In meta-analysis: How do we convert hazard ratios in some studies to odds ratio? There are case control and cohort studies to be included and some of them report hazard ratios. The raw data is not reported in a way to calculate odds ratio.
Solved – Convert hazards ratio to odds ratio
meta-analysis
Related Solutions
It depends on why they were doing so, and what additional information you might have to work with - like do you have specific cell-counts that you might calculate your own effect measures from. However, some initial thoughts:
- There's two logical groups here. Odds ratios and relative-risks, if they're being reported in any of your studies are logically grouped (in that the odds ratio is typically trying to estimate a relative risk when the actual relative risk cannot be calculated). Similarly, rate-ratios (which I'm going to assume are = incidence density ratios from a Poisson regression) and hazard ratios both deal with time data. I really wouldn't cross-compare ORs and HRs, for example.
- Relative risks and ORs: Honestly, I'd probably run parallel analyses for these two measures. If a study is a cohort or cross-sectional population design, and reports its numbers, you can calculate your own ORs from that. If you chose to do that however, I'd definitely look at heterogeneity based on study design.
- Rate Ratios and HRs: These you might be more capable of getting away with. If the rate ratio is the ratio of two rates calculated as
cases/person-time, then that is actually a hazard ratio estimate as well. It's just a hazard ratio made under the assumption of both proportional and constant hazards. You can convert those directly to an HR, but again, I'd look at study heterogenity by which measure it reported, as rate ratios and a HR that came out of something like a Cox model are performed under different assumptions. - When in doubt, its probably best to split up the studies and look at each sub-group. Don't necessarily look at this as a failure. If different effect measures and study designs are reporting different results, that is, all by itself, a finding. To paraphrase a professor of mine, heterogeneity that prevents the estimation of a single pooled estimate is a result worth reporting.
Systematic Reviews in Health Care: Meta-analysis In Context is an excellent resource if you're looking to do a meta-analysis (in healthcare or otherwise - if you're not in health, ignore their overt fondness for clinical trials).
They also include extensive documentation for conducting a meta-analysis in Stata beyond just a pooled estimate of effect. That is where I would head to first.
Best Answer
If there was an extremely low proportion of subjects with an event in all experiments (let's say <10%) and the hazard and odds ratios are vey close to 1, then hazard, odds and relative risk ratios will be relatively close to each other.
If that is not the case the fundamental differences between these measures will be more and more noticable. For a given trial duration, particular distribution for event occurence and a particular drop-out pattern, there is a correspondence of hazard ratio to odds ratio to relative risk ratio. If all your experiments in your meta-analysis are similar in these respects, it might be possible to convert them. Once you have experiments with different durations, different drop-out patterns or different event time distributions, a hazard ratio might be constant across experiments and is probably the better relative risk measure, but an odds or risk ratio will essentially never be (even if the hazard ratio is, while the same odds ratio would correspond to different hazard ratios across experiments).