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Volumn 21, Issue 4, 2006, Pages 487-500

Dynamic modeling and statistical analysis of event times

Author keywords

Counting process; Generalized Nelson Aalen estimator; Generalized product limit estimator; Hazard function; Martingale; Partial likelihood

Indexed keywords


EID: 34249337065     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/088342306000000349     Document Type: Review
Times cited : (38)

References (49)
  • 1
    • 0000047140 scopus 로고
    • Nonparametric inference for a family of counting processes
    • MR0491547
    • AALEN, O. (1978). Nonparametric inference for a family of counting processes. Ann. Statist. 6 701-726. MR0491547
    • (1978) Ann. Statist , vol.6 , pp. 701-726
    • AALEN, O.1
  • 2
    • 0025817963 scopus 로고
    • Statistical analysis of repeated events forming renewal processes
    • AALEN, O. and HUSEBYE, E. (1991). Statistical analysis of repeated events forming renewal processes. Statistics in Medicine 10 1227-1240.
    • (1991) Statistics in Medicine , vol.10 , pp. 1227-1240
    • AALEN, O.1    HUSEBYE, E.2
  • 3
    • 0347872819 scopus 로고    scopus 로고
    • A dynamic competing risks model
    • MR1695124
    • AGUSTIN, M. A. and PEÑA, E. A. (1999). A dynamic competing risks model. Probab. Engrg. Inform. Sci. 13 333-358. MR1695124
    • (1999) Probab. Engrg. Inform. Sci , vol.13 , pp. 333-358
    • AGUSTIN, M.A.1    PEÑA, E.A.2
  • 4
    • 18944382239 scopus 로고    scopus 로고
    • A basis approach to goodness-of-fit testing in recurrent event models
    • MR2194479
    • AGUSTIN, Z. and PEÑA, E. (2005). A basis approach to goodness-of-fit testing in recurrent event models. J. Statist. Plann. Inference 133 285-303. MR2194479
    • (2005) J. Statist. Plann. Inference , vol.133 , pp. 285-303
    • AGUSTIN, Z.1    PEÑA, E.2
  • 5
    • 34249298742 scopus 로고    scopus 로고
    • ANDERSEN, P., BORGAN, Ø., GILL, R. and KEIDING, N. (1993). Statistical Models Based on Counting Processes. Springer, New York. MR1198884
    • ANDERSEN, P., BORGAN, Ø., GILL, R. and KEIDING, N. (1993). Statistical Models Based on Counting Processes. Springer, New York. MR1198884
  • 6
    • 0001646484 scopus 로고
    • Cox's regression model for counting processes: A large sample study
    • MR0673646
    • ANDERSEN, P. and GILL, R. (1982). Cox's regression model for counting processes: A large sample study. Ann. Statist. 10 1100-1120. MR0673646
    • (1982) Ann. Statist , vol.10 , pp. 1100-1120
    • ANDERSEN, P.1    GILL, R.2
  • 7
    • 34249328921 scopus 로고    scopus 로고
    • BARLOW, R. and PROSCHAN, F. (1981). Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York. MR0438625
    • BARLOW, R. and PROSCHAN, F. (1981). Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York. MR0438625
  • 8
    • 0030352612 scopus 로고    scopus 로고
    • A point process model for the reliability of a maintained system subject to general repair
    • MR1374870
    • BAXTER, L., KIJIMA, M. and TORTORELLA, M. (1996). A point process model for the reliability of a maintained system subject to general repair. Comm. Statist. Stochastic Models 12 37-65. MR1374870
    • (1996) Comm. Statist. Stochastic Models , vol.12 , pp. 37-65
    • BAXTER, L.1    KIJIMA, M.2    TORTORELLA, M.3
  • 9
    • 0022082818 scopus 로고
    • Age-dependent minimal repair
    • MR0789360
    • BLOCK, H., BORGES, W. and SAVITS, T. (1985). Age-dependent minimal repair. J. Appl. Probab. 22 370-385. MR0789360
    • (1985) J. Appl. Probab , vol.22 , pp. 370-385
    • BLOCK, H.1    BORGES, W.2    SAVITS, T.3
  • 10
    • 0020903272 scopus 로고
    • Imperfect repair
    • MR0720476
    • BROWN, M. and PROSCHAN, F. (1983). Imperfect repair. J. Appl. Probab. 20 851-859. MR0720476
    • (1983) J. Appl. Probab , vol.20 , pp. 851-859
    • BROWN, M.1    PROSCHAN, F.2
  • 11
    • 0000336139 scopus 로고
    • Regression models and life-tables (with discussion)
    • MR0341758
    • COX, D. (1972). Regression models and life-tables (with discussion). J. Roy. Statist. Soc. Ser. B 34 187-220. MR0341758
    • (1972) J. Roy. Statist. Soc. Ser. B , vol.34 , pp. 187-220
    • COX, D.1
  • 12
    • 0002629270 scopus 로고
    • Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion)
    • MR0501537
    • DEMPSTER, A., LAIRD, N. and RUBIN, D. (1977). Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion). J. Roy. Statist. Soc. Ser. B 39 1-38. MR0501537
    • (1977) J. Roy. Statist. Soc. Ser. B , vol.39 , pp. 1-38
    • DEMPSTER, A.1    LAIRD, N.2    RUBIN, D.3
  • 13
    • 0031491526 scopus 로고    scopus 로고
    • Nonparametric estimation for a general repair model
    • MR1447744
    • DORADO, C., HOLLANDER, M. and SETHURAMAN, J. (1997). Nonparametric estimation for a general repair model. Ann. Statist. 25 1140-1160. MR1447744
    • (1997) Ann. Statist , vol.25 , pp. 1140-1160
    • DORADO, C.1    HOLLANDER, M.2    SETHURAMAN, J.3
  • 14
    • 34249317321 scopus 로고    scopus 로고
    • FLEMING, T. and HARRINGTON, D. (1991). Counting Processes and Survival Analysis. Wiley, New York. MR1100924
    • FLEMING, T. and HARRINGTON, D. (1991). Counting Processes and Survival Analysis. Wiley, New York. MR1100924
  • 15
    • 0019026254 scopus 로고
    • An analysis of comparative carcinogenesis experiments based on multiple times to tumor
    • MR0672325
    • GAIL, M., SANTNER, T. and BROWN, C. (1980). An analysis of comparative carcinogenesis experiments based on multiple times to tumor. Biometrics 36 255-266. MR0672325
    • (1980) Biometrics , vol.36 , pp. 255-266
    • GAIL, M.1    SANTNER, T.2    BROWN, C.3
  • 16
    • 34249278493 scopus 로고    scopus 로고
    • GILL, R. (1980). Censoring and Stochastic Integrals. Mathematisch Centrum, Amsterdam. MR0596815
    • GILL, R. (1980). Censoring and Stochastic Integrals. Mathematisch Centrum, Amsterdam. MR0596815
  • 17
    • 0001156454 scopus 로고
    • Testing with replacement and the product-limit estimator
    • MR0619288
    • GILL, R. D. (1981). Testing with replacement and the product-limit estimator. Ann. Statist. 9 853-860. MR0619288
    • (1981) Ann. Statist , vol.9 , pp. 853-860
    • GILL, R.D.1
  • 18
    • 0001232443 scopus 로고
    • A survey of product-integration with a view toward application in survival analysis
    • MR1074422
    • GILL, R. D. and JOHANSEN, S. (1990). A survey of product-integration with a view toward application in survival analysis. Ann. Statist. 18 1501-1555. MR1074422
    • (1990) Ann. Statist , vol.18 , pp. 1501-1555
    • GILL, R.D.1    JOHANSEN, S.2
  • 19
    • 30944434398 scopus 로고    scopus 로고
    • Modelling intervention effects after cancer relapses
    • MR2221978
    • GONZÁLEZ, J., PEÑA, E. and SLATE, E. (2005). Modelling intervention effects after cancer relapses. Statistics in Medicine 24 3959-3975. MR2221978
    • (2005) Statistics in Medicine , vol.24 , pp. 3959-3975
    • GONZÁLEZ, J.1    PEÑA, E.2    SLATE, E.3
  • 20
    • 0001241617 scopus 로고
    • Nonparametric Bayes estimators based on beta processes in models for life history data
    • MR1062708
    • HJORT, N. L. (1990). Nonparametric Bayes estimators based on beta processes in models for life history data. Ann. Statist. 18 1259-1294. MR1062708
    • (1990) Ann. Statist , vol.18 , pp. 1259-1294
    • HJORT, N.L.1
  • 21
    • 0029420024 scopus 로고
    • Dynamic reliability models with conditional proportional hazards
    • MR1371991
    • HOLLANDER, M. and PEÑA, E. A. (1995). Dynamic reliability models with conditional proportional hazards. Lifetime Data Anal. 1 377-401. MR1371991
    • (1995) Lifetime Data Anal , vol.1 , pp. 377-401
    • HOLLANDER, M.1    PEÑA, E.A.2
  • 22
    • 0002979446 scopus 로고
    • Software reliability research
    • W. Freiberger, ed, Academic Press, New York
    • JELINSKI, Z. and MORANDA, P. (1972). Software reliability research. In Statistical Computer Performance Evaluation (W. Freiberger, ed.) 465-484, Academic Press, New York.
    • (1972) Statistical Computer Performance Evaluation , pp. 465-484
    • JELINSKI, Z.1    MORANDA, P.2
  • 23
    • 0002192597 scopus 로고
    • Some results for repairable systems with general repair
    • MR0981254
    • KIJIMA, M. (1989). Some results for repairable systems with general repair. J. Appl. Probab. 26 89-102. MR0981254
    • (1989) J. Appl. Probab , vol.26 , pp. 89-102
    • KIJIMA, M.1
  • 24
    • 0026473380 scopus 로고
    • Reliability analysis of hydraulic systems of LHD machines using the power law process model
    • KUMAR, U. and KLEFSJÖ, B. (1992). Reliability analysis of hydraulic systems of LHD machines using the power law process model. Reliability Engineering and System Safety 35 217-224.
    • (1992) Reliability Engineering and System Safety , vol.35 , pp. 217-224
    • KUMAR, U.1    KLEFSJÖ, B.2
  • 25
    • 14944352003 scopus 로고    scopus 로고
    • Estimating load-sharing properties in a dynamic reliability system
    • MR2156836
    • KVAM, P. and PEÑA, E. (2005). Estimating load-sharing properties in a dynamic reliability system. J. Amer. Statist. Assoc. 100 262-272. MR2156836
    • (2005) J. Amer. Statist. Assoc , vol.100 , pp. 262-272
    • KVAM, P.1    PEÑA, E.2
  • 26
    • 0032298110 scopus 로고    scopus 로고
    • Asymptotic and monotonicity properties of some repairable systems
    • MR1671097
    • LAST, G. and SZEKLI, R. (1998). Asymptotic and monotonicity properties of some repairable systems. Adv. in Appl. Probab. 30 1089-1110. MR1671097
    • (1998) Adv. in Appl. Probab , vol.30 , pp. 1089-1110
    • LAST, G.1    SZEKLI, R.2
  • 27
    • 0000153163 scopus 로고
    • Regression methods for Poisson process data
    • MR0909986
    • LAWLESS, J. (1987). Regression methods for Poisson process data. J. Amer. Statist. Assoc. 82 808-815. MR0909986
    • (1987) J. Amer. Statist. Assoc , vol.82 , pp. 808-815
    • LAWLESS, J.1
  • 28
    • 0000176545 scopus 로고
    • Relation de domination entre deux processus
    • MR0471069
    • LENGLART, E. (1977). Relation de domination entre deux processus. Ann. Inst. H. Poincaré Sect. B (N.S.) 13 171-179. MR0471069
    • (1977) Ann. Inst. H. Poincaré Sect. B (N.S.) , vol.13 , pp. 171-179
    • LENGLART, E.1
  • 30
    • 0037321815 scopus 로고    scopus 로고
    • The trend-renewal process for statistical analysis of repairable systems
    • MR1956189
    • LINDQVIST, B. H., ELVEBAKK, G. and HEGGLAND, K. (2003). The trend-renewal process for statistical analysis of repairable systems. Technometrics 45 31-44. MR1956189
    • (2003) Technometrics , vol.45 , pp. 31-44
    • LINDQVIST, B.H.1    ELVEBAKK, G.2    HEGGLAND, K.3
  • 31
    • 84945593245 scopus 로고
    • Smooth test for goodness of fit
    • NEYMAN, J. (1937). "Smooth" test for goodness of fit. Skand. Aktuarietidskrift 20 149-199.
    • (1937) Skand. Aktuarietidskrift , vol.20 , pp. 149-199
    • NEYMAN, J.1
  • 32
    • 0002133303 scopus 로고
    • A counting process approach to maximum likelihood estimation in frailty models
    • MR1172965
    • NIELSEN, G., GILL, R., ANDERSEN, P. and SØRENSEN, T. (1992). A counting process approach to maximum likelihood estimation in frailty models. Scand. J. Statist. 19 25-43. MR1172965
    • (1992) Scand. J. Statist , vol.19 , pp. 25-43
    • NIELSEN, G.1    GILL, R.2    ANDERSEN, P.3    SØRENSEN, T.4
  • 33
    • 17044454987 scopus 로고    scopus 로고
    • PEÑA, E. A. (1998a). Smooth goodness-of-fit tests for composite hypothesis in hazard based models. Ann. Statist. 26 1935-1971. MR1673285
    • PEÑA, E. A. (1998a). Smooth goodness-of-fit tests for composite hypothesis in hazard based models. Ann. Statist. 26 1935-1971. MR1673285
  • 34
    • 17044459724 scopus 로고    scopus 로고
    • Smooth goodness-of-fit tests for the baseline hazard in Cox's proportional hazards model
    • MR1631357
    • PEÑA, E. A. (1998b). Smooth goodness-of-fit tests for the baseline hazard in Cox's proportional hazards model. J. Amer. Statist. Assoc. 93 613-692. MR1631357
    • (1998) J. Amer. Statist. Assoc , vol.93 , pp. 613-692
    • PEÑA, E.A.1
  • 35
    • 34249310734 scopus 로고    scopus 로고
    • PEÑA, E. and HOLLANDER, M. (2004). Models for recurrent events in reliability and survival analysis. In Mathematical Reliability: An Expository Perspective (R. Soyer, T. Mazzuchi and N. Singpurwalla, eds.) 105-123. Kluwer, Boston. MR2065001
    • PEÑA, E. and HOLLANDER, M. (2004). Models for recurrent events in reliability and survival analysis. In Mathematical Reliability: An Expository Perspective (R. Soyer, T. Mazzuchi and N. Singpurwalla, eds.) 105-123. Kluwer, Boston. MR2065001
  • 36
    • 34249314086 scopus 로고    scopus 로고
    • PEÑA, E. and SLATE, E. (2005). Dynamic modeling in reliability and survival analysis. In Modern Statistical and Mathematical Methods in Reliability (A. Wilson, N. Limnios, S. Keller-McNulty and Y. Armijo, eds.) 55-71. World Scientific, Singapore. MR2230700
    • PEÑA, E. and SLATE, E. (2005). Dynamic modeling in reliability and survival analysis. In Modern Statistical and Mathematical Methods in Reliability (A. Wilson, N. Limnios, S. Keller-McNulty and Y. Armijo, eds.) 55-71. World Scientific, Singapore. MR2230700
  • 37
    • 33846364650 scopus 로고    scopus 로고
    • Semiparametric inference for a general class of models for recurrent events
    • To appear
    • PEÑA, E., SLATE, E. and GONZÁLEZ, J. (2007). Semiparametric inference for a general class of models for recurrent events. J. Statist. Plann. Inference. To appear.
    • (2007) J. Statist. Plann. Inference
    • PEÑA, E.1    SLATE, E.2    GONZÁLEZ, J.3
  • 38
    • 34249278158 scopus 로고    scopus 로고
    • PEÑA, E. A., STRAWDERMAN, R. L. and HOLLANDER, M. (2000). A weak convergence result relevant in recurrent and renewal models. In Recent Advances in Reliability Theory (Bordeaux, 2000) (N. Limnios and M. Nikulin, eds.) 493-514. Birkhäuser, Boston. MR1783501
    • PEÑA, E. A., STRAWDERMAN, R. L. and HOLLANDER, M. (2000). A weak convergence result relevant in recurrent and renewal models. In Recent Advances in Reliability Theory (Bordeaux, 2000) (N. Limnios and M. Nikulin, eds.) 493-514. Birkhäuser, Boston. MR1783501
  • 39
    • 1542679214 scopus 로고    scopus 로고
    • Nonparametric estimation with recurrent event data
    • MR1946578
    • PEÑA, E. A., STRAWDERMAN, R. L. and HOLLANDER, M. (2001). Nonparametric estimation with recurrent event data. J. Amer. Statist. Assoc. 96 1299-1315. MR1946578
    • (2001) J. Amer. Statist. Assoc , vol.96 , pp. 1299-1315
    • PEÑA, E.A.1    STRAWDERMAN, R.L.2    HOLLANDER, M.3
  • 40
    • 70349813434 scopus 로고
    • On the regression analysis of multivariate failure time data
    • MR0626396
    • PRENTICE, R., WILLIAMS, B. and PETERSON, A. (1981). On the regression analysis of multivariate failure time data. Biometrika 68 373-379. MR0626396
    • (1981) Biometrika , vol.68 , pp. 373-379
    • PRENTICE, R.1    WILLIAMS, B.2    PETERSON, A.3
  • 41
    • 0001069341 scopus 로고
    • Central limit theorems for local martingales
    • MR0566321
    • REBOLLEDO, R. (1980), Central limit theorems for local martingales. Z. Wahrsch. Verw. Gebiete 51 269-286. MR0566321
    • (1980) Z. Wahrsch. Verw. Gebiete , vol.51 , pp. 269-286
    • REBOLLEDO, R.1
  • 42
    • 34249284207 scopus 로고    scopus 로고
    • SELLKE, T. (1988). Weak convergence of the Aalen estimator for a censored renewal process. In Statistical Decision Theory and Related Topics IV (S. Gupta and J. Berger, eds.) 2 183-194. Springer, New York. MR0927132
    • SELLKE, T. (1988). Weak convergence of the Aalen estimator for a censored renewal process. In Statistical Decision Theory and Related Topics IV (S. Gupta and J. Berger, eds.) 2 183-194. Springer, New York. MR0927132
  • 43
    • 84972500509 scopus 로고
    • Survival in dynamic environments
    • SINGPURWALLA, N. D. (1995). Survival in dynamic environments. Statist. Sci. 10 86-103.
    • (1995) Statist. Sci , vol.10 , pp. 86-103
    • SINGPURWALLA, N.D.1
  • 44
    • 0001439067 scopus 로고
    • Optimal maintenance strategies for repairable systems with general degree of repair
    • MR1104574
    • STADJE, W. and ZUCKERMAN, D. (1991). Optimal maintenance strategies for repairable systems with general degree of repair. J. Appl. Probab. 28 384-396. MR1104574
    • (1991) J. Appl. Probab , vol.28 , pp. 384-396
    • STADJE, W.1    ZUCKERMAN, D.2
  • 45
    • 34249334694 scopus 로고    scopus 로고
    • STOCKER, R. (2004). A general class of parametric models for recurrent event data. Ph.D. dissertation, Univ. South Carolina.
    • STOCKER, R. (2004). A general class of parametric models for recurrent event data. Ph.D. dissertation, Univ. South Carolina.
  • 46
    • 34248995832 scopus 로고    scopus 로고
    • A general class of parametric models for recurrent event data
    • To appear
    • STOCKER, R. and PEÑA, E. (2007). A general class of parametric models for recurrent event data. Technometrics. To appear.
    • (2007) Technometrics
    • STOCKER, R.1    PEÑA, E.2
  • 47
    • 34249327784 scopus 로고    scopus 로고
    • THERNEAU, T. and GRAMBSCH, P. (2000). Modeling Survival Data: Extending the Cox Model. Springer, New York. MR1774977
    • THERNEAU, T. and GRAMBSCH, P. (2000). Modeling Survival Data: Extending the Cox Model. Springer, New York. MR1774977
  • 48
    • 0442293851 scopus 로고    scopus 로고
    • Nonparametric estimation of a recurrent survival function
    • MR1689220
    • WANG, M.-C. and CHANG, S.-H. (1999), Nonparametric estimation of a recurrent survival function. J. Amer. Statist. Assoc. 94 146-153. MR1689220
    • (1999) J. Amer. Statist. Assoc , vol.94 , pp. 146-153
    • WANG, M.-C.1    CHANG, S.-H.2
  • 49
    • 79953752268 scopus 로고
    • Regression analysis of multivariate incomplete failure time data by modeling marginal distributions
    • MR1134494
    • WEI, L., LIN, D. and WEISSFELD, L. (1989). Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. J. Amer. Statist. Assoc. 84 1065-1073. MR1134494
    • (1989) J. Amer. Statist. Assoc , vol.84 , pp. 1065-1073
    • WEI, L.1    LIN, D.2    WEISSFELD, L.3


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