**Pooling different measures of risk in a meta-analysis (created 2010-07-26)**.

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Someone on the MEDSTATS email discussion group asked about how to pool results in a meta-analysis where some of the summary measures are reported as odds ratios, others as relative risks, and still others as hazard ratios. There's actually a fourth measure that is commonly used when the outcome measure is binary (live/dead, improved/not improved, relapsed/relapse free, etc.). That is the risk difference, and its inverse, the number needed to treat. Here's what I wrote in response.

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, relative risk, or risk difference. 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.