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# st: RE: Poisson Regression

 From jhilbe@aol.com To statalist@hsphsun2.harvard.edu Subject st: RE: Poisson Regression Date Tue, 15 Feb 2011 11:28:51 -0500 (EST)

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
```
```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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