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st: ORs for non-rare outcomes

From   "roger webb" <>
Subject   st: ORs for non-rare outcomes
Date   Thu, 8 Apr 2004 10:17:15 +0100

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 

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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