A Modified X 2 Approach for Fitting Weibull Models to Synthetic Life Tables a Modified X 2 Approach for Fitting Weibull Models to Synthetic Life Tables

SUMMARY Weibul1 models are fitted to synthetic life table data by applying weighted least squares analysis to log log functions which are constructed from appropriate underlying contingency tables. As such, the resulting estitnates and'test 'statistics are based on the linear±zed minimwullfOd'tfied x2-criterion and thus have satisfactory properties in moderately large 1 samples. The basic methodology is illustrated in terms of, an example which is bivariate in the sense of involving two simultaneous, but non-competing, vital events. For this situation, the estimation of Weibull model parameters is described for both marginal as well as certain conditional distri-but ions either individually or jointly.

[1]  G. Koch,et al.  Analysis of categorical data by linear models. , 1969, Biometrics.

[2]  R. Doll,et al.  A mathematical model for the age distribution of cancer in man , 1969, International journal of cancer.

[3]  P. Armitage,et al.  Multistage models of carcinogenesis. , 1985, Environmental health perspectives.

[4]  P. Armitage,et al.  The age distribution of cancer and a multi-stage theory of carcinogenesis , 1954, British Journal of Cancer.

[5]  P. Lee,et al.  Weibull distributions for continuous-carcinogenesis experiments. , 1973, Biometrics.

[6]  G G Koch,et al.  An analysis for compounded functions of categorical data. , 1973, Biometrics.

[7]  P. Armitage,et al.  A Two-stage Theory of Carcinogenesis in Relation to the Age Distribution of Human Cancer , 1957, British Journal of Cancer.

[8]  E. J. Gumbel Statistics of Extremes - Gumbel, E.J. , 1962 .

[9]  H. Dennis Tolley,et al.  A Linear Models Approach to the Analysis of Survival and Extent of Disease in Multidimensional Contingency Tables , 1972 .

[10]  P N Lee,et al.  Statistical Analysis of the Bio-assay of Continuous Carcinogens , 1972, British Journal of Cancer.

[11]  J. Kaprio,et al.  Multivariate logit analysis of concordance ratios for quantitative traits in twin studies. , 1981, Acta geneticae medicae et gemellologiae.

[12]  R. Fisher,et al.  Limiting forms of the frequency distribution of the largest or smallest member of a sample , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.

[13]  N. Mantel,et al.  A logistic reanalysis of Ashford and Sowden's data on respiratory symptoms in British coal miners. , 1973, Biometrics.

[14]  R. Doll The Age Distribution of Cancer: Implications for Models of Carcinogenesis , 1971 .

[15]  N. Dubin Mathematical Model , 2022 .

[16]  J. C. FISHER,et al.  Multiple-Mutation Theory of Carcinogenesis , 1958, Nature.

[17]  C. L. Chiang A STOCHASTIC STUDY OF THE LIFE TABLE AND ITS APPLICATIONS III. THE FOLLOW-UP STUDY WITH THE CONSIDERATION OF COMPETING RISKS"'2 , 1961 .

[18]  S. Kullback,et al.  Partitioning Second‐Order Interaction in Three‐Way Contingency Tables , 1973 .

[19]  M. Pike,et al.  AGE AT ONSET OF LUNG CANCER: SIGNIFICANCE IN RELATION TO EFFECT OF SMOKING. , 1965, Lancet.

[20]  R. Doll,et al.  Mortality in Relation to Smoking: Ten Years' Observations of British Doctors , 1964, British medical journal.

[21]  Milton C. Chew Distributions in Statistics: Continuous Univariate Distributions-1 and 2 , 1971 .

[22]  J. Ashford,et al.  Multi-variate probit analysis. , 1970, Biometrics.

[23]  J. Neyman,et al.  Contribution to the Theory of the {χ superscript 2} Test , 1949 .

[24]  E. Gumbel Statistical Theory of Extreme Values and Some Practical Applications : A Series of Lectures , 1954 .