of the life table and product limit estimates under random censorship. Ann. Statist. 2, 437-453.
36. Buckley, J., and James, I. (1979) Linear regression with censored data. Biometrika 66, 429-436.
37. Caroni, C., Crowder, M.J., and Kimber, A.C. (2010) Proportional hazards models with discrete frailty. LIDA 16, 374-384.
38. Cox, D.R. (1972) Regression models and life tables (with discussion). J. Roy. Statist. Soc. B 34, 187-220.
39. Cox, D.R. (1975) Partial likelihood. Biometrika 62, 269-276.
40. Crowder, M.J. (1990) On some nonregular tests for a modified Weibull distribution. Biometrika 77, 499-506.
41. Crowder, M.J. (1996) Some tests based on extreme values for a parametric survival model. J. Roy. Statist. Soc. 58, 417-424.
42. Crowder, M.J. (2000) Tests for a family of survival models based on extremes. In Recent Advances in Reliability Theory, Eds. N. Limnios and M. Nikulin, Birkhauser, Boston, 307-321.
43. Davison, A.C., and Snell, E.J. (1991) Residuals and diagnostics. In Statistical Theory and Modelling: In Honour of Sir David Cox, Eds. D.V. Hinkley, N. Reid, and E.J. Snell, Chapman & Hall, London, 83-106.
44. Desmond, A.F., and Chapman, G.R. (1993) Modelling task completion data with inverse Gaussian mixtures. Applied Statistics 42, 603-613.
45. Gompertz, B. (1825) On the nature of the function expressive of the law of human mortality. Phil. Trans. Roy. Soc. (London) 115, 513-583.
46. Grambsch, P.M., and Therneau, T.M. (1994) Proportional hazards tests and diagnostics based on weighted residuals. Biometrika 81, 515-526.
47. Hill, D.L., Saunders, R., and Purushottam, W.L. (1980) Maximumlikelihood estimation for mixtures. Can. J. Statist. 8, 87-93.
48. Hougaard, P. (1984) Life table methods for heterogeneous populations: distributions describing the heterogeneity. Biometrika 71, 75-83.
49. Hougaard, P. (1986a) Survival models for heterogeneous populations derived from stable distributions. Biometrika 73, 387-396.
50. Huang, J. (1996) Efficient estimation for the proportional hazards model with interval censoring. Ann. Statist. 24, 540-568.
51. Huang, J., and Wellner, J.A. (1995) Asymptotic normality of the NPMLE of linear functionals for interval censored data: Case I. Statist. Neerlandica 49, 153-163.
52. Jewell, N.P. (1982) Mixtures of exponential distributions. Ann. Statist. 10, 479-484.
53. Kalbfleisch, J.D., and Prentice, R.L. (1973) Marginal likelihoods based on Cox’s regression and life model. Biometrika 60, 267-279.
54. Kaplan, E.L., and Meier, P. (1958) Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53, 457-481.
55. Kimber, A.C., and Hansford, A.R. (1993) A statistical analysis of batting in cricket. J. Roy. Statist. Soc. A 156, 443-455.
56. Laird, N. (1978) Nonparametric maximum likelihood estimation of a mixing distribution. J. Amer. Statist. Assoc. 73, 805-811.
57. Lawless, J.F. (1983) Statistical methods in reliability (with comments). Technometrics 25, 305-335.
58. Lawless, J.F., Crowder, M.J., and K.-A Lee (2009) Analysis of reliability and warranty claims in products with age and usage scales. Technometrics 51, 14-24.
59. Lesperance, M.L., and Kalbfleisch, J.D. (1992) An algorithm for computing the nonparametric MLE of a mixing distribution. J. Amer. Statist. Assoc. 87, 120-126.
60. Lindsay, B.G. (1983a) The geometry of mixture likelihoods: A general theory. Ann. Statist. 11, 86-94.
61. Lindsay, B.G. (1983b) The geometry of mixture likelihoods, Part II: The exponential family. Ann. Statist. 11, 783-792.
62. Maguluri, G., and Zhang, C.-H. (1994) Estimation in the mean residual lifetime regression model. J. Roy. Statist. Soc. 56, 477-489.
63. Makeham, W.M. (1860) On the law of mortality and the construction of annuity tables. J. Inst. Actuaries 8, 301-310.
64. McGilchrist, C.A., and Aisbett, C.W. (1991) Regression with frailty in survival analysis. Biometrics 47, 461-466.
65. Meier, P. (1975) Estimation of a distribution function from incomplete observations. In Perspectives in Probability and Statistics, Ed. J. Gani, Applied Probability Trust, Sheffield, 67-87.
66. Miller, R.G. (1976) Least squares with censored data. Biometrika 63, 449-464.
67. Nadas, A. (1970a) On proportional hazard functions. Technometrics 12, 413-416.
68. North, P., and Cormack, R.M. (1981) On Seber’s method for estimating age-specific bird survival rates from ringing recoveries. Biometrics 37, 103-112.
69. Oakes, D. (1981) Survival times: Aspects of partial likelihood. Int. Statist. Rev. 49, 235-264.
70. Oakes, D., and Desu, T. (1990) A note on residual life. Biometrika 77, 409-410.
71. Peacock, S.T., Keller, A.Z., and Locke, N.J. (1985) Reliability predictions for diesel generators. Reliability ’85, 4C/5/1-4C/5/12.
72. Peto, R. (1972) Contribution to discussion of paper by D.R. Cox. J. Roy. Statist. Soc. B 34, 205-207.
73. Peto, R. (1973) Experimental survival curves for interval-censored data. Applied Statistics 22, 86-91.
74. Peto, R., and Lee, P. (1973) Weibull distributions for continuous carcinogenesis experiments. Biometrics 29, 457-470.
75. Peto, R., and Peto, J. (1972) Asymptotically efficient rank invariant test procedures (with discussion). J. Roy. Statist. Soc. 135, 185-206.
76. Pike, M.C. (1966) A method of analysis of a certain class of experiments in carcinogenesis. Biometrics 22, 142-161.
77. Prentice, R.L., and El Shaarawi, A. (1973) A model for mortality rates and a test of fit for the Gompertz force of mortality. Applied Statistics 22, 301-314.
78. Prentice, R.L., and Breslow, N.E. (1978) Retrospective studies and failure time models. Biometrika 65, 153-158.
79. Schoenfeld, D. (1982) Partial residuals for the proportional hazards regression model. Biometrika 69, 239-241.
80. Simar, L. (1976) Maximum likelihood estimation of a compound Poisson process. Ann. Statist. 4, 1200-1209.
81. Singpurwalla, N.D., and Youngren, M.A. (1990) Models for dependent lifelengths induced by common environments. In Topics in Statistical Dependence, Eds. H.W. Block, A.R. Sampson, and T.H. Savits, Institute of Mathematical Statistics, Hayward, CA, 435-441.
82. Singpurwalla, N.D. (1995) Survival in dynamic environments. Statistical Science 10, 86-103.
83. Smith, R.L. (1991) Weibull regression models for reliability data. Rel. Eng. System Safety 34, 35-57.
84. Turnbull, B.W. (1974) Nonparametric estimation of a survivorship function with doubly censored data. J. Amer. Statist. Assoc. 69, 169-173.
85. Turnbull, B.W. (1976) The empirical distribution function with arbitrarily grouped, censored and truncated data. J. Roy. Statist. Soc. B 38, 290-295.
86. Vaupel, J.W., Manton, K.G., and Stallard, E. (1979) The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16, 439-454.
87. Weinberg, C.R., and Gladen, B.C. (1986) The beta-geometric distribution applied to comparative fecundability studies. Biometrics 42, 547-560.
88. Whitmore, G.A., Crowder, M.J., and Lawless, J.F. (1998) Failure inference from a marker process based on a bivariate Wiener model. Lifetime Data Analysis 4, 229-251.
89. Wong, W.H. (1986) Theory of partial likelihood. Ann. Statist. 14, 88-123.
90. Aalen, O.O., and Johansen, S. (1978) An empirical transition matrix for nonhomogeneous Markov chains based on censored observations. Scand. J. Statist. 5, 141-150.
91. Akritas, M.G., and Van Heilegon, I. (2003) Estimation of bivariate and marginal distributions with censored data. J. Roy. Statist. Soc. 65, 457-471.
92. Ali, M.M., Mikhail, N.N., and Haq, M.S. (1978) A class of bivariate distributions including the bivariate logistic. J. Multiv. Anal. 8, 405-412.
93. Balka, J., Desmond, A.F., and McNicholas, P.D. (2009) Review and implementation of cure models based on first hitting times for Wiener processes. Lifetime Data Analysis 15, 147-176.
94. Baxter, L.A. (1994) Estimation from quasi-life tables. Biometrika 81, 567-577.
95. Bhattacharyya, G.K., and Fries, A. (1982) Fatigue-failure models: Birnbaum-Saunders vs. Gaussian. IEEE Trans. Rel. R-31, 439-441.
96. Birnbaum, Z.W., and Saunders, S.C. (1969) A new family of life distributions. J. Appl. Prob. 6, 319-327.
97. Cai, J. (1999) Hypothesis testing of hazard ratio parameters in marginal models for multivariate failure time data. Lifetime Data Analysis 5, 39-53.
98. Cai, J., and Kim, J. (2003) Nonparametric quantile estimation with correlated failure time data. Lifetime Data Analysis 9, 357-371.
99. Cai, J., and Prentice, R.L. (1997) Regression estimation using multivariate failure time data and a common baseline hazard function model. Lifetime Data Analysis 3, 197-213.
100. Chen, M.-C. and Bandeen-Roche, K. (2005) A diagnostic for association in bivariate survival models. Lifetime Data Analysis 11, 245-264.
101. Chiao, C.-H., and Hamada, M. (1995) Experiments with degradation data for improving reliability and for achieving robust reliability. IIQP Research Report RR-95-10, University of Waterloo, Canada.
102. Clayton, D. (1978) A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65, 141-151.
103. Clayton, D., and Cuzick, J. (1985) Multivariate generalisations of the proportional hazards model (with discussion). J. Roy. Statist. Assoc. A 148, 82-117.
104. Cook, R.D., and Johnson, M.E. (1981) A family of distributions for modelling nonelliptically symmetric multivariate data. J. Roy. Statist. Soc. B 43, 210-218.
105. Cowan, R. (1987) A bivariate exponential distribution arising in random geometry. Ann. Inst. Statist. Math. 39, 103-111.
106. Cowling, B.J., Hutton, J.L., and Shaw, J.E.H. (2006) Joint modelling of event counts and survival times. Applied Statistics 55, 31-39.
107. Cox, D.R. (1962) Renewal Theory. Methuen, London.
108. Cox, D.R.(1999) Some remarks on failure times, surrogate markers, degradation, wear, and the quality of life. Lifetime Data Analysis 5, 307-314.
109. Crowder, M.J. (1985) A distributional model for repeated failure time measurements. J. Roy. Statist. Soc. B 47, 447-452.
110. Crowder, M.J. (1989) A multivariate distribution with Weibull connections. J. Roy. Statist. Soc. B 51, 93-107.
111. Crowder, M.J. (1991) A statistical approach to a deterioration process in reinforced concrete. Applied Statistics 40, 95-103.
112. Crowder, M.J. (1996) Keep timing the tablets: Statistical analysis of pill dissolution rates. Applied Statistics 45, 323-334.
113. Crowder, M.J. (1998) A multivariate model for repeated failure time measurements. Scand. J. Statist. 25, 53-67.
114. Crowder, M.J., and Kimber, A.C. (1997) Ascore test for the multivariate Burr and other Weibull mixture distributions. Scand. J. Statist. 24, 419-432.
115. Crowder, M.J., and Lawless, J.F. (2007) On a scheme for predictive maintenance. European J. Oper. Res. 176, 1713-1722.
116. Crowder, M.J., and Hand, D.J. (2005) On loss distributions from installment-repaid loans. Lifetime Data Analysis 11, 545-564.
117. Crowder, M.J., and Stephens, D.A. (2003) On the analysis of quasi-life tables. Lifetime Data Analysis 9, 345-355.
118. Crowder, M.J., Hand, D.J., and Krzanowski, W. (2007) On optimal intervention for customer lifetime value. European J. Oper. Res. 183, 1550-1559.
119. Cuzick, J. (1981) Boundary crossing probabilities for stationary Gaussian processes and Brownian motion. Trans. Amer. Math. Soc. 263, 469-492.
120. Doksum, K.A., and Hoyland, A. (1992) Models for variable-stress accelerated life testing experiments based onWiener processes and the inverse Gaussian distribution. Technometrics 34, 74-82.
121. Drezner, Z., and Wesolowsky, G.O. (1989) On the computation of the bivariate normal integral. J. Statist. Comput. Simul. 35, 101-107.
122. Durbin, J. (1985) The first-passage density of a continuous Gaussian process to a general boundary. J. Appl. Prob. 22, 99-122.
123. Fan, J., Hsu, L., and Prentice, R.L. (2000) Dependence estimation over a finite bivariate failure time region. Lifetime Data Analysis 6, 343-355.
124. Farewell, D., and Henderson, R. (2010) Longitudinal perspectives on event history analysis. Lifetime Data Analysis 16, 102-117.
125. Freund, J.E. (1961) Abivariate extension of the exponential distribution. J. Amer. Statist. Assoc. 56, 971-977.
126. Genest, C., and MacKay, J. (1986) The joy of copulas: bivariate distributions with uniform marginals. American Statistician 40, 280-283.
127. Genest, C., and Rivest, L-P. (1993) Statistical inference for bivariate Archimedean copulas. J. Amer. Statist. Assoc. 88, 1034-1043.
128. Gesch, C.B., Hammond, S.M., Hampson, S.E., Eves, A., and Crowder, M.J. (2002) Influence of supplementary vitamins, minerals and essential fatty acids on the antisocial behaviour of young adult prisoners. Brit. J. Psychiatry 181, 22-28.
129. Ghurye, S.G. (1987) Some multivariate lifetime distributions. Adv. Appl. Prob. 19, 138-155.
130. Giampieri, G., Davis, M., and Crowder, M.J. (2005) Analysis of default data using hidden Markov chains. Quantitative Finance 5, 27-34.
131. Grambsch, P.M., and Therneau, T.M. (1994) Proportional hazards tests and diagnostics based on weighted residuals. Biometrika 81, 515-526.
132. Gray, R.J. (2003) Weighted estimating equations for linear regression analysis of clustered failure time data. Lifetime Data Analysis 9, 123-138.
133. Gumbel, E.J. (1960) Bivariate exponential distributions. J. Amer. Statist. Assoc. 55, 698-707.
134. Hanley, J.A., and Parnes, M.N. (1983) Nonparametric estimation of a multivariate distribution in the presence of censoring. Biometrics 39, 129-139.
135. Hougaard, P. (1986b) A class of multivariate failure time distributions. Biometrika 73, 671-678.
136. Hougaard, P. (1987) Modelling multivariate survival. Scand. J. Statist 14, 291-304.
137. Hougaard, P. (1999) Multi-state models: A review. Lifetime Data Analysis 5, 239-264.
138. Johnson, N.L., and Kotz, S. (1972) Distributions in Statistics: Continuous Multivariate Distributions. Wiley, New York.
139. Jones, M.P., and Yoo, B. (2005) Linear signed-rank tests for paired survival data subject to a common censoring time. Lifetime Data Analysis 11, 351-365.
140. Jung, S-H., and Jeong, J-H. (2003) Rank tests for clustered survival data. Lifetime Data Analysis 9, 21-33.
141. Karim, Md. R., Yamamoto, W., and Suzuki, K. (2001) Statistical analysis of marginal count failure data. Lifetime Data Analysis 7, 173-186.
142. Karimi, A.R., Ramachandran, K., Buenfeld, N., and Crowder, M.J. (2005) Probabilistic analysis of reinforcement corrosion with spatial variability. In Safety and Reliability of Engineering Systems and Structures, Proceedings of the 9th Conference on Structural Safety and Reliability, Eds. G. Augusti, G.I. Schueller, and M. Ciampoli, Rome, Italy.
143. Kotz, S., and Singpurwalla, N.D. (1999) On a bivariate distribution with exponential marginals. Scand. J. Statist. 26, 451-464.
144. Lawless, J.F., and Crowder, M.J. (2004) Covariates and random effects in a gamma process model with application to degradation and failure. Lifetime Data Analysis 10, 213-227.
145. Lawrance, A.J., and Lewis, P.A.W (1983) Simple dependent pairs of exponential and uniform random variables. Operations Research 31, 1179-1197.
146. Lee, M-L.T., and Whitmore, G.A. (2006) Threshold regression for survival analysis: Modeling event times by a stochastic process reaching a boundary. Statist. Science 21, 501-513.
147. Lehmann, E.L. (1966) Some concepts of dependence. Ann. Math. Statist. 37, 1137-1153.
148. Li, Q.H., and Lagakos, S.W. (2004) Comparisons of test statistics arising from marginal analyses of multivariate survival data. Lifetime Data Analysis 10, 389-405.
149. Liang, K-Y., Self, S.G., and Chang, Y-C. (1993) Modelling marginal hazards in multivariate failure time data. J. Roy. Statist. Soc. B 55, 441-453.
150. Liang, K-Y., Self, S.G., Bandeen-Roche, K.J., and Zeger, S.L. (1995) Some recent developments for regression analysis of multivariate failure time data. Lifetime Data Analysis 1, 403-415.
151. Lu, C.J., and Meeker, W.Q. (1993) Using degradation measurements to estimate a time-to-failure distribution. Technometrics 35, 161-174.
152. Lu, W. (2007) Tests of independence for censored bivariate failure time data. Lifetime Data Analysis 13, 75-90.
153. Lu, S-E., and Wang, M-C. (2005) Marginal analysis for clustered failure time data. Lifetime Data Analysis 11, 61-79.
154. Marshall, A.W., and Olkin, I. (1967a) Ageneralized bivariate exponential distribution. J. Appl. Prob. 4, 291-302.
155. Marshall, A.W., and Olkin, I. (1967b) A multivariate exponential distribution. J. Amer. Statist. Assoc. 62, 30-44.
156. Marshall, A.W., and Olkin, I. (1988) Families of multivariate distributions. J. Amer. Statist. Assoc. 83, 834-841.
157. McGilchrist, C.A., and Aisbett, C.W. (1991) Regression with frailty in survival analysis. Biometrics 47, 461-466.
158. Molenberghs, G., Verbeke, G., and Demetrio, C.G.B. (2007) An extended randomeffects approach to modeling repeated, overdispersed count data. Lifetime Data Analysis 13, 513-531.
159. Oakes, D. (1982) A model for association in bivariate survival data. J. Roy. Statist. Soc. B 44, 414-422.
160. Oakes, D. (1986) Semiparametric inference in a model for association in bivariate survival data. Biometrika 73, 353-361.
161. Oakes, D. (1989) Bivariate survival models induced by frailties. J. Amer. Statist. Assoc. 84, 487-493.
162. Park, C., and Padgett, W.J. (2005) Accelerated degradation models for failure based on geoemetric Brownian motion and gamma processes. Lifetime Data Analysis 11, 511-527.
163. Peng, Y., Taylor, J.M.G., and Yu, B. (2007) Amarginal regression model for multivariate failure time data with a surviving fraction. Lifetime Data Analysis 13, 351-369.
164. Petersen, J.H. (1998) An additive frailty model for correlated life times. Biometrics 54, 646-661.
165. Pons, O. (1986) A test of independence between two censored survival times. Scand. J. Statist. 13, 173-185.
166. Quale, C.M., and Van der Laan, M.J. (2000) Inference with bivariate truncated data. Lifetime Data Analysis 6 391-408.
167. Raftery, A.E. (1984) Acontinuous multivariate exponential distribution. Comm. Statist. Theory Meth. 13, 947-965.
168. Raftery, A.E. (1985) Some properties of a new continuous bivariate exponential distribution. Statistics and Decisions, Supplement Issue 2, 53-58.
169. Robinson, M.E., and Crowder, M.J. (2000) Bayesian methods for a growth-curve degradation model with repeated measures. Lifetime Data Analysis 6, 357-374.
170. Scholtens, D., and Betensky, R.A. (2006) A computationally simple bivariate survival estimator for efficacy and safety. Lifetime Data Analysis 12, 365-387.
171. Segal, M.R., Neuhaus, J.M., and James, I.R. (1997) Dependence estimation for marginal models of multivariate survival data. Lifetime Data Analysis 3, 251-268.
172. Shaked, M. (1982) A general theory of some positive dependence notions. J. Multiv. Anal. 12, 199-218.
173. Shih, J.H. (1998) Modeling multivariate discrete failure time data. Biometrics 54, 1115-1128.
174. Singpurwalla, N.D., and Youngren, M.A. (1993). Multivariate distributions induced by dynamic environments. Scand. J. Statist. 20, 251-261.
175. Sobczyk, K. (1986) Modelling random fatigue crack growth. Eng. Fract. Mech. 24, 609-623.
176. Spencer, B.F., and Tang, J. (1988) A Markov process model for fatigue crack growth. J. Eng. Mech. 114, 2134-2157.
177. Suzuki, K., Yamamoto, W., Karim, Md. R., and Wang, L. (2000) Data analysis based on warranty database. In Recent Advances in Reliability Theory, Eds. N. Limnios and M. Nikulin, Birkhauser, Boston, 213-227.
178. Takahasi, K. (1965) Note on the multivariate Burr’s distribution. Ann. Inst. Statist. Math. 17, 257-260.
179. Tang, J., and Spencer, Jr., B.F. (1989) Reliability solution for the stochastic fatigue crack growth problem. Eng. Fract. Mech. 34, 419-433.
180. Tortorella, M. (1996) Life estimation from pooled discrete renewal counts. In Lifetime Data: Models in Reliability and Survival Analysis. Ed. N.P. Jewell, Kluwer Academic Publishers, 331-338.
181. Tseng, S.T., Hamada, M.S., and Chiao, C.H. (1994) Using degradation data from a fractional factorial experiment to improve fluorescent lamp reliability. IIQP Research Report RR-94-05, University ofWaterloo, Canada.
182. Tsiatis, A.A., and Davidian M. (2004) Joint modelling of longitudinal and time-to-event data: an overview. Statist. Sci. 14, 793-818.
183. Virkler, D.A., Hillberry, B.M., and Goel, P.K. (1979) The statistical nature of fatigue crack propagation. J. Eng. Mat. and Technology, ASME 101, 148-153.
184. Walker, S.G., and Stephens, D. (1999) Amultivariate family of distributions on (0,∞) p. Biometrika 86, 703-709.
185. Whitmore, G.A. (1995) Estimating degradation by a Wiener diffusion process subject to measurement error. Lifetime Data Analysis 1, 307-319.
186. Yilmaz, Y.E., and Lawless, J.F. (2011) Likelihood ratio procedures and tests of fit in parametric and semiparametric copula models with censored data. Lifetime Data Analysis 17, 386-408.
187. Yin, G., and Cai, J. (2004) Additive hazards model with multivariate failure time data. Biometrika 91 801-818.
188. Zeng, D., and Cai, J. (2010) Additive transformation models for clustered failure time data. Lifetime Data Analysis 16, 333-352.
189. Zhang, S., Zhang, Y., Chaloner, K., and Stapleton, J.T. (2010) A copula model for bivariate hybrid censored survival data with application to the MACS study. Lifetime Data Analysis 16, 231-249.
190. Zucchini, W., and MacDonald, I.L. (2009) Hidden Markov Models for Time Series: An Introduction Using R. Chapman & Hall/CRC Press, Boca Raton, FL.
191. Aalen, O.O. (1976) Nonparametric inference in connection with multiple decrement models. Scand. J. Statist. 3, 15-27.
192. Abbring, J.H., and van den Berg, G.J. (2003) The identifiability of the mixed proportional hazards competing risks model. J. Roy. Statist. Soc. B 65, 701-710.
193. Altshuler, B. (1970) Theory for the measurement of competing risks in animal experiments. Math. Biosci. 6, 1-11.
194. Andersen, J., Goetghebeur, E., and Ryan, L. (1996) Missing cause of death information in the analysis of survival data. Statist. Med. 15, 1191-2201.
195. Anderson, T.W., and Ghurye, S.G. (1977) Identification of parameters by the distribution of a maximum random variable. J. Roy. Statist. Soc. B 39, 337-342.
196. Arjas, E., and Greenwood, P. (1981) Competing risks and independent minima: a marked point process approach. Adv. Appl. Prob. 13, 669-680.
197. Arjas, E., and Haara, P. (1984) A marked point process approach to censored failure data with complicated covariates. Scand. J. Statist. 11, 193-209.
198. Arnold, B., and Brockett, P. (1983) Identifiability for dependent multiple decrement/competing risk models. Scand. Actuar. J. 10, 117-127.
199. Bagai, I., Deshpande, J.V., and Kocher, S.C. (1989a) A distribution-free test for the equality of failure rates due to two competing risks. Comm. Statist. Theor. Meth. 18, 107-120.
200. Bagai, I., Deshpande, J.V., and Kocher, S.C. (1989b) Distribution-free tests for stochastic ordering in the competing risks model. Biometrika 76, 775-781.
201. Bancroft, G.A., and Dunsmore, I.R. (1976) Predictive distributions in life tests under competing causes of failure. Biometrika 63, 195-217.
202. Barlow, R.E., and Proschan, F. (1975) Importance of system components and fault tree events. Stoch. Proc. App. 3, 153-173.
203. Basu, A.P. (1981) Identifiability problems in the theory of competing and complementary risks: A survey. In Statistical Distributions in Scientific Work, Eds. C. Taillie, G.P. Patil, and B. Baldesari, Reidel Publ. Co., Dortrecht, Holland, 335-348.
204. Basu, A.P., and Ghosh J.K. (1978) Identifiability of the multinormal and other distributions under competing risks model. J. Multiv. Anal. 8, 413-429.
205. Basu, A.P., and Ghosh J.K. (1980) Identifiability of distributions under competing risks and complementary risks model. Comm. Statist.—Theory and Meth. A9, 1515-1525.
206. Basu, A.P., and Klein, J.P. (1982) Some recent results in competing risks theory. In Survival Analysis, Vol 2, Eds. J. Crowley and R.A. Johnson, IMS Monograph Series, Hayward, CA.
207. Beck, G. (1979) Stochastic survival models with competing risks and covariates. Biometrics 35, 427-438.
208. Berkson, J., and Elveback, L. (1960) Competing exponential risks, with particular reference to the study of smoking and lung cancer. J. Amer. Statist. Assoc. 55, 415-428.
209. Berman, S.M. (1963) Note on extreme values, competing risks and semi-Markov processes. Ann. Math. Statist. 34, 1104-1106.
210. Bernoulli, D. (1760, 1765) Essai d’une nouvelle analyse de la mortalite causee par la petite Verole, et des avantages de l’inoculation pour la prevenir. Mem. de l’Academie Royale de Science 1760, 1-45.
211. Beyersmann, J., Dettenkofer, M., Bertz, H., and Schumacher, M. (2007) A competing risks analysis of bloodstream infection after stem-cell transplantation using subdistribution hazards and cause-specific hazards. Statist. Med. 26, 5360-5369.
212. Block, H.W., and Basu, A.P. (1974) A continuous bivariate exponential distribution. J. Amer. Statist. Assoc. 69, 1031-1037.
213. Boag, J.W. (1949) Maximum likelihood estimates of the proportion of patients cured by cancer therapy. J. R. Statist. Soc. B11, 15-44.
214. Bond, S.J., and Shaw, J.E.H. (2006) Bounds on the covariate-time transformation for competing-risks survival analysis. Lifetime Data Analysis 12, 285-303.
215. Carling, K., and Jacobson, T. (1995) Modeling unemployment duration in a dependent competing risks framework: Identification and estimation. Lifetime Data Analysis 1, 111-122.
216. Carriere, K.C., and Kochar, S.C. (2000) Comparing sub-survival functions in a competing risks model. Lifetime Data Analysis 6, 85-97.
217. Chiang, C.L. (1961a) A stochastic study of the life table and its applications: III. The follow-up study with the consideration of competing risks. Biometrics 17, 57-78.
218. Chiang, C.L. (1961b) On the probability of death from specific causes in the presence of competing risks. Proc. 4th Berk. Symp. 4, 169-180.
219. Chiang, C.L. (1964) A stochastic model of competing risks of illness and competing risks of death. In Stochastic Models in Medicine and Biology, Ed. J. Gurland, University Wisconsin Press, Madison, 323-354.
220. Chiang, C.L. (1970) Competing risks and conditional probabilities. Biometrics 26, 767-776.
221. Cornfield, J. (1957) The estimation of the probability of developing a disease in the presence of competing risks. Amer. J. Public Health 47, 601-607.
222. Couper, D., and Pepe, M.S. (1997) Modelling prevalence of a condition: chronic graftversus-host disease after bone marrow transplantation. Statist. Med. 16, 1551-1571.
223. Cox, D.R. (1959) The analysis of exponentially distributed lifetimes with two types of failure. J. Roy. Statist. Soc. B 21, 411-421.
224. Craiu, R.V., and Reiser, B. (2006) Inference for the dependent competing risks model with masked causes of failure. Lifetime Data Analysis 12, 21-33.
225. Crowder, M.J. (1991) On the identifiability crisis in competing risks analysis. Scand. J. Statist. 18, 223-233.
226. Crowder, M.J. (1994) Identifiability crises in competing risks. Int. Statist. Rev. 62, 379-391.
227. Crowder, M.J. (1995) Analysis of fracture toughness data. Lifetime Data Analysis 1, 59-71.
228. Crowder, M.J. (1996) On assessing independence of competing risks when failure times are discrete. Lifetime Data Analysis 2, 195-209.
229. Crowder, M.J. (1997) A test for independence of competing risks with discrete failure times. Lifetime Data Analysis 3, 215-223.
230. Crowder, M.J. (2000) Characterisations of competing risks in terms of independentrisks proxy models. Scand. J. Statist. 27, 57-64.
231. Cutler, S., and Ederer, F. (1958) Maximum utilization of the life table method in analyzing survival. J. Cron. Dis. 8, 699-712.
232. D’Alembert, J. (1761) Sur l’application du Calcul des Probabilites a l’inoculation de la petite Verole. Opuscules II, 26-95.
233. David, H.A. (1957) Estimation of means of normal populations fromobserved minima. Biometrika 44, 282-286.
234. David, H.A. (1970)OnChiang’s proportionality assumption in the theory of competing risks. Biometrics 26, 336-339.
235. David, H.A. (1974) Parametric approaches to the theory of competing risks. In Reliability and Biometry: Statistical Analysis of Lifelength, Eds. F. Proschan and R.J. Serfling, Society for Industrial and Applied Mathematics, Philadelphia, PA, 275-290.
236. Davis, T.P., and Lawrance, A.J. (1989) The likelihood for competing risk survival analysis. Scand. J. Statist. 16, 23-28.
237. Desu, M.M., and Narula, S.C. (1977) Reliability estimation under competing causes of failure. In The Theory and Applications of Reliability, Vol. 2, Eds. C.P. Tsokos and I.N. Shimi, Academic Press, New York, 471-481.
238. Dewanji, A. (1992) A note on a test for competing risks with missing failure type. Biometrika 79, 855-857.
239. Dewanji, A., and Sengupta, D. (2003) Estimation of competing risks with general missing pattern in failure types. Biometrics 59, 1063-1070.
240. Dinse, G.E. (1982) Nonparametric estimation for partially complete time and type of failure. Biometrics 38, 417-431.
241. Dinse, G.E. (1986) Nonparametric prevalence and mortality estimators for animal experiments with incomplete cause of death. J. Amer. Statist. Assoc. 81, 328-336.
242. Dinse, G.E. (1988) Estimating tumour incidence rates in animal carcinogeneity experiments. Biometrics 44, 405-415.
243. DiRienzo, A.G. (2003) Nonparametric comparison of two survival-time distributions in the presence of dependent censoring. Biometrics 59, 497-504.
244. Dixon, S.N., Darlington, G.A., and Desmond, A.F. (2011) A competing risks model for correlated data based on the subdistribution hazard. Lifetime Data Analysis 17, 473-495.
245. Doganaksoy, N. (1991) Interval estimation from censored and masked failure data. IEEE Trans. Reliab. 40, 280-285.
246. Ebrahimi, N. (1996) The effects of misclassification of the actual cause of death in competing risks analysis. Statist. Med. 15, 1557-1566.
247. Elandt-Johnson, R. (1976) Conditional failure time distributions under competing risk theory with dependent failure times and proportional hazard rates. Scand. Actuar. J. 59, 37-51.
248. Elveback, L. (1958) Estimation of survivorship in chronic disease: the actuarial method. J. Amer. Statist. Assoc. 53, 420-440.
249. Farragi, D., and Korn, E.L. (1996) Competing risks with frailty models when treatment affects only one failure type. Biometrika 83, 467-471.
250. Faulkner, J.E., and McHugh, R.B. (1972) Bias in observable cancer age and life-time of mice subject to spontaneous mammary carcinogenesis. Biometrics 28, 489-498.
251. Finch, P.D. (1977) On the crude analysis of survivorship data. Austral. J. Statist. 19, 1-21.
252. Fine, J.P., and Gray, R.J. (1999) A proportional hazards model for the subdistribution of a competing risk. J. Amer. Statist. Assoc. 94, 496-509.
253. Fisher, L., and Kanarek, P. (1974) Presenting censored survival data when censoring and survival times may not be independent. In Reliability and Biometry: Statistical Analysis of Lifelength, Eds. F. Proschan and R.J. Serfling, Society for Industrial and Applied Mathematics, Philadelphia, PA, 303-326.
254. Fix, E., and Neyman, J. (1951) A simple stochastic model of recovery, relapse, death and loss of patients. Human Biology 23, 205-241.
255. Flinn, C.J., and Heckman, J.J. (1982) New methods for analyzing structural models of labor force dynamics. J. Econometrics 18, 115-168.
256. Flinn, C.J., and Heckman, J.J. (1983a) Are unemployment and out of the labor force behaviourally distinct labor force states? J. Labor Econ. 1, 28-42.
257. Flinn, C.J., and Heckman, J.J. (1983b) The likelihood function for the multistatemulti-episode model in “models for the analysis of labor force dynamics.” In Advances in Econometrics, Vol. 3, Eds. R. Bassman and G. Rhodes, JAI Press, Greenwich, CT, 115-168.
258. Gail, M. (1975)Areview and critique of some models used in competing risks analysis. Biometrics 31, 209-222.
259. Gail, M., Lubin, J.H., and Rubenstein, L.V. (1981) Likelihood calculations for matched case-control studies and survival studies with tied death times. Biometrika 68, 703-707.
260. Gasemyr, J., and Natvig, B. (1994) Bayesian estimation of component lifetimes based on autopsy data. Statistical Research Report No. 8, Institute of Mathematics, University of Oslo.
261. Gaynor, J.J., Feuer, E.J., Tan, C.C., Wu, D.H., Little, C.R., Straus, D.J., Clarkson, B.D., and Brennan, M.F. (1993) Onthe use of cause-specific failure and conditional failure probabilities: Examples from clinical oncology data. J. Amer. Statist. Assoc. 88, 400-409.
262. Goetghebeur, E., and Ryan, L. (1990) Amodified log rank test for competing risks with missing failure type. Biometrika 77, 207-211.
263. Goetghebeur, E., and Ryan, L. (1995) Analysis of competing risks survival data when some failure types are missing. Biometrika 82, 821-833.
264. Grambauer, N., Schumacher, M., and Beyersmann, J. (2010) Proportional subdistribution hazards modeling offers a summary analysis, even if misspecified. Statist. Med. 29, 875-884.
265. Greenwood, M. (1926) The natural duration of cancer. In Reports on Public Health and Medical Subjects, No. 33, 1-26, HMSO, London.
266. Greville, T.N.E. (1948) Mortality tables analyzed by cause of death. Record, Amer. Inst. Actuaries 37, 283-294.
267. Greville, T.N.E. (1954) On the formula for the L-function in a special mortality table eliminating a given cause of death. Trans. Soc. Act. 6, 1-5.
268. Gross, A.J. (1970) Minimization of misclassification of component failure in a twocomponent system. IEEE Trans. Reliab. 19, 120-122.
269. Gross, A.J. (1973) A competing risk model: a one organ subsystem plus a two organ subsystem. IEEE Trans. Reliability 22, 24-27.
270. Gross, A.J., Clark, V.A., and Liu, V. (1971) Estimation of survival parameters when one of two organs must function for survival. Biometrics 27, 369-377.
271. Guess, F.M., Usher, J.S., and Hodgson, T.J. (1991) Estimating system and component reliabilities under partial information on cause of failure. J. Statist. Plan. Inf. 29, 75-85.
272. Guttman, I., Lin, D.K.J., Reiser, B., and Usher, J.S. (1995) Dependent masking and system life data: Bayesian inference for two-component systems. Lifetime Data Anal. 1, 87-100.
273. Heckman, J.J., and Honore, B.E. (1989) The identifiability of the competing risks model. Biometrika 76, 325-330.
274. Herman, R.J., and Patell, R.K.N. (1971) Maximum likelihood estimation for multi-risk model. Technometrics 13, 385-396.
275. Hoel, D.G. (1972) A representation of mortality data by competing risks. Biometrics 28, 475-488.
276. Holt, J.D. (1978) Competing risk analyses with special reference to matched pair experiments. Biometrika 65, 159-165.
277. Horrocks, J., and Thompson, M.E. (2012) Modelling event times with multiple outcomes using the Wiener process with drift. Lifetime Data Analysis 10, 29-49.
278. Huang, X., Li, G., Elashoff, R.M., and Pan, J. (2011) Ageneral joint model for longitudinal measurements and competing risks survival data with heterogeneous random effects. Lifetime Data Analysis 17, 80-100.
279. Jeong, J-H., and Fine, J.P. (2006) Direct parametric inference for the cumulative incidence function. Applied Statist. 55, 1-14.
280. Kalbfleisch, J.D., and Mackay, R.J. (1979) On constant-sum models for censored survival data. Biometrika 66, 87-90.
281. Karia, S.R., and Deshpande, J.V. (1997) Bounds for Hazard Gradients and Rates in the Competing Risks Set Up. Technical Report 285, Department of Statistics, University of Michigan, Ann Arbor.
282. Karn, M.N. (1931) An inquiry into various death rates and the comparative influence of certain diseases on the duration of life. Ann. Eugenics 4, 279-326.
283. Karn M.N. (1933) A further study of methods of constructing life tables when certain causes of death are eliminated. Biometrika 25, 91.
284. Kay, R. (1986) Treatment effects in competing risks analysis of prostate cancer data. Biometrics 42, 203-211.
285. Keyfitz, N., Preston, S.H., and Schoen, R. (1972) Inferring probabilities from rates: extension to multiple decrement. Skand. Aktuar. 55, 1-13.
286. Kimball, A.W. (1958) Disease incidence estimation in populations subject to multiple causes of death. Bull. Int. Statist. Inst. 36, 193-204.
287. Kimball, A.W. (1969) Models for the estimation of competing risks from grouped data. Biometrics 25, 329-337.
288. Kimball, A.W. (1971) Model I vs. Model II in competing risk theory. Biometrics 27, 462-465.
289. Klein, J.P., and Andersen, P.K. (2005) Regression modeling of competing risks data based on pseudovalues of the cumulative incidence function. Biometrics 61, 223-229.
290. Klein, J.P., and Basu, A.P. (1981) Weibull accelerated life tests when there are competing causes of failure. Comm. Statist. Theor. Meth. A 10, 2073-2100.
291. Klein, J.P., and Moeschberger, M.L. (1988) Bounds on net survival probabilities for dependent competing risks. Biometrics 44, 529-538.
292. Kochar, S.C., and Proschan, F. (1991) Independence of time and cause of failure in the multiple dependent competing risks model. Statistica Sinica 1, 295-299.
293. Kochar, S.C., Lam, K.F., and Yip, P.S.F. (2002) Generalized supremum tests for the equality of cause specific hazard rates. Lifetime Data Analysis 8, 277-288.
294. Kodell, R.L., and Chen, J.J. (1987) Handling cause of death in equivocal cases using the EM algorithm. With rejoinder. Comm. Statist. A 16, 2565-2585.
295. Krall, J.M., and Hickman, J.C. (1970) Adjusting multiple decrement tables. Trans. Soc. Act. 22, 163-179.
296. Kulathinal, S.B., and Gasbarra, D. (2002) Testing equality of cause-specific hazard rates corresponding to m competing risks among K groups. Lifetime Data Analysis 8, 147-161.
297. Lagakos, S.W. (1978) A covariate model for partially censored data subject to competing causes of failure. Appl. Statist. 27, 235-241.
298. Lagakos, S.W., and Louis, T.A. (1988) Use of tumour lethality to interpret tumorigenicity experiments lacking cause of death data. Appl. Statist. 37, 169-179.
299. Lagakos, S.W., andWilliams, J.S. (1978) Models for censored survival analysis: a cone class of variable-sum models. Biometrika 65, 181-189.
300. Langberg, N.A., and Proschan, F. (1979) A reliability growth model involving dependent components. Ann. Prob. 7, 1082-1087.
301. Langberg, N., Proschan, F., and Quinzi, A.J. (1977) Converting dependent models into independent ones, with applications in reliability. In The Theory and Applications of Reliability, Vol. 1, Eds. C.P. Tsokos and I.N. Shimi, Academic Press, New York, 259-276.
302. Langberg, N., Proschan, F., and Quinzi, A.J. (1978) Converting dependent models into independent ones, preserving essential features. Ann. Prob. 6, 174-181.
303. Langberg, N., Proschan, F., and Quinzi, A.J. (1981) Estimating dependent life lengths, with applications to the theory of competing risks. Ann. Statist. 9, 157-167.
304. Langberg, N., and Shaked, M. (1982) On the identifiability of multivariate life distribution functions. Ann. Prob. 10, 773-779.
305. Larson, M.G., and Dinse, G.E. (1985) A mixture model for the regression analysis of competing risks data. Appl. Statist. 34, 201-211.
306. Lee, L., and Thompson, Jr., W.A. (1974) Results on failure time and pattern for the series system. In Reliability and Biometry: Statistical Analysis of Lifelength, Eds. F. Proschan and R.J. Serfling, Society for Industrial and Applied Mathematics, Philadelphia, PA, 291-302.
307. Lin, D.K.J., and Guess, F.M. (1994) System life data analysis with dependent partial knowledge on the exact cause of system failure. Microelec. and Reliab. 34, 535-544.
308. Lindkvist, H., and Belyaev, Y. (1998) A class of non-parametric tests in the competing risks model for comparing two samples. Scand. J. Statist. 25, 143-150.
309. Lu, K., and Tsiatis, A.A. (2001) Multiple imputation methods for estimating regression coefficients in the competing risks model with missing cause of failure. Biometrics 57, 1191-1197.
310. Lu, K., and Tsiatis, A.A. (2005) Comparison between two partial likelihood approaches for the competing risks model with missing cause of failure. Lifetime Data Analysis 11, 29-40.
311. Lu, W., and Peng, L. (2008) Semiparametric analysis of mixture regression models with competing risks data. Lifetime Data Analysis 14, 231-252.
312. Makeham, W.M. (1874) On an application of the theory of the composition of decremental forces. J. Inst. Actuaries 18, 317-322.
313. Matthews, D.E. (1984) Efficiency considerations in the analysis of a competing risk problem. Can. J. Statist. 12, 207-210.
314. Mendenhall, W., and Hader, R.J. (1958) Estimation of parameters of mixed exponentially distributed failure time distributions from censored life test data. Biometrika 45, 504-520.
315. Miller, D.R. (1977) A note on independence of multivariate lifetimes in competing risk models. Ann. Statist. 5, 576-579.
316. Miyakawa, M. (1984) Analysis of incomplete data in competing risks model. IEEE Trans. Reliability 33, 293-296.
317. Moeschberger, M.L. (1974) Life tests under dependent competing causes of failure. Technometrics 16, 39-47.
318. Moeschberger, M.L., and David, H.A. (1971) Life tests under competitive causes of failure and the theory of competing risks. Biometrics 27, 909-933.
319. Moeschberger, M.L., and Klein, J.P. (1995) Statistical methods for dependent competing risks. Lifetime Data Analysis 1, 195-204.
320. Nadas, A. (1970b) On estimating the distribution of a random vector when only the smallest co-ordinate is observable. Technometrics 12, 923-924.
321. Nadas, A. (1971) The distribution of the identified minimum of a normal pair determines the distribution of the pair. Technometrics 13, 201-202.
322. Nair, V.J. (1993) Bounds for reliability estimation under dependent censoring. Int. Statist. Rev. 61, 169-182.
323. Nelson, W.B. (1970) Hazard plotting methods for analysis of life data with different failure modes. J. Qual. Tech. 2, 126-149.
324. Reiser, B., Guttman, I., Lin, D.K.J., Guess, F.M., and Usher, J.S. (1995) Bayesian inference for masked system lifetime data. Appl. Statist. 44, 79-90.
325. Pepe, M.S. (1991) Inference for events with dependent risks in multiple endpoint studies. J. Amer. Statist. Assoc. 86, 770-778.
326. Pepe, M.S., and Mori, M. (1993) Kaplan-Meier, marginal or conditional probability curves in summarizing competing risks failure time data? Statist. Med. 12, 737-751.
327. Peterson, A.V. (1976) Bounds for a joint distribution function with fixed subdistribution functions: Application to competing risks. Proc. Nat. Acad. Sci. USA 73, 11-13.
328. Peterson, A.V. (1977) Expressing the Kaplan-Meier estimator as a function of empirical sub-survival functions. J. Amer. Statist. Assoc. 72, 854-858.
329. Pike, M.C., and Roe, F.J.C. (1963) An actuarial method of analysis in an experiment in two-stage carcinogenesis. Brit. J. Cancer 17, 605-610.
330. Pike, M.C. (1970) A note on Kimball’s paper “Models for the estimation of competing risks from grouped data.” Biometrics 26, 579-581.
331. Prentice, R.L., Kalbfleisch, J.D., Peterson, A.V., Flournoy, N., Farewell, V.T., and Breslow, N.E. (1978) The analysis of failure times in the presence of competing risks. Biometrics 34, 541-554.
332. Proschan, F., and Sullo, P. (1974) Estimating parameters of a bivariate exponential distribution in several sampling situations. In Reliability and Biometry: Statistical Analysis of Lifelength, Society for Industrial and Applied Mathematics, Philadelphia, PA, 423-440.
333. Rachev, S.T., and Yakovlev, A.Y. (1985) Some problems of the competing risks theory. Fifth Int. Summer School on Prob. Theory and Math. Statist., Varna 1985. Publ: Bulgarian Acad. Sci.
334. Racine-Poon, A.H., and Hoel, D.G. (1984) Nonparametric estimation of the survival function when the cause of death is uncertain. Biometrics 40, 1151-1158.
335. Sampford, M.R. (1952) The estimation of response-time distributions: II. Multistimulus distributions. Biometrics 8, 307-369.
336. Scheike, T.H., and Zhang, M-J. (2008) Flexible competing risks regression modeling and goodness-of-fit. Lifetime Data Analysis 14, 464-483.
337. Seal, H.L. (1954) The estimation of mortality and other decremental probabilities. Skand. Aktuarietidskr. 37, 137-162.
338. Seal, H.L. (1977) Studies in the history of probability and statistics. XXXV Multiple decrements or competing risks. Biometrika 64, 429-439.
339. Sen, P.K. (1974) Nonparametric tests for interchangeability under competing risks. Inst. of Statist. Mimeo Series No. 905, University of North Carolina.
340. Serio, C.D. (1997) The protective impact of a covariate on competing failures with an example from a bone marrow transplantation study. Lifetime Data Analysis 3, 99-122.
341. Shen, Y., and Cheng, S.C. (1999) Confidence bands for cumulative incidence curves under the additive risk model. Biometrics 55, 1093-1100.
342. Slud, E.V., and Rubenstein, L.V. (1983). Dependent competing risks and summary survival curves. Biometrika 70, 643-649.
343. Solari, A., Salmaso, L., El Barmi, H., and Pesarin, F. (2008) Conditional tests in a competing risks model. Lifetime Data Analysis 14, 154-166.
344. Sun, L., Liu, J., Sun, J., and Zhang, M. (2006) Modeling the subdistribution of a competing risk. Statist. Sinica 16, 1367-1385.
345. Tsiatis, A. (1975) A nonidentifiability aspect of the problem of competing risks. Proc. Nat. Acad. Sci. USA 72, 20-22.
346. Tsiatis, A.A., Davidian, M., and McNeney, B. (2002) Multiple imputation methods for testing different treatment differences in survival distributions with missing cause of failure. Biometrika 89, 238-244.
347. Usher, J.S., and Hodgson, T.J. (1988) Maximum likelihood analysis of component reliability using masked system life-test data. IEEE Trans. Reliab. 37, 550-555.
348. Usher, J.S., and Guess, F.M. (1989) An iterative approach for estimating component reliability from masked system life data. Qual. Reliab. Eng. Inst. 5, 257-261.
349. Wang, O. (1977) A competing risk model based on the life table procedure in epidemiologic studies. Int. J. Epidemiology 6, 153-159.
350. Williams, J.S. and Lagakos, S.W. (1976) Independent and dependent censoring mechanisms. Proc. 9th Int. Biometric Conf., Vol. 1, 408-427.
351. Williams, J.S., and Lagakos, S.W. (1977) Models for censored survival analysis: Constant-sum and variable-sum models. Biometrika 64, 215-224.
352. Yashin, A.I., Manton, K.G., and Stallard, E. (1986) Dependent competing risks: a stochastic process model. J. Math. Biol. 24, 119-164.
353. Zheng, M., and Klein, J.P. (1995) Estimates of marginal survival for dependent competing risks based on an assumed copula. Biometrika 82, 127-138.
354. Andersen, P.K., and Gill, R.D. (1982) Cox’s regression model for counting processes: a large sample study. Ann. Statist. 10, 1100-1120.
355. Andersen, P.K., and Borgan, O. (1985) Counting process models for life history data: A review. Scand. J. Statist. 12, 97-158.
356. Arjas, E. (1985) Contribution to discussion of Andersen and Borgan. Scand. J. Statist. 12, 150-153.
357. Borgan, O. (1984) Maximum likelihood estimation in parametric counting process models, with applications to censored survival data. Scand. J. Statist. 11, 1-16 (Correction 11, 275).
358. Doob, J.L. (1940) Regularity properties of certain families of chance variables. Trans. Amer. Math. Soc. 47, 455-486.
359. Doob, J.L. (1953) Stochastic Processes. John Wiley and Sons, New York.
360. Gill, R.D. (1984) Understanding Cox’s regression model: a martingale approach. J. Amer. Statist. Assoc. 79, 441-447.
361. Gill, R.D., and Johansen, S. (1990) Asurvey of product-integration with a view toward application in survival analysis. Ann. Statist. 4, 1501-1555.
362. Lan, K.K.G., and Lachin, J.M. (1995) Martingales without tears. Lifetime Data Analysis 1, 361-375.
363. Rivest, L-P., and Wells, M.T. (2001) A martingale approach to the copula-graphic estimator for the survival function under dependent censoring. J. Multiv. Anal. 79, 138-155.
364. Therneau, T.M., Grambsch, P.M., and Fleming, T.R. (1990) Martingale-based residuals for survival models. Biometrika 77, 147-160.
365. Abate, J., Choudhury, G.L., and Whitt, W. (1996) On the Laguerre method for numerically inverting Laplace transforms. INFORMS Journal on Computing 8, 413-427.
366. Andrews, D.F., and Herzberg, A.M. (1985) Data: A Collection of Problems from Many Fields for the Student and Research Worker. Springer, New York.
367. Archbold, J.W. (1970) Algebra, Fourth Edition. Pitman Publishing, London.
368. Atkinson, A.C. (1985) Plots, Transformations and Regression. Clarendon Press, Oxford.
369. Bowers, L., Allan, T., Simpson, A., Jones, J., and Van Der Merwe, M. (2009) Identifying key factors associated with aggression on acute inpatient psychiatric wards. Issues in Mental Health Nursing 30, 260-271.
370. Brooks, S.P., and Morgan, B.J.T. (1995) Optimisation using simulated annealing. Statistician 44, 241-257.
371. Buonaccorsi, J.P. (2010) Measurement Error: Models, Methods and Applications. Chapman & Hall/CRC Press, Boca Raton, FL.
372. Cappe, O., Moulines, E., and Ryden, T. (2005) Inference in Hidden Markov Models. Springer, New York.
373. Cheng, R.C.H., and Stevens, M.A. (1989) A goodness-of-fit test using Moran’s statistic with estimated parameters. Biometrika 76, 385-392.
374. Cody, W.J., and Thacher, H.C. Jr. (1969) Chebyshev approximations for the exponential integral E1(x). Math. Comp. 23, 289-303.
375. Cook, R.D., and Weisburg, S. (1982) Residuals and Influence in Regression. Chapman & Hall, London. Copas, J. B. (1983) Plotting p against x. Appl. Statist. 32, 25-31.
376. Cox, D.R. (1970) The Analysis of Binary Data. Methuen, London.
377. Cox, D.R., and Hinkley, D.V. (1974) Theoretical Statistics. Chapman & Hall, London.
378. Cox, D.R., and Miller, H.D. (1965) The Theory of Stochastic Processes. Methuen, London.
379. Cox, D.R., and Reid, N. (1987) Parameter orthogonality and approximate conditional inference (with discussion). J. Roy. Statist. Soc. B49, 1-39.
380. Crompton, R. (1922) Just William. Newnes, London.
381. Crowder, M.J. (1986) On consistency and inconsistency of estimating equations. Econ. Theory 2, 305-330.
382. Crowder, M.J. (1987) On linear and quadratic estimating functions. Biometrika 74, 591-597.
383. Crowder, M.J. (2001) Corrected p-values for tests based on estimated parameters. Statistics and Computing 11, 347-354.
384. Crowder, M.J., and Hand, D.J. (1990) Analysis of Repeated Measures. Chapman & Hall, London.
385. Crowder, M.J., Dixon, M.J., Robinson, M.E., and Ledford, A.W. (2002) Dynamic modelling and prediction of English football league matches. The Statistician 51, 157-168.
386. DeGroot, M.H. (1973) Doing what comes naturally: interpreting a tail area as a posterior probability or a likelihood ratio. J. Amer. Statist. Assoc. 68, 966-969.
387. Diggle, P.J., Heagerty, P.J., Liang, K-Y., and Zeger, S.L. (2002) Analysis of Longitudinal Data, Second Edition. Oxford University Press, Oxford.
388. Dixon, M.J., and Coles, S.G. (1997) Modelling association football scores and inefficiencies in the football betting market. Applied Statistics 46, 265-280.
389. Doyle, A.C. (1950) Silver Blaze. In The Memoirs of Sherlock Holmes. Penguin, London.
390. Efron, B., and Hinkley, D.V. (1978) Assessing the accuracy of the maximum likelihood estimator: observed versus expected Fisher information. Biometrika 65, 457-487.
391. Everitt, B.S., and Hothorn, T. (2010)A Handbook of Statistical Analyses Using R.Chapman & Hall/CRC Press, Boca Raton, FL.
392. Feller, W. (1962) An Introduction to Probability Theory and Its Applications, Vol. 1, Second Edition.Wiley, New York.
393. Fitzmaurice, G., Davidian, M., Verbeke, G., and Molenberghs, G. (2009) Longitudinal Data Analysis. CRC Press, Boca Raton, FL.
394. Fletcher, R., and Powell, M.J.D. (1963) A rapidly convergent descent method for minimisation. Comp. J. 6, 163-168.
395. Galambos, J. (1978) The Asymptotic Theory of Extreme Order Statistics. Wiley, New York.
396. Gelfand, A.E., and Smith, A.F.M. (1990) Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85, 398-409.
397. Genz, A. (1993) A comparison of methods for numerical computation of multivariate normal integrals. Comp. Sci. Statist. 25, 400-405.
398. Geyer, C.J. (1992) Practical Markov chain Monte Carlo. Statist. Sci. 7, 473-511.
399. Gilks, W.R., Richardson, S., and Spiegelhalter, D.J. (1996) Markov Chain Monte Carlo in Practice. Chapman & Hall, London.
400. Gill, P.E., Murray, W., and Wright, M.H. (1981) Practical Optimization. Academic Press, London.
401. Hand, D.J., and Crowder, M.J. (1996) Practical Longitudinal Data Analysis. Chapman & Hall/CRC Press, London.
402. Johnson, N.L., and Kotz, S. (1972) Distributions in Statistics: Continuous Multivariate Distributions. Wiley, New York.
403. Kalbfleisch, J.D., and Sprott, D.A. (1970) Application of likelihood methods to models involving large numbers of parameters (with discussion). J. Roy. Statist. Soc. B 32, 175-208.
404. Karlin, S., and Taylor, H.M. (1975) A First Course in Stochastic Processes, Second Edition. Academic Press, London.
405. Little, R.J.A., and Rubin, D.B. (2002) Statistical Analysis with Missing Data, Second Edition.Wiley, New York.
406. Lodge, D. (1990) Famous Cricketers, Series No. 15: W.G. Grace. Association of Cricket Statisticians and Historians, West Bridgford, Nottingham, U.K.
407. MacDonald, I.L., and Zucchini, W. (1997) Hidden Markov and Other Models for Discrete-Valued Time Series. Chapman & Hall/CRC Press, Boca Raton, FL.
408. Moler, M., andVan Loan, C. (2003) Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review 45, 3-49.
409. Morgan, B.J.T. (1995) Elements of Simulation. Chapman & Hall, London.
410. O’Hagan, A., and Forster, J. (2004) Kendall’s Advanced Theory of Statistics, Second Edition, Vol. 2B, Bayesian Inference. Arnold, London.
411. Olver, F.W.J., Lozier, D.W., Boisvert, R.F., and Clark, C.W. (2010) NIST Handbook of Mathematical Functions. National Institute for Standards and Technology and Cambridge University Press, Cambridge.
412. Rabe-Hesketh, S., and Skrondal, A. (2008) Multilevel and Longitudinal Modeling Using Stata, Second Edition. Stata Press, College Station, Texas.
413. Rayner, J., and Best, D. (1999) Smooth tests of goodness of fit: An overview. Int. Statist. Rev. 58, 9-17.
414. Ripley, B.D. (1987) Stochastic Simulation. John Wiley & Sons, New York.
415. Ross, G.J.S. (1970) The efficient use of function minimization in nonlinear maximum likelihood estimation. Appl. Statist. 19, 205-221.
416. Ross, S. (1996) Stochastic Processes, Second Edition. Wiley, New York.
417. Self, S.G., and Liang, K. (1987) Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610.
418. Sethuraman, J. (1965) On a characterization of the three limiting types of the extreme. Sankhya A 27, 357-364.
419. Smith, A.F.M. (1991) Bayesian computational methods. Phil. Trans. Roy. Soc. London. A 337, 369-386.
420. Smith, A.F.M., and Roberts, G.O. (1993) Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. J. Roy. Statist. Soc. B55, 3-23.
421. Stewart, D., Bowers, L., and Warburton, F. (2009) Constant special observation and self-harm on acute psychiatric wards: A longitudinal analysis. General Hospital Psychiatry 31, 523-530.
422. Venables, W.N., and Ripley, B.D. (1999) Modern Applied Statistics with S-PLUS, Third Edition. Springer-Verlag, New York.
423. Walker, S.G., Damien, P., Land, P.W., and Smith, A.F.M. (1999) Bayesian nonparametric inference for random distributions and related functions (with discussion). J. Roy. Statist. Soc. B 61, 485-527.
424. Wang, Y. (2007) On fast computation of the non-parametric maximum likelihood estimate of a mixing distribution. J. R. Statist. Soc. 69, 185-198.
425. Watson, A.S., and Smith, R.L. (1985) An examination of statistical theories for fibrous materials in the light of experimental data. J. Mat. Sci. 20, 3260-3270.
426. Whittaker, E.T., and Watson, G.N. (1927) A Course of Modern Analysis. Cambridge University Press, Cambridge.
427. Wu, L. (2010) Mixed Effects Models for Complex Data. Chapman & Hall/CRC Press, Boca Raton, FL.