Methods Inf Med 1992; 31(03): 215-218
DOI: 10.1055/s-0038-1634875
Original Article
Schattauer GmbH

Maximum Likelihood Estimation and Testing of a Poisson Regression Model

J. Y. Wan
1   Departments of Biostatistics and Geriatric Research and Training Center
,
A. T. Galecki
2   University of Michigan, Ann Arbor, Michigan, USA
› Author Affiliations
Further Information

Publication History

Publication Date:
08 February 2018 (online)

Abstract:

A Poisson regression model is proposed for the analysis of incidence rates presented in a two-way table classified by two categorical variables. It is shown that the likelihood function is the same as that using Glasser’s exponential covariate model. An algorithm is given to solve the maximum likelihood estimates of the regression parameters. The model is evaluated via deviance and the method is illustrated with an example. Some extensions of the model are discussed.

 
  • REFERENCES

  • 1 Mantel N, Haenszel W. Statistical aspects of the analysis of data from retrospective studies of disease. J National Cancer Inst 1959; 22: 719-48.
  • 2 Tarone RE. On summary estimators of relative risk. J Chron Dis 1981; 34: 463-8.
  • 3 Glasser M. Exponential survival with covariance. J Amer Statist Assoc 1967; 62: 561-8.
  • 4 Prentice RL. Exponential survivals with censoring and explanatory variables. Biometrika 1973; 60: 279-88.
  • 5 Cramer EM, Appelbaum Ml. Nonorthogonal analysis of variance - once again. Psychol Bull 1980; 87: 51-7.
  • 6 Laird N, Olivier D. Covariance analysis of censored survival data using log-linear analysis techniques. J Amer Statist Assoc 1981; 76: 231-40.
  • 7 Holford TR. The analysis of rates and of survivorship using log-linear models. Biometrics 1980; 36: 299-305.
  • 8 Breslow NE, Day NE. Statistical Methods in Cancer Research: Volume 2 - The Design and Analysis of Cohort Studies. IARC Scientific Publications No. 82. 1987
  • 9 Cutler S, Young J. eds. NCI Monograph 41, DHEW No. NIH-75-787. Third National Cancer Survey: Incidence Data. Bethesda Md: National Cancer Institute; 1975
  • 10 Gail M. The analysis of heterogeneity for indirect standardized mortaliy ratios. J Royal Statist Soc Ser A 1978; 141: 224-34.
  • 11 SAS Institute Inc. SAS Technical Report P-200, SAS/STAT Software: CALIS and LOGISTIC Procedures, Release 6.04. Carry. NC: SAS Institute Inc; 1990
  • 12 Bartholomew DJ. The sampling distribution of an estimate arising in the life testing. Technometrics 1963; 05: 361-74.
  • 13 Armitage P. Statistical Methods in Medical Research. 2nd ed.. Oxford: Blackwell Scientific Publications; 1987
  • 14 Frame EL, Checkoway H. Use of Poisson regression models in estimating incidence rates and ratios. Amer J Epidemiol 1985; 121: 309-23.
  • 15 Rao CR. Linear Statistical Inference and its Applications. 2nd ed.. New York: Wiley; 1973