 # Arguments against reporting adjusted odds ratios as risk ratios

#1

We recently submitted a paper that reports covariate (disease severity) adjusted odds ratios from logistic regression model using data from a cross-sectional study.

A reviewer has argued that since the outcome is not rare, we should report relative risks rather than odds ratios. We do not interpret these odds ratios as risk ratios. I found several counter arguments (below), but would be interested what experts see as best practice.

https://www.bmj.com/rapid-response/2011/10/27/rare-distinction-and-common-fallacy

Cook TD. Advanced statistics: up with odds ratios! A case for odds ratios when outcomes are common. Acad Emerg Med [Internet] 2002;9(12):1430–4. https://www.ncbi.nlm.nih.gov/pubmed/12460851

#2

You report odds ratios from logistic regression analysis. It does not use risk ratios.

If you report risk ratios they are complex functions of all the covariates as described in the first logistic regression chapter here.

The prevalence of the outcome variable should have no bearing on what you report in the multivariable case. Risk ratios are not very useful in general when the base risk is high, because a risk ratio of 2 cannot apply to a base risk > 0.5.

#3

Hi Dale: it seems that the reviewer is caught up in the notion that odds ratios can be interpreted as risk ratios, but only when the outcome is rare. The reviewer’s concern may be more or less true, but if you are not interested in interpreting the odds ratios as risk ratios, then maybe just leave out the odds ratios and the risk ratios.

Instead, just present the “adjusted” prevalence in the two groups of interest (the expected proportion when all predictors are at their mean value, other than the grouping variable which is either on or off), and a Wald test statistic or likelihood ratio chi-square and associated P-value.

The remaining issue is a need for an interpretable measure of effect size. Odds ratios are by themselves not great indices of effect size. There is some literature on this. Chen, Cohen and Chen (2010) discuss it and provide some guidelines for interpreting ORs when the prevalence in the unexposed ranges from 1-10%. I would think you could also use Cohen’s arcsin transformed differences on the expected proportions given the model.

#4

Hi there,

I would agree and disagree (at the same time) with that reviewer! I agree with him/her that you should use an alternative measure of association. That is because I do not think that odds and odds ratios are good measures of occurrence/association. Odds have a less intuitive interpretation than risks (except for gamblers, mathematicians, and horse-racing enthusiasts!), and odds ratios are also non-collapsible. So, unless you have case control data, you might be better off using an alternative measure that is more intuitive and has a better public health relevance.

I disagree with the reviewer on reporting risk ratios. In epidemiology, risk is a population measure that is used when you have longitudinal data that allows you to observe cumulative incidence over a period of time. For example, you can report 5-year risk or the 10-year risk of an outcome by observing the number of people who became cases among those at risk over a certain time period. Since your data is cross-sectional (a snapshot in time), you can estimate prevalence differences or prevalence ratios. I hope this helps.

-Walid

#5

Odds ratios must be non-collapsible for them to have all the good properties they possess, including

• they are invariant to the choice of the reference category (e.g., interchanging disease with non-disease will just take the reciprocal of the odds ratio)
• odds ratios are capable of being constant over a wide range of patient types

These reasons tell me that it is worth educating everyone about odds ratios, and using them routinely. But couple them with simple charts for computing absolute risk reduction on demand.

#6

i might be inclined to present the adjusted prevalence estimate as @rnjma says when prevalence is low, because i don’t like the look of “OR=800” when all the risk falls in one category. You see this in regisrty-based studies looking at gestational age and mortality and mortality rates are low and the preterm babies have all the risk