### Article

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Alternatives for logistic regression in cross-sectional studies: A comparison of six models estimating the prevalence ratio

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### Authors

Published: | September 8, 2005 |
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### Outline

### Text

#### Background

Logistic regression is commonly used to analyse cross-sectional studies with binary outcome. The odds ratio as an estimate for the prevalence ratio is frequently reported although prevalence ratios can be estimated. However, it may lead to extreme overestimation when the prevalence is greater than 10 %.

The aim of this discussion is to compare different alternatives which calculate the prevalence ratio directly. The comparison was made regarding validity, precision, hypothesis testing and confounding behaviour.

#### Methods

Several simulations were used to test the performance of regression models including (1) unadjusted Cox / Poisson, (2) Cox with robust sandwich variance , (3) log-binomial, (4) Poisson with scale parameter adjusted by Pearson , (5) Poisson with scale parameter adjusted by deviance and (6) a GEE-approach based on the logistic model. Additionally, the unconditional logistic regression model was performed to notice overestimation.

#### Results

All six models gave valid point estimates for the prevalence ratio. Cox with robust variance, log-binomial, Poisson with scale parameter adjusted by Pearson and the GEE- logistic model performed well and had similar results concerning precision, power and confounding. The unadjusted Cox / Poisson model produced standard errors that were too large and had less power, especially with increasing prevalence. When testing whether the estimate is equal to the true parameter, the Poisson model adjusted by deviance rejected too often.

#### Conclusion

When the prevalence ratio is the measure of interest in cross-sectional studies, there are very suitable alternatives for logistic regression. When using the Cox model, adjusting with the robust variance improves precision and power remarkable. Although precautions are needed regarding convergence problems, the log-binomial model is also preferable.

### Literatur

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- Zocchetti C, Consonni D, Bertazzi PA. Relationship between prevalence rate ratios and odds ratios in cross-sectional studies. Int J Epidemiol 1997;26(1):220-3.