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Re: st: ORs for non-rare outcomes

From   Marcello Pagano <>
Subject   Re: st: ORs for non-rare outcomes
Date   Thu, 08 Apr 2004 06:25:12 -0400

Some have this aversion to odds which is difficult to understand. Odds are just as natural as probabilities, ask anyone at a race track. Indeed, as someone pointed out, here is a sector of society not known for its intelligence, punters, who understand odds thoroughly, but health scientists, some even pursuing a Nobel, for some reason cannot understand odds? It does not compute.

This is especially troublesome with case control studies because odds ratios are estimable but relative risks are not. This is inherent in the design of a case control study, something that is immutable.

Someone made the observation that for rare diseases the OR and the RR are approximately equal. Unfortunately, this crutch has had the stunting effect of not dealing with odds ratios as the natural measure that they are.

Make odds even with risk!


roger webb wrote:

Dear Statalist,

I’d be grateful for any comments concerning the interpretation of odds ratio in situations when the outcome is not rare.

I am investigating the predictors of ‘significant parenting problems’ in a sample of women (n=239) admitted for inpatient treatment for schizophrenia immediately following childbirth. The outcome variable is coded in a binary fashion and poor outcome is common in this sample (i.e. 50% of the women).

So far my strategy has been to analyse the data as if they were from a case-control study, with the mothers who have poor outcome treated as cases and those that have good outcome treated as controls. I have used logistic regression as I wish to generate multivariate models.

In a univaraite model I have a binary coded explanatory variable (‘mother has a partner with psychiatric illness’: ‘Yes’ vs. ‘No’). Calculating the exposure odds ratio, 38.5% of the ‘cases’ have a partner who is ill compared with 7% of the ‘controls’ (OR=8.1). However, if I compare the prevalence of poor outcome among mothers with ill partners (82%) against those without ill partners (36%) the risk ratio is considerably lower (RR=2.3).

(Here is the cross-tabulation from which I calculated the OR/RR):
Case (+) Control (-)
Exposed (+) 37 8
Unexposed (-) 59 103

I presume that the considerable discrepancy between the OR and RR has occurred due to an extreme violation of the rare disease assumption.

Does anyone know of any alternative modelling strategies (preferably that can implemented in Stata) that would enable me to estimate relative risks with covariate adjustment with a commonly occurring binary outcome variable?

Alternatively, would it be appropriate to proceed with logistic regression but state that the odds ratios grossly overestimate relative risks in this data set?

Thanks in advance.

Roger Webb
University of Manchester (UK)

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