Can I combine univariate and multivariate HR?

Hi guys.
I'm doing a meta-analysis of survival based on a blood marker, and not all the studies have provided a multivariate hazard ratio. Some have given a univariate hazard ratio (usually where it is not significant) and I would like to put them into the random effects analysis also. Should I do this, or is there another way to incorporate the studies?


Less is more. Stay pure. Stay poor.
Theoretically would the missing control variables impact the effect of the variable of interest. So is there any omitted variable bias resulting from say not controlling for an interaction, confounding, or mediation variable. Or could some variables be correlated, but are excluded, so SEs may be more inflated in multivariate analyses than the univariate?

What hypothetical threats could exist?

P.S., I am not overly familiar with MA using HR results, there could be other issues.


Less is more. Stay pure. Stay poor.
That is given there is actually a plausible relationship. If the other variable are just being controlled for then you could have a little wiggle room. Not sure of the protocol how to handle this in MA, but you could always run the MA with and without them. Do the univariate studies list in there limitations why or why not the control variables may have been used.

Are any of these randomized control trials?
They are not RCT's, mainly observational case series looking at various markers for prognosis (tumour size etc). The univariate HRs I want to include are all for non significant variables and hence their lack of further analysis in the original studies.


Less is more. Stay pure. Stay poor.
If they come from observational studies, well that may mean the underlying patient baseline characteristics may differ between studies and univariate estimates COULD possibly be biased, depending on what they are for in particular. An example, you may not be controlling for treatment differences, type of hospital or interventions, comorbidities, etc. The variable of interest may be influenced by these things and not controlling for them, given they could differ between sample (e.g., study), may be a potential issue.
The first question you should ask is how many studies do you have (i.e. if you have 50 studies without the univariate studies, its probably not worth inclusion and having a reviewer get upset over it...which they probably will for the reasons raised thus far).

At worst, if you want to include them, they should be flagged with a dummy variable in your analysis. Its very likely that these univariate studies will fall within the normal distribution of your meta-analysis. So when you run your meta-regression, include a dummy variable that signifies "univariate studies" and include that in your results.