The analysis of rates using Poisson regression models - PubMed

• PMID: 6652201

The analysis of rates using Poisson regression models

E L Frome. Biometrics. 1983 Sep.

Abstract

Models are considered in which the underlying rate at which events occur can be represented by a regression function that describes the relation between the predictor variables and the unknown parameters. Estimates of the parameters can be obtained by means of iteratively reweighted least squares (IRLS). When the events of interest follow the Poisson distribution, the IRLS algorithm is equivalent to using the method of scoring to obtain maximum likelihood (ML) estimates. The general Poisson regression models include log-linear, quasilinear and intrinsically nonlinear models. The approach considered enables one to concentrate on describing the relation between the dependent variable and the predictor variables through the regression model. Standard statistical packages that support IRLS can then be used to obtain ML estimates, their asymptotic covariance matrix, and diagnostic measures that can be used to aid the analyst in detecting outlying responses and extreme points in the model space. Applications of these methods to epidemiologic follow-up studies with the data organized into a life-table type of format are discussed. The method is illustrated by using a nonlinear model, derived from the multistage theory of carcinogenesis, to analyze lung cancer death rates among British physicians who were regular cigarette smokers.

Similar articles

• [Meta-analysis of the Italian studies on short-term effects of air pollution].

  Biggeri A, Bellini P, Terracini B; Italian MISA Group. Biggeri A, et al. Epidemiol Prev. 2001 Mar-Apr;25(2 Suppl):1-71. Epidemiol Prev. 2001. PMID: 11515188 Italian.

• Multinomial analysis of smoothed HIV back-calculation models incorporating uncertainty in the AIDS incidence.

  Bellocco R, Pagano M. Bellocco R, et al. Stat Med. 2001 Jul 15;20(13):2017-33. doi: 10.1002/sim.818. Stat Med. 2001. PMID: 11427957

• The analysis of rates and of survivorship using log-linear models.

  Holford TR. Holford TR. Biometrics. 1980 Jun;36(2):299-305. Biometrics. 1980. PMID: 7407317

• Bayesian ranking of sites for engineering safety improvements: decision parameter, treatability concept, statistical criterion, and spatial dependence.

  Miaou SP, Song JJ. Miaou SP, et al. Accid Anal Prev. 2005 Jul;37(4):699-720. doi: 10.1016/j.aap.2005.03.012. Epub 2005 Apr 12. Accid Anal Prev. 2005. PMID: 15949462 Review.

• Use and abuse of variance models in regression.

  van Houwelingen JC. van Houwelingen JC. Biometrics. 1988 Dec;44(4):1073-81. Biometrics. 1988. PMID: 3069138 Review.

Cited by

• Patterns of home- and community-based services in older adults with dementia: an analysis of the long-term care system in Taiwan.

  Wang WF, Su YY, Jhang KM, Chen CM. Wang WF, et al. BMC Geriatr. 2021 May 1;21(1):290. doi: 10.1186/s12877-021-02231-9. BMC Geriatr. 2021. PMID: 33933031 Free PMC article.

• Association of oncogenic and nononcogenic human papillomavirus with HIV incidence.

  Auvert B, Lissouba P, Cutler E, Zarca K, Puren A, Taljaard D. Auvert B, et al. J Acquir Immune Defic Syndr. 2010 Jan;53(1):111-6. doi: 10.1097/QAI.0b013e3181b327e7. J Acquir Immune Defic Syndr. 2010. PMID: 19779357 Free PMC article.

• Political economy of US states and rates of fatal occupational injury.

  Loomis D, Schulman MD, Bailer AJ, Stainback K, Wheeler M, Richardson DB, Marshall SW. Loomis D, et al. Am J Public Health. 2009 Aug;99(8):1400-8. doi: 10.2105/AJPH.2007.131409. Epub 2009 Jun 18. Am J Public Health. 2009. PMID: 19542025 Free PMC article.

• Mortality and cognitive status among elderly Canadians living in the community and in institutions: the Canadian Study of Health and Aging.

  Hill GB, Forbes WF, Lindsay J, McDowell I, Ostbye T. Hill GB, et al. Can J Public Health. 1997 Sep-Oct;88(5):303-4. doi: 10.1007/BF03403893. Can J Public Health. 1997. PMID: 9401162 Free PMC article. No abstract available.

• End-stage renal disease in Canada: prevalence projections to 2005.

  Schaubel DE, Morrison HI, Desmeules M, Parsons DA, Fenton SS. Schaubel DE, et al. CMAJ. 1999 Jun 1;160(11):1557-63. CMAJ. 1999. PMID: 10373996 Free PMC article.

Publication types

MeSH terms