st: RE: Poisson Regression

[jhilbe@aol.com]

I want to caution you  on the use of the oddsrisk program. I wrote it 
so that it provided software support for the
algorithm proposed by Zhang and Yu in 1998. The confidence intervals of 
the produced risk ratios appear to be baised as the number of 
predictors in the model increases. Other caveats exist as well, which I 
discuss at some length in my
    Logistic Regression Models, Chapter 5.5 (Odds ratios as 
approximations to risk ratios), pages 106-132.

There are definitely times when it is appropriate to interpret odds 
ratios as risk ratios, but some calculations need to be done in order 
to determine when this is the case. There are also many occasions when 
such a conversion is tenuous. Then, when you report the odds ratios of 
a logistic model as if they were risk ratios it is important to provide 
an accompanying justification. I recommend that one should interpret 
odds ratios as odds ratios and not as risk ratios for all binary 
response logistic models, unless there are very good reasons for doing 
otherwise. When there is a binomial denominator, however, as in grouped 
logistic regression, one may compare it to a rate parameterized Poisson 
or negative binomial model, where the exponentiated coefficients are 
risk ratios.

Joseph Hilbe





Date: Mon, 14 Feb 2011 17:15:05 -0200
From: _Maria_Pacheco_de_Souza?= <jmpsouza@usp.br>
Subject: st: RES: RE: Poisson Regression

Dear Alexandra and Paul:

The user written -oddsrisk- by Joseph M. Hilbe, Arizona State University
- ---- Hilbe@asu.edu; jhilbe@aol.com may be a good approach:

	
			"Conversion from Logistic Odds Ratios to Risk Ratios


        oddsrisk y(1/0) riskfactor(1/0) varlist [fw=countvariable] <if> 
<in>

oddsrisk converts logistic regression odds ratios to relative risk 
ratios by
the formula described below. Source: Zhang and K. Yu, 1998. Frequency 
weights
are allowed in order to calculate odds and risk ratios from 2 x 2 
tables. The
response must be binary, as does the first predictor, which is 
considered to be
the risk factor or exposure..."

Jos? Maria Pacheco de Souza
Professor Titular, aposentado; Colaborador S?nior
Departamento de Epidemiologia/Faculdade de Sa?de P?blica/Universidade 
de S?oPaulo
Av. Dr. Arnaldo, 715 - S?o Paulo, Capital - cep 01246-904
Fones: FSP= (11)3061-7747  Res= (11)3714-2403; (11)3768-8612
www.fsp.usp.br/~jmpsouza


Alexandra,

There is a growing literature on alternatives to logistic regression if 
the
outcome is common. I've attached some of the literature below. Just a 
quick overview:

In general, two approaches are suggested: log-binomial and Poisson
regression with robust standard errors. The log-binomial approach is
preferred, unless the model fails to converge (which if frequently does)
(see Petersen & Deddens 2008; Deddens & Petersen 2008).  Stata provides 
two
approaches to log-binomial: -glm- with the family and link specified, 
and
- -binreg-, with the rr option.

I think that Poisson regression with robust standard errors (the robust
option) will be used more often in practice because it seldom has 
problems
converging.  Zou (2004) suggests its use (as do Barros & Hirakata 2003) 
for
cohort studies where the relative risk is of interest and the base 
incidence
is common.

Spiegelman & Hertzmark (2005) in a commentary go as far as to recommend 
that
logistic regression not be used for risk or prevalence ratios when the
outcome is common.


*************

Wacholder S. Binomial regression in GLIM: estimating risk ratios and 
risk
differences. Am J Epidemiol. Jan 1986;123(1):174-184.

Skov T, Deddens J, Petersen MR, Endahl L. Prevalence proportion ratios:
estimation and hypothesis testing. Int J Epidemiol. Feb 
1998;27(1):91-95.

McNutt LA, Wu C, Xue X, Hafner JP. Estimating the relative risk in 
cohort
studies and clinical trials of common outcomes. Am J Epidemiol. May 15
2003;157(10):940-943.

McNutt LA, Hafner JP, Xue X. Correcting the odds ratio in cohort 
studies of
common outcomes. JAMA. Aug 11 1999;282(6):529.

Zou G. A modified Poisson regression approach to prospective studies 
with
binary data. American Journal of Epidemiology. 2004;159:702-706.

Barros AJ, Hirakata VN. Alternatives for logistic regression in
cross-sectional studies: an empirical comparison of models that directly
estimate the prevalence ratio. BMC Med Res Methodol. Oct 20 2003;3:21.

Deddens JA, Petersen MR. Approaches for estimating prevalence ratios. 
Occup
Environ Med. Jul 2008;65(7):481, 501-486.

Petersen MR, Deddens JA. A comparison of two methods for estimating
prevalence ratios. BMC Med Res Methodol. 2008;8:9.

Spiegelman D, Hertzmark E. Easy SAS calculateons for risk or prevalence
ratios and differences. Am J Epidemiol. Aug 1 2005;162(3):199-200.

Paul F. Visintainer, PhD
Baystate Medical Center
Springfield, MA 01199




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