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Zbl 0243.62041
Cox, D.R.
Regression models and life-tables. (English)
[J] J. R. Stat. Soc., Ser. B 34, 187-220 (1972). ISSN 0035-9246

The statistical analysis is considered of observations on non-negative variables subject to censoring on the right. That is, for each individual we may observe either the value of the random variable $T$ or that $T$ exceeds some given value, not necessarily the same for all individuals. Such data arise commonly in medical, actuarial and industrial contexts. For simplicity, call $T$ a failure time. Further it is assumed that there is available for each individual a vector of explanatory variables which may influence $T$. Possible approaches to the analysis are reviewed. Primarily the paper deals with a model in which the age-specific failure rate (hazard function) has the form $$\exp(\beta_1z_1+\dots+\beta_pz_p)\lambda_0(t),$$ where $\lambda_0(\cdot)$ is an arbitrary unknown function, $\beta_1,\dots, \beta_p$ are unknown parameters and $(z_1,\dots, z_p)$ is the vector of explanatory variables. A modified likelihood function is obtained for inference about $\beta_1,\dots, \beta_p$ by arguing conditionally on the observed failure times. From this likelihood tests and confidence regions are obtained. In the special case of a two-sample problem with proportional hazards, the test of the null hypothesis of zero difference reduces to a generalization to censored data of the most efficient two-sample rank test for exponential distributions. A number of generalizations are considered and the relation with stochastic models discussed. Discussion of the paper by 15 contributors is included togeher with the author's reply.

Display scanned Zentralblatt-MATH page with this review.
[D. R. Cox]

MSC 2000:: *62J05 Linear regression
62N05 Reliability, etc. (statistics)
62F10 Point estimation

Cited in: Zbl 1238.62118 Zbl 1238.62116 Zbl 1236.62130 Zbl 1234.62028 Zbl 1238.62133 Zbl 1234.62128 Zbl 1231.62063 Zbl 1215.62102 Zbl 1209.62244 Zbl 1200.62123 Zbl 1192.62209 Zbl 1192.62231 Zbl 1211.62183 Zbl 1176.62096 Zbl 1171.62062 Zbl 1170.62066 Zbl 1170.62078 Zbl 1229.90050 Zbl 1125.62112 Zbl 1102.62084 Zbl 1102.62108 Zbl 1085.62037 Zbl 1160.62352 Zbl 1152.62380 Zbl 1094.62107 Zbl 1079.62109 Zbl 1071.62111 Zbl 1071.62096 Zbl 1058.62084 Zbl 1113.60019 Zbl 1054.62114 Zbl 1047.62090 Zbl 1017.62093 Zbl 1210.62184 Zbl 1195.62119 Zbl 1127.62405 Zbl 1009.62082 Zbl 1009.62093 Zbl 0998.62087 Zbl 0988.62059 Zbl 0985.62086 Zbl 0984.62085 Zbl 1061.62563 Zbl 1060.62607 Zbl 1054.62113 Zbl 0977.62102 Zbl 0968.62519 Zbl 1059.62668 Zbl 0954.65006 Zbl 0944.60089 Zbl 0942.62090 Zbl 0939.62033 Zbl 0939.62101 Zbl 0938.62116 Zbl 1067.62575 Zbl 0927.62104 Zbl 0920.62090 Zbl 0918.62077 Zbl 0945.62105 Zbl 0929.62048 Zbl 0916.62082 Zbl 0897.62074 Zbl 0896.62126 Zbl 0929.62007 Zbl 0899.62139 Zbl 0896.62123 Zbl 0878.62086 Zbl 0830.62016 Zbl 0823.62042 Zbl 0803.62078 Zbl 0802.62037 Zbl 0761.62063 Zbl 0692.62082 Zbl 0707.62209 Zbl 0678.62081 Zbl 0659.62068 Zbl 0676.62042 Zbl 0613.62129 Zbl 0657.62114 Zbl 0655.62100 Zbl 0591.62034 Zbl 0698.62102 Zbl 0655.62101 Zbl 0588.62172 Zbl 0565.62094 Zbl 0565.62022 Zbl 0544.60079 Zbl 0538.90020 Zbl 0535.62039 Zbl 0528.62034 Zbl 0526.62081 Zbl 0526.62043 Zbl 0509.62015 Zbl 0504.62098 Zbl 0503.62090 Zbl 0527.62094 Zbl 0503.62091 Zbl 0479.62080 Zbl 0472.62053 Zbl 0454.62091 Zbl 0432.62077 Zbl 0392.62087

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