You have a serious problem Pedro. As Spyridon says, Median and IQR are used when there is not a normal distribution of data, and that is going to be a problem in the metanalysis. You have three options:

1. Ask for that information to the authors. It seems that is not going to be possible.

2. Exclude those papers. One of the inclusion criteria of a papaer in a metanalysis must be that you can have all the data that you need to do the analysis. It seems that in this case you can't.

3. Calcuate the SD and the media. This is not the best way, I guess, but ione way could be to assume that those data have a normal distribution (?). if you assume this, you could thnk that the media is going to be similar to the median. One way to calculate the SD, assuming normal distribution(?), is to divide the IQR by 1,35, that is approximately the equivalence in SD of the IQR.

For example, if you IQR is 4,0 - 6,0, and the median is 5, then:

2,0 (IQR) divided by 1,35 is = 1,48

So the "new" media and SD will be:

5,0 (SD 1,48)

Again, this is not the best way, but if you can't do the first two, this an optional way.

But if tyou do this, it will be interesting to do a subgroup analysis when you have all the information, and tou can compare the effect, between thea anlysis iof all the studies, and those analysis including only those data from studies where you had media and SD, and those where you had to calculate them. You can do sensitivity analysis and you realize if these data, do change to much the results or not.

Good luck!

Have you tried asking the authors of the papers for those numbers (mean, SD, etc)? From my own experience, people tend to help out on this.

Yes. This approach was considered. Once more it was very disappointing.

Different from you, I have a pretty bad experience in asking original authors for additional data, mainly if the review included "old" reports. I would say that in general is a lot of effort for a very disappointing result.

One way of looking it is that you could inquire about the raw data from the authors or ask them to calculate means and SDs for them.

The other point however, is to see what kind of data you have. It is most common, that median and IQR are used (instead of mean and SD) to describe the distribution of data that is not-normally distributed. That is to say, if the assumption of normality is not satisfied, you will also have a problem with your meta-analysis. Most meta-analyses are about parametric data and that is why the software asks for means and sds. There are however also non-parametric approaches to meta-analysis. Should you however consider to use one I would suggest asking for statistical expertise. You could always of course omit this one study that reports non-normal data, although this could also have an effect on your results...

Hope I helped a little and didn't make the matter even more complicated..

You have a serious problem Pedro. As Spyridon says, Median and IQR are used when there is not a normal distribution of data, and that is going to be a problem in the metanalysis. You have three options:

1. Ask for that information to the authors. It seems that is not going to be possible.

2. Exclude those papers. One of the inclusion criteria of a papaer in a metanalysis must be that you can have all the data that you need to do the analysis. It seems that in this case you can't.

3. Calcuate the SD and the media. This is not the best way, I guess, but ione way could be to assume that those data have a normal distribution (?). if you assume this, you could thnk that the media is going to be similar to the median. One way to calculate the SD, assuming normal distribution(?), is to divide the IQR by 1,35, that is approximately the equivalence in SD of the IQR.

For example, if you IQR is 4,0 - 6,0, and the median is 5, then:

2,0 (IQR) divided by 1,35 is = 1,48

So the "new" media and SD will be:

5,0 (SD 1,48)

Again, this is not the best way, but if you can't do the first two, this an optional way.

But if tyou do this, it will be interesting to do a subgroup analysis when you have all the information, and tou can compare the effect, between thea anlysis iof all the studies, and those analysis including only those data from studies where you had media and SD, and those where you had to calculate them. You can do sensitivity analysis and you realize if these data, do change to much the results or not.

Good luck!

Hello all,

Thank you for your comments. Unfortunately, nothing new came up when compared to what I thought on my own before this post. But this is all not bad, as the feeling of "a simple and embarrassing answer will come" is gone.

I also posted this question at medstats mail list and Martin Bland kindly provided an unpublished manuscript on this topic. He extended Hozo's formula to estimate means and SDs from median and ranges, and he argues in a simulation study that this new estimator is less biased in all scenarios when compared to Hozo's approach. Unfortunately this approach does not solve my problem, as it also require the range of the outcome from original trials, which I do not have. May the force be with you all.

He posted the manuscript here:

https://groups.google.com/forum/?hl=pt&fromgroups=#!searchin/MedStats/Medians$20IQR$20meta-analysis/medstats/hN2NFtuDwUE/JN1FnygpEEUJ

Hey Pedro,

I might be late to answer your question but hope this help someone else. I found this paper "Estimating the mean and variance from the median, range, and the size of a sample" available on this link http://www.biomedcentral.com/1471-2288/5/13

I'm not sure though if this Hozo's paper you mentioned is the one martin already developed, anyway I thought to help as I'm also doing a meta-analysis !

Good luck :)

Dear,

Simply to solve this problem, i calculate the HR from the 2 medians when they -only- are available. Refer to the following article:

Article Michiels S, Piedbois P, Burdett S, Syz N, Stewart L, Pignon ...

Hi Ivan D Florez

Thanks for your very helpful answer.

Do you have any reference for the third option i.e. dividing IQR by 1.35? Would like to add the reference in my paper. 

Masood 

Hello Dr. Masood

The reference for this calculation (SD= IQR/1.35) is the Cochrane handbook of SR of interventions.

Regards

Hi Mohd Masood,

I am glad it was helpful. It is a statistical concept that you could find in some statistics textbooks. Please check the following (Beyond ANOVA textbook)

https://books.google.ca/books?id=nz241IjmSGgC&pg=PA275&dq=iqr+standard+deviation+relationship+calculation+1.35&hl=en&sa=X&ved=0ahUKEwjz9c21psDLAhXJiCwKHRsdDWwQ6AEIGzAA#v=onepage&q=iqr%20standard%20deviation%20relationship%20calculation%201.35&f=false

Nevertheless, following a more accesible source and the most important in the field of Systematic Reviews, the Cochrane Handbook would be the best to cite:

http://handbook.cochrane.org/chapter_7/7_7_3_5_mediansand_interquartile_ranges.htm

I hope this is useful for you. Good luck with your paper,

Iván F.

Excellent!

Thanks Ivan and Ahmed. 

Regards

Masood 

Hi Mohamed, check out this paper by Hozo et al.

http://bmcmedresmethodol.biomedcentral.com/articles/10.1186/1471-2288-5-13

Best regards,

Ivan

That is correct, my friend.

Best,

Ivan

Exclusion of some studies due to these issues may lead to bias in the metaanalysis results;and if this approach is taken,it must be stated explicitly in the methods,result,and discussion sections.And,if mean and SD are roughly estimated from the given data using some formula;as advised earlier,it will be nice to do a sensitivity analysis- comparing metaanalysis including roughly estimated mean and SD values,and metaanalysis using only papers which explicitly report these values.Also,one must remember that authors usually report mean and SD for normal data.

Dear Colleagues,

Thank you for your excellent explanations and summaries. Based on your references, I made a spreadsheet for quick calculations. I would like to share it with you.

I hope it will be helpful!

Thanks again for your valuable contributions. 

Best,

Nigar

Thanks for providing this excel.Just a question, n here is total sample size or sample size of one group..

Dear all,

This is an old discussion and several colleagues are referring to the Hozo et al paper that has been severely criticized. Wax et al (2014) addressed the problem and provided a better estimate for the mean and SD:

Article Estimating the sample mean and standard deviation from the s...

Dear Girish C. Bhatt

sample sizeof one group

Dear all,

I recently had to conduct a meta analysis on median survival times coming from single arm phase 2 studies and I found the Statistics in Medicine paper by McGrath et al. (2019) really helpful. Basically, among other transformation-based methods, they suggest to use the (weighted) median of the study-specific medians. As far as I know, this is the only statsitcal methodological paper addressing the topic at hand.

Article One-sample aggregate data meta-analysis of medians

Thanks. In your spreadsheet, does range mean range in the traditional sense or are you referring to the IQR?

I'm a bit late to this, but has the OP considered using the Generalized Odds Ratio that can be derived from a Wilcoxon-Mann-Whitney statistic? The following articles should help.

Article The Missing Medians: Exclusion of Ordinal Data from Meta-Analyses

Article U is for Unease: Reasons for Mistrusting Overlap Measures fo...

The second paper is by Stephen Senn -- a statistical expert in clinical trials. He shows the advantages of the log-odds as an effect size statistic, as well as describes the cautions and caveats when using it.

The log-odds also has applications in meta-regression.

If you can't do a meta-analysis using the natural units (ie. you have heterogenous outcome measures), then the log-odds ratio should be preferred, based on my readings from the literature.

Nonparametric Effect Size estimation, Likelihood Methods, and Meta Analysis

https://discourse.datamethods.org/t/nonparametric-effect-size-estimation-likelihood-methods-and-meta-analysis/1525/3