Convert hazards ratio to odds ratio 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.
 A: 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).
A: $$\text{RR} = (1 - e^{\text{HR}\ln(1-r)})/r$$ where HR is the hazard ratio and r is the rate for the reference group.  If r is not reported, it is probably reported elsewhere (e.g. baseline death rate). 
See Shor et al. (2017) doi: 10.1016/j.socscimed.2017.05.049 
Zhang and Yu (1998), doi: 10.1001/jama.280.19.1690 provide an approximate of RR based on the odds ratio (OR).
$$\text{RR} = \frac{\text{OR}}{(1-P_o)+(P_o\cdot \text{OR})}$$ where Po is the incidence of the outcome of interest in the non-exposed group.  
You can then calculate OR.
A: Exploiting the assumption that hazard ratios are asymptotically similar to relative risks, you can use exploit the formula recommendeed by Grant et al, BMJ 2014: 
RR = OR / (1 - p + (p * OR)
where RR is the relative risk, OR is the odds ratio, and p is the control event rate, which leads to the following:
OR = ((1 - p) * RR) / (1 - RR * p). 
Thus, for instance, a RR of 2.0 with a p of 0.1 would lead to an OR of 2.25, whereas if p increases to 0.2 it would lead to an OR of 2.67.
