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Suppose I have 3 means, standard deviations and sample counts of a substance in plasma from 3 studies:

Study 1: 15.0 +/- 7.7 mg/L, n = 227
Study 2: 20.8 +/- 8.3 mg/L, n = 44
Study 3: 22.0 mg/L (no standard deviation), n = 107
Study 4: 18.9 mg/L, 14.0-22.4 mg/L, n = 55

The studies have been conducted at different times, using different methods, with a different population.

I would like to get an average, mean of means, weighted average, or whatever would be the best way, of the 3 studies, ideally with an accompanying average/mean standard deviation, like this:

Average: 17.2 +/- 7.9 mg/L

This average doesn't have to be exact, it should be a summary to get an idea of what the 3 studies (and possibly many more) tend to measure. After long reading, I think now that the only way is using meta-analysis methods. So far, I read about "inverse variance" and "random effect models".

  • Question 1: Can I apply one of these methods to achieve this outcome?
  • Question 2: Is someone able to provide a step-by-step guide on how to achieve this, using the data above?
  • Question 3: Is it possible to include study 3 without a standard Deviation, or should I better exclude it?
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1 Answer 1

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You may want to read up on how to meta-analyze continuous outcomes (e.g., this Cochrane Handbook for Systematic Reviews of Interventions).

As for the missing SDs, you can 'borrow' the measure of variance from other studies. For example, you can use the largest variance from another study in the analysis. The end result would like something like below (computed in Review Manager 5.3.1).

enter image description here

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  • $\begingroup$ Thanks! Not only did you point me to this handbook, but you showed me a tool to test my own calculations, great! I downloaded Review Manager but couldn't configure it to work with example data, so can I ask a question on your screenshot? "Mean difference" suggest just a difference between 2 values to me, but here it seems to be a value on its own. Is 19.08 the "average" of the different studies, just like the result in the example in my question? $\endgroup$
    – poshtad
    Commented Sep 14, 2015 at 14:10
  • $\begingroup$ Review Manager is developed by the Cochrane Collaboration for the production of Cochrane Reviews. It has an inverse variance function that can pool any point estimates and SEs. Traditional effect estimates are OR, RR, MD, SMD, but you can specify your own (e.g. HR, Rate ratio, etc.). It's all under the properties. The program has a nice guide (tech.cochrane.org/revman/documentation/rm5userguide.pdf) that explains how to work with RevMan. Also, there's lots of online youtube videos and tutorials to help you explore the capabilities in RevMan. $\endgroup$
    – abousetta
    Commented Sep 14, 2015 at 18:04
  • $\begingroup$ Yes, 19.08 is the "weighted average" of the different studies. They are weighted according to their variance with studies that have less variance getting more weight in the analysis. Additionally, it seems that Study 1 is somehow different from the others and is a source of statistical heterogeneity that should be explored. $\endgroup$
    – abousetta
    Commented Sep 14, 2015 at 18:07
  • $\begingroup$ Dear abousetta, thank you so much. Sorry for the late answer, I had troubles logging in. I am still working through the userguide, but have yet not managed to create an example as above, but I'm going to get there, I'm sure. Just to be sure: The mean differences in your example (15.00, 20.80...) are absolute values, such as 3 mg/L or 5 apples :) ? And so is 19.08? $\endgroup$
    – poshtad
    Commented Sep 17, 2015 at 20:18
  • $\begingroup$ Sorry for my later response. Yes, those are absolute values. Youtube is friend when learning RevMan. Lot of tutorials. This was done using the Generic Inverse Variance Method. $\endgroup$
    – abousetta
    Commented Mar 18, 2016 at 15:07

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