Jeremy
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Jeremy Miles
Psychology Research Methods Wiki: www.researchmethodsinpsychology.com
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There is no consensus in the research community about how best to
summarize results that could use an odds ratio or a relative risk (or
risk difference/number needed to treat) as the statistical measurement.
One important consideration is heterogeneity. Since the relative risk
and risk difference have restrictions on range that change depending on
the proportion improved in the control group, there is a strong chance
for heterogeneity if there is heterogeneity in the severity of illness
(which would, of course, affect the proportion improved in the control
group). This is less of a problem, potentially, for the odds ratio. I
believe there is some empirical evidence to suggest that the odds ratio
is less likely to suffer heterogeneity, but I can't remember where I saw
this.
There is general consensus, though, that if you want to summarize data
using a hazard ratio, you need access to the individual patient level
data, as the pattern of censoring and other features of the data will
have an influence over what your pooled estimate might be.
I don't think there is any precedent to pool estimates from studies
where some studies report a hazard ratio and other studies report an
odds ratio or relative risk. While there is a conceptual relationship
between these measures, they are still different enough that you should
probably report separate pooled estimates for the studies using a hazard
ratio and the studies using odds ratios/relative risks.
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