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!
m.p.
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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