estimating means and SD from medians and IQR

[Pedro Emmanuel Alvarenga Americano do Brasil]

Dear StatMasters,

Im involved in a meta-analysis where some trials show outcomes as mean and standard deviation but most show median and inter-quantile range. I took look at some R packages, and there several for conducting meta-analysis, but the few I spent some time in trying to solve my issue always requested means and SDs. I looked around and found the following paper http://www.biomedcentral.com/1471-2288/5/13. 

However, this simulation study states that it is possible to estimate mean and SD given the median and range (min and max values), not from median and IQR. My research mates checked again on each paper for min and max value but it was very disappointing as none informed these values. Therefore, I would like very much if any one have a tip to help me workaround this issue.

Kind regards to all, 

Dr. Pedro Emmanuel A. A. do Brasil

Curriculum Lattes:  http://lattes.cnpq.br/6597654894290806 
Instituto de Pesquisa Clínica Evandro Chagas
Fundação Oswaldo Cruz
Rio de Janeiro - Brasil
Av. Brasil 4365,
CEP 21040-360,
Tel 55 21 3865-9648
email: pedro....@ipec.fiocruz.br
email: emmanue...@gmail.com

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[Martin Bland]

I have an unpublished paper on this, which I have forwarded to Pedro.

Anybody interested can have it.

Martin

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[Kornbrot, Diana]

Yes please
Best
diana

On 04/04/2013 14:50, "Martin Bland" <martin...@york.ac.uk> wrote:

I have an unpublished paper on this, which I have forwarded to Pedro.

Anybody interested can have it.

Martin


On 4 April 2013 13:42, Pedro Emmanuel Alvarenga Americano do Brasil <emmanue...@gmail.com> wrote:

Dear StatMasters,

Im involved in a meta-analysis where some trials show outcomes as mean and standard deviation but most show median and inter-quantile range. I took look at some R packages, and there several for conducting meta-analysis, but the few I spent some time in trying to solve my issue always requested means and SDs. I looked around and found the following paper http://www.biomedcentral.com/1471-2288/5/13. 

However, this simulation study states that it is possible to estimate mean and SD given the median and range (min and max values), not from median and IQR. My research mates checked again on each paper for min and max value but it was very disappointing as none informed these values. Therefore, I would like very much if any one have a tip to help me workaround this issue.

Kind regards to all, 

Dr. Pedro Emmanuel A. A. do Brasil
Curriculum Lattes:  http://lattes.cnpq.br/6597654894290806 
Instituto de Pesquisa Clínica Evandro Chagas
Fundação Oswaldo Cruz
Rio de Janeiro - Brasil
Av. Brasil 4365,
CEP 21040-360,

Tel 55 21 3865-9648 <tel:21%203865-9648>

email: pedro....@ipec.fiocruz.br
email: emmanue...@gmail.com

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[Martin Bland]

You are welcome,

Martin

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[Nikolaos Pandis]

Dear Dr Bland,

 

I would be grateful if I could also have this paper.

 

Thank you,

 

Nick

 

Nikolaos Pandis DDS MS Dr. med. dent. MSc DLSHTM

Orthodontist

29 P. Zafiropoulou Street

Corfu, 49100

Greece

+30-26610-35087

 

Visiting Assistant Professor

University of Bern, Switzerland

From: Martin Bland <martin...@york.ac.uk>
To: meds...@googlegroups.com
Sent: Thursday, April 4, 2013 5:50 PM
Subject: Re: {MEDSTATS} estimating means and SD from medians and IQR

I have an unpublished paper on this, which I have forwarded to Pedro.

Anybody interested can have it.

Martin

On 4 April 2013 13:42, Pedro Emmanuel Alvarenga Americano do Brasil <emmanue...@gmail.com> wrote:

Dear StatMasters,

Im involved in a meta-analysis where some trials show outcomes as mean and standard deviation but most show median and inter-quantile range. I took look at some R packages, and there several for conducting meta-analysis, but the few I spent some time in trying to solve my issue always requested means and SDs. I looked around and found the following paper http://www.biomedcentral.com/1471-2288/5/13. 

However, this simulation study states that it is possible to estimate mean and SD given the median and range (min and max values), not from median and IQR. My research mates checked again on each paper for min and max value but it was very disappointing as none informed these values. Therefore, I would like very much if any one have a tip to help me workaround this issue.

Kind regards to all, 

Dr. Pedro Emmanuel A. A. do Brasil

Curriculum Lattes:  http://lattes.cnpq.br/6597654894290806 
Instituto de Pesquisa Clínica Evandro Chagas
Fundação Oswaldo Cruz
Rio de Janeiro - Brasil
Av. Brasil 4365,
CEP 21040-360,
Tel 55 21 3865-9648
email: pedro....@ipec.fiocruz.br
email: emmanue...@gmail.com

---Apoio aos softwares livres

http://www.zotero.org/ - gerenciamento de referências bibliográficas.
http://www.broffice.org/ ou http://www.libreoffice.org/ - textos, planilhas ou apresentações.
http://www.epidata.dk/ - entrada de dados.
http://www.r-project.org/ - análise de dados.
http://www.ubuntu.com/ - sistema operacional

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[Nikolaos Pandis]

I can see it also

many thanks

 

Nikolaos Pandis DDS MS Dr. med. dent. MSc DLSHTM

Orthodontist

29 P. Zafiropoulou Street

Corfu, 49100

Greece

+30-26610-35087

 

Visiting Assistant Professor

University of Bern, Switzerland

From: Martin Bland <martin...@york.ac.uk>
To: meds...@googlegroups.com
Sent: Thursday, April 4, 2013 6:25 PM
Subject: Re: {MEDSTATS} estimating means and SD from medians and IQR

You are welcome,

Martin

http://www.zotero.org/ <http://www.zotero.org>  - gerenciamento de referências bibliográficas.
http://www.broffice.org/ <http://www.broffice.org>  ou http://www.libreoffice.org/ <http://www.libreoffice.org/>  - textos, planilhas ou apresentações.
http://www.epidata.dk/ <http://www.epidata.dk>  - entrada de dados.
http://www.r-project.org/ <http://www.r-project.org>  - análise de dados.
http://www.ubuntu.com/ <http://www.ubuntu.com>  - sistema operacional

Emeritus Professor Diana Kornbrot
email:  d.e.ko...@herts.ac.uk    
 web:    http://dianakornbrot.wordpress.com/
Work
Department of Psychology
School of Life and Medical Sciences
University of Hertfordshire
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voice:   +44 (0) 170 728 4626
Home
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voice:   +44 (0) 208  444 2081
mobile: +44 (0) 740 318 1612

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[Martin Bland]

welcome.

Martin

[Steve Simon, P.Mean Consulting]

On 4/4/2013 7:42 AM, Pedro Emmanuel Alvarenga Americano do Brasil wrote:

> Im involved in a meta-analysis where some trials show outcomes as
> mean and standard deviation but most show median and inter-quantile
> range. I took look at some R packages, and there several for
> conducting meta-analysis, but the few I spent some time in trying to
> solve my issue always requested means and SDs. I looked around and
> found the following paper
> http://www.biomedcentral.com/1471-2288/5/13.
>
> However, this simulation study states that it is possible to
> estimate mean and SD given the median and range (min and max values),
> not from median and IQR. My research mates checked again on each
> paper for min and max value but it was very disappointing as none
> informed these values. Therefore, I would like very much if any one
> have a tip to help me workaround this issue.

This comes up a lot with power and sample size calculations. For
example, see
--> http://www.pmean.com/news/201205.html#2

If you assume a standard bell shaped curve, then the interquartile range
is about 4/3 of a standard deviation. Sure it's a pretty big assumption.
People use medians and interquartile ranges most often when the data is
decidedly non-normal. Still, it may be your only choice. You may want to
run a sensitivity analysis where you exclude those studies where you
estimated the standard deviation from the interquartile range and see if
your conclusions change markedly.

There may be one other option. Have you thought about writing to the
authors and asking them for the mean and standard deviation?

Steve Simon, n...@pmean.com, Standard Disclaimer.
Sign up for the Monthly Mean, the newsletter that
dares to call itself average at www.pmean.com/news

[John Whittington]

At 12:19 04/04/2013 -0500, Steve Simon, P.Mean Consulting wrote:
>If you assume a standard bell shaped curve, then the interquartile range
>is about 4/3 of a standard deviation. Sure it's a pretty big assumption.
>People use medians and interquartile ranges most often when the data is

>decidedly non-normal. Still, it may be your only choice. ... There may be

>one other option. Have you thought about writing to the authors and asking
>them for the mean and standard deviation?

Does this not illustrate another potential problem?

As you say, it may not even be necessary to invoke iffy assumptions in
order to estimate the values of the arithmetic mean and SD of the published
data - the authors may be able to _tell_ you what the actual arithmetic
mean and SD of the observed data were. However, given that (as you say) a
very likely reason for their not having published these figures would be
that the distribution was highly non-Normal, is it necessarily appropriate
to use the arithmetic mean and SD of these data in a meta-analysis (which
was Pedro's wish), even when one knows exactly what they were?

Kind Regards,


John

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[Pedro Emmanuel Alvarenga Americano do Brasil]

Stat Masters,

Asking authors for additional data was the first approach, most of the authors did not even answered. From more than 20 trials we included in the review only two gave a positive feedback. In general it was very disappointing.  For example, the very first answer the author said his personal computer was stolen couple months before and he had no back up data. I remember the first review I was involved in. I selected some original work to ask for additional data and at the first one, the email was not available at the report. I typed the author name at google and first thing that came up was his obituary. Despite many consider this approach reasonable, my personal experience  with this approach was very very disappointing. 

John has a good point, the very fist thing I tough was to look for functions to run a meta-analysis of medians and IQR. It seems more reasonable to me to replace medians by the mean then the other way around due to the reasons John pointed out. It is a good suggestions to conduct a sensitivity analysis on this. 

Nevertheless Im pasting below the little R function I made last week to apply Hozo's estimator to my data. This function should return the data in the input with two additional columns with the new means and SDs

# Sample Size   n <= 15      15 < n <= 25  25 < n <= 70  70 < n

# Mean          formula 5    formula 5     median        median

# SD            formula 16   range/4       range/4       range/6

# m = variable name with the medians

# a = variable name with the minimum range

# b = variable name with the maximum range 

# n = variable name with the group sample size

# data containing the information above

# n.M character indicating the name of the new variable with the means

# n.SD character indicating the name of the new variable with SDs

mtrans <- function(a,m,b,n,data,n.M,n.SD){

  data[,n.M] <- NA

  data[,n.SD] <- NA

  cond <- which(data[,n] <= 25)

  data[cond,n.M] <- (data[cond,a] + 2*data[cond,m] + data[cond,b])/4

  cond <- which(data[,n] > 25)

  data[cond,n.M] <- data[cond,m]

  cond <- which(data[,n] <= 15)

  data[cond,n.SD] <- sqrt((1/12)*(((data[cond,a] + 2*data[cond,m] + data[cond,b])^2)/4 + (data[cond,b]-data[cond,a])^2))    

  cond <- which(15 < data[,n]  & data[,n] <= 70)

  data[cond,n.SD] <- (data[cond,b]-data[cond,a])/4

  cond <- which(70 < data[,n])

  data[cond,n.SD] <- (data[cond,b]-data[cond,a])/6

  invisible(data)

}

Is anyone developing an R function to conduct meta-analysis of medians? ;D

Kind Regards,

Dr. Pedro Emmanuel A. A. do Brasil

Curriculum Lattes:  http://lattes.cnpq.br/6597654894290806 
Instituto de Pesquisa Clínica Evandro Chagas
Fundação Oswaldo Cruz
Rio de Janeiro - Brasil
Av. Brasil 4365,
CEP 21040-360,
Tel 55 21 3865-9648
email: pedro....@ipec.fiocruz.br
email: emmanue...@gmail.com

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2013/4/4 John Whittington <Joh...@mediscience.co.uk>

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[Kornbrot, Diana]

Obviously, asking the authors is a 1st step and you have done that.
However, there is a further consideration. QUALITY of study – important in meta-analysis.  How do you WEIGHT the QUALITY of a study that: 1. fails to report mean & SD; and 2. Fails to respond to requests for clarification?
Best

Diana

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[Kornbrot, Diana]

And did the dog eat his homework?

I would do the analysis both with and without these dubious studies
Best
Diana

Stat Masters,

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2013/4/4 John Whittington <Joh...@mediscience.co.uk>

At 12:19 04/04/2013 -0500, Steve Simon, P.Mean Consulting wrote:

If you assume a standard bell shaped curve, then the interquartile range is about 4/3 of a standard deviation. Sure it's a pretty big assumption. People use medians and interquartile ranges most often when the data is decidedly non-normal. Still, it may be your only choice. ... There may be one other option. Have you thought about writing to the authors and asking them for the mean and standard deviation?

Does this not illustrate another potential problem?

As you say, it may not even be necessary to invoke iffy assumptions in order to estimate the values of the arithmetic mean and SD of the published data - the authors may be able to _tell_ you what the actual arithmetic mean and SD of the observed data were.  However, given that (as you say) a very likely reason for their not having published these figures would be that the distribution was highly non-Normal, is it necessarily appropriate to use the arithmetic mean and SD of these data in a meta-analysis (which was Pedro's wish), even when one knows exactly what they were?

Kind Regards,


John

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[MacLennan, Graeme]

Just to chip in a couple pennies’ worth: 

 

On 05/04/2013 02:56, "Pedro Emmanuel Alvarenga Americano do Brasil" <emmanue...@gmail.com> wrote:

Stat Masters,

Asking authors for additional data was the first approach, most of the authors did not even answered. From more than 20 trials we included in the review only two gave a positive feedback. In general it was very disappointing.

<snip>

 

If you get no response from authors, then write to the funding agency and/or head of department to let them know that no data has been forthcoming.  This is, anecdotally of course!,  effective.  I have experience from the other side of the fence where researchers wrote to us for IPD from one of our trials, but only for a subgroup.   We disagreed with their protocol and intended analysis strategy, so stalled whilst weighting the spirit of data sharing against (our perceived) sub-optimal use of the data.  This person then wrote to someone high up (as in the Minister) which was then passed on to our university through various levels until it was my top priority (trust me, it was my top priority).   

 

 

Graeme MacLennan

Senior Statistician

Health Services Research Unit

Health Sciences Building

University of Aberdeen

Foresterhill

Aberdeen AB25 2ZD

Tel: +44 (0)1224 438147

Fax +44 (0)1224 438165

Email: g.mac...@abdn.ac.uk

Web: www.abdn.ac.uk/hsru

The University of Aberdeen is a charity registered in Scotland, No SC013683.

[John Whittington]

At 23:56 04/04/2013 -0300, Pedro Emmanuel Alvarenga Americano do Brasil wrote (in small part):

John has a good point, the very fist thing I tough was to look for functions to run a meta-analysis of medians and IQR. It seems more reasonable to me to replace medians by the mean then the other way around due to the reasons John pointed out.

I'm not sure that I fully understand that second sentence.  If one assumes that arithmetic means and SDs are usually reported when the distribution is fairly close to Normal, then it would seem much more reasonable to estimate median (equal to mean) and IQR (~median +/- {SD*0.67}) than to estimate mean/SD from median/IQR from an unknown (and quite probably highly non-Normal) distribution.  hence one could get data from all the studies in terms of mean and IQR.

However, as you imply, that would only be useful to you if you had a way of undertaking a meta-analysis on the basis of medians and IQRs - and I am not aware of a 'recognised' way of doing that.

[Martin Bland]

In meta-analysis, we are often comparing two groups in each individual study.  We might guess that the difference between medians provides an approximation to the difference between means which would be better than the approximation of a single median to a single mean.

I think we should do our studies so well that nobody would ever need to do another study of the same thing and meta-analysis would be unnecessary.  I can dream!

Martin

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[John Whittington]

At 13:18 05/04/2013 +0100, Martin Bland wrote:
>In meta-analysis, we are often comparing two groups in each individual
>study. We might guess that the difference between medians provides an
>approximation to the difference between means which would be better than
>the approximation of a single median to a single mean.

Indeed. That would seem a very reasonable guess in most
circumstances. However, there would still be the issue of needing a
measure of the variability of those differences if one was going to
undertake any analysis.

>I think we should do our studies so well that nobody would ever need to do
>another study of the same thing and meta-analysis would be unnecessary. I
>can dream!

Ah, Utopia! Even if we talk your tongue out of your cheek, I don't think
it's usually the direct fault of those undertaking studies. Most of us
have the ability to design an (inevitably large) study that would
definitively answer a question with 'near 100% confidence', precluding the
need for any further study of the same question or any
meta-analysis. However, considerations of cost, resources, ethics and
practicalities will often/usually make it impossible to undertake such a
study. Furthermore, one imagines that there would be people who would be
unhappy with the idea of only have one study addressing a question -
'reproducibility' and 'corroboration' of results are generally regarded as
important concepts.

[Nikolaos Pandis]

Hi to all,

 

I need to extract data from a small study (23 and 22 patients in the 2 groups respectively).

 

The available information includes n, median, Q1 and Q3.

 

I looked at the Bland paper extending the methods of Hozo and if I understood correctly we still need the min-max values for the formulas to work.

 

Any thoughts in the case the min-max values are missing?

 

Many thanks,

 

Nick

[Peter Flom]

There can’t be any perfect solution – it is easy to generate two data sets with the same median and IQR but vastly different means, just add an outlier.

 

e.g.

 

1 1 2 3 4 4

 

Vs.

 

1 1 2 3 4 1000

 

So, I think you’d have to make some assumptions about outliers.  You might also be able to make some assumptions about the distribution given median and IQR: ….

 

Peter

[John Whittington]

At 08:40 05/05/2013 -0400, Peter Flom wrote:
>There can t be any perfect solution it is easy to generate two data sets
>with the same median and IQR but vastly different means, just add an outlier.
>e.g. 1 1 2 3 4 4 Vs. 1 1 2 3 4 1000
>So, I think you d have to make some assumptions about outliers. You might
>also be able to make some assumptions about the distribution given median

>and IQR: &.

Indeed, and I fear that 'no perfect solution' probably understates the
problem. All median+IQR really tells us (assuming that 'IQR' means that we
are told the upper and lower quartiles, not just the difference between
them) about distribution is the symmetry of the central part of the
distribution. As you say, what is happening out in the tails is totally
unknown, and one will rarely have any information to permit more than
'blind guesses' about that. Worse, the fact that one is presented with
mean+IQR will quite often mean that the distribution is anything but
'nice', particularly in the tail(s).

I fear the real answer is that one cannot make estimates of mean and SD in
which one can have any real confidence based on median and IQR alone.

[Nikolaos Pandis]

Dear All,

 

Thank you for the comments.

 

We do have Q1 and Q3 but again notidea of what is happening at the tales.

I guess the only hope now is a response from the authors.

 

Best wishes,

 

Nick

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[1448...@life.hkbu.edu.hk]

Dear Nick,
     Hi.  For you situation, I have two articles that might help you to fix this issue. 
     (1) To transform n, q1, q3 and m to sample mean, you may read the article: http://arxiv.org/abs/1505.05687
     (2) To estimate the standard deviation, you may read the article: http://www.biomedcentral.com/1471-2288/14/135/
    
     In these two articles, the authors discuss 3 cases of reporting summary data in meta-analysis, including the one you are facing.  I hope this may help you to fix your problem.  If you have any other questions, please feel free to contact me.


Best,
April

welcome.

Martin

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[Kornbrot, Diana]

but note that these estimations typically assume population has normal distribution and likely reason that these ordinal statistics are used is that sample data looks very un-normal

hence if using in meta-analysis one might want to downgrade the weight???

best

diana

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