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• What is the difference between a meta-analysis and a systematic review?
• Which software can I use to carry out a meta-analysis?
• I want to pool the prevalence (1 arm) across different studies; which software is available for this?
• How can I pool the mean and standard deviation of a treatment and a control group to obtain the mean and standard deviation of both groups combined?
• How can I compare two paired means described in different studies?
• Can I report p-values instead of confidence intervals?
• Can I pool medians?
• How can I carry out a meta-analysis on quality of life?
• How can I summarize the results of different studies in my thesis?
• How can I carry out an individual patient data meta-analysis?
• References
• Information on other websites

In a meta-analysis, results or data from different studies are combined to arrive at a more reliable conclusion [1]. If you are considering carrying out a meta-analysis, it is important to realize that you need advanced statistical techniques. It is advisable to take at least an introductory statistics course for this, and preferably also an advanced course or a course specifically focused on meta-analysis.

The term systematic review mainly concerns the systematic searching, appraisal and description of the literature. A meta-analysis is a statistical analysis in which the, usually summarized, results of different studies are combined into an 'overall' result. This therefore has more to do with performing certain calculations in which the results of each of the studies found serve as input. Sometimes the study results of different studies are combined in such a way that it is not the summarized results of each study that serve as input, but information from every patient of every study. Pooling such per-patient data is referred to as an 'individual patient data' meta-analysis. The tutorial article How to do a meta-analysis [1] describes step by step how to carry out a meta-analysis.

There are options in various software packages for performing the calculations.

You can perform this analysis in R using the metaprop function from the meta package.

For a review, I want to describe the mean and standard deviation of the entire study population for an overview of the included articles. However, the articles often report a separate mean and standard deviation for the treatment group and for the control group. How can I use these to calculate a mean and standard deviation for the entire study population?

Suppose we call the mean and standard deviation of the control group $m_1$ and $s_1$, and the mean and standard deviation of the treatment group $m_2$ and $s_2$. Say the control group contains $n_1$ patients and the treatment group $n_2$. The mean of the two groups combined $m$ is then simply a weighted average of the two means:

$m = \frac{(n_1*m_1+n_2*m_2)}{(n_1+n_2)}$

Calculating the pooled standard deviation requires more. You can use the following formulas for this. It is important to know here that the variance equals the standard deviation squared, i.e. $\operatorname{Var}_{1}=s_{1}^{2}$ and $\operatorname{Var}_{2}=s_{2}^{2}$. Then

$\operatorname{Var} = \frac{(n_{1}*\operatorname{Var}_{1}+n_{2}*\operatorname{Var}_{2}+n_{1}*(m_{1}-m)^{2}+n_{2}*(m_{2}-m)^{2})}{(n_{1}+n_{2})}$

Finally, you can obtain the standard deviation of both groups combined, $s$, by taking the square root: $s = \sqrt{\operatorname{Var}}$.

For a systematic review on a particular surgical procedure, I have collected data from 5 publications. This procedure reduces hypertrophy, expressed in grams, a continuous variable. In these 5 studies, the mean preoperative hypertrophy is known with a standard deviation. The mean hypertrophy after follow-up is also known, also with a standard deviation. All studies show a decrease in mean hypertrophy after the procedure. We now wonder whether it is possible to determine whether the decrease is significant. I think I would need the raw data so that I could do a paired t-test. However, I do not have the raw data. How can I test the decrease reported in the different studies?

To perform a formal test on this, additional information is indeed needed beyond the mean + SD preoperatively and after follow-up. Because of the paired design, you need data on the degree of correlation between the before and after measurements. You could derive this if the articles report, in addition to the mean and SD mentioned, one of the following:

• mean difference between before and after + SD or SE

• or: test result, e.g. a paired t-test: t-statistic or p-value is sufficient

See also Section 16.1.3.2 of the Cochrane Handbook for further explanation. Indeed, the paired t-test cannot be done. A possible analysis would be a meta-analysis based on changes + SDs (which you can therefore possibly derive from SEs or paired test statistics).

I am working on a systematic review of the effect of an intervention on a dichotomous outcome. In my article, I would like to present a table with odds ratios from univariate analyses, but these are not reported in all articles of the included studies. The p-values are reported, however. Using the information in the articles, we have calculated the odds ratio, but we are then missing the confidence intervals. Is it advisable to report the p-value instead of the confidence interval?

It is better to aim for a uniform presentation in an article and therefore to report the confidence intervals for all studies. If you succeed in calculating the odds ratios, you probably also have enough information to calculate the confidence intervals yourself; see for example [2].

For a review, I would like to pool values for median survival time from the literature. What options are available for this? Hazard ratios are usually not reported, and an individual patient data meta-analysis is not possible. Is converting the median to a mean and then pooling statistically correct in this situation? Is there a possibility of calculating the median of the medians?

Researchers have developed methods to calculate the mean and standard deviation based on the median, range and sample size [3]. However, in general, the median and interquartile range (rather than the mean and standard deviation) are reported precisely because the outcome (here, survival time) does not follow a normal distribution. The mean and standard deviation therefore do not give a good representation of the distribution. Other researchers claim to have achieved an improvement in this regard [4]. However, the quality of the estimates also does not appear to be optimal for a non-normal distribution.

Methods have indeed been developed to obtain pooled estimators of medians, but it is also immediately noted that they are not entirely satisfactory [5]. The technical details are in a paper (ref 22 of [5]) that is not easily obtainable. Other researchers propose a different method, but unfortunately provide few technical details [6]. Unfortunately, there is no simple way to properly conduct a meta-analysis on this. The simple option is to describe the results of the different studies.

I am working on a systematic review in which one of the outcomes is quality of life. In five articles, quality of life is described as an outcome measure. The tricky part is that they use different generic and disease-specific questionnaires for this. Can I somehow equate these with each other and still perform a meta-analysis on them?

In this situation, one often chooses to convert the results of the different studies into a measure of effect size, such as the standardized mean difference (the mean difference between two groups divided by the standard deviation of this difference). However, it can be difficult to attach a clinical meaning to this measure. Researchers have found various solutions to this [7].

I am writing a thesis and have already carried out a systematic review. I now want to summarize the results from the different studies, but I do not have enough statistical knowledge to carry out a meta-analysis. What can I do, and what should I especially not do?

Many students need to write one or more systematic reviews during the course of their studies. They often run into the problem that they want to summarize the results of the different studies, but that their statistical knowledge is not yet sufficient to carry out a meta-analysis properly. There are options, but also pitfalls.

• You can summarize the results of the different studies in the text of your thesis. With a small number of studies, this may already be sufficient. With a larger number of studies, in addition to describing all the studies together, you can describe subgroups of studies. It may be interesting for your research question to describe the studies on "healthy" and "ill" people separately. Or it may provide more insight if you discuss the methodologically "good" studies separately.

• It can be a good idea to always report your results using the same units and the same number of decimal places. This makes it easier for the reader to compare all the information. It is quite possible that you will need to convert the results from some studies to different units. For example, think of converting serum glucose from mg/dL to mmol/L. Use a standard value from the field for this and also state in your methods how you did this.

• Often, not all studies report all the information you are looking for. It is not a problem to indicate that a certain piece of information is not available. But it is good to check whether you can find this information. Sometimes more information is presented in supplementary tables accompanying the relevant publication, or a group of patients is described in more detail in another publication. But it may also be possible to derive a value, such as a standard error, standard deviation or confidence interval, from other values in a publication.

• With a larger number of studies, a table can provide more insight into the results of the different studies. Below is an example of a table in which the outcome of interest is serum glucose at hospital admission. In this example, the studies are ordered by number of patients. But it can also be informative to order the studies by another characteristic. You could think of year of publication, the score on an instrument used to assess study quality, or a patient characteristic, such as the proportion of patients with diabetes or whether or not patients were fasting on admission.

					Serum glucose (mmol/L) on hospital admission
First author and year of publication	Total number of patients	Number of patients with diabetes	Proportion of patients with diabetes	Fasting on admission	Mean	Standard deviation	95% Confidence interval for the mean
Koopman, 2013	1096	94	0.09	Yes	4.6	2.1
Buurman, 2011	532	0	0.00	Yes	5.5	3.0
Smit, 2011	789	562	0.71	Yes	7.5	5.9
Jansen, 2015	372	102	0.27	No	8.3	5.1
van de Berg, 2009	104	Unknown	Unknown	Unknown	6.7	3.7
Bakker, 1996	57	57	1.00	No	16.3	10.1
Meijer, 1973	45	Unknown	Unknown	Yes	4.8	1.7
Visser, 1981	30	10	0.33	Unknown	10.4	5.1

• A forest plot can be even more informative than a table [8]. If you do not perform a meta-analysis, you cannot provide a summary measure at the bottom, but you can list the confidence intervals for all studies one below the other. Here too, it can be informative to present the studies grouped in a particular way.
• If you are interested in an association between two outcomes, for example the proportion of patients with diabetes and the mean blood glucose at hospital admission, consider making a bubble chart.

The guidance in this article may be useful [9].

1. Field AP, Gillett R. How to do a meta-analysis. Br J Math Stat Psychol. 2010 Nov;63(Pt 3):665-94. DOI 10.1348/000711010X502733
2. Morris JA, Gardner MJ. Calculating confidence intervals for relative risks (odds ratios) and standardised ratios and rates. Br Med J (Clin Res Ed). 1988 May 7;296(6632):1313-6. http://www.ncbi.nlm.nih.gov/pubmed/3133061
3. Hozo SP, Djulbegovic B, Hozo I. Estimating the mean and variance from the median, range, and the size of a sample. BMC Med Res Methodol. 2005 Apr 20;5:13. DOI 10.1186/1471-2288-5-13
4. Wan X, Wang W, Liu J, Tong T. Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Med Res Methodol. 2014 Dec 19;14:135. DOI 10.1186/1471-2288-14-135
5. Michiels S, Piedbois P, Burdett S, Syz N, Stewart L, Pignon JP. Meta-analysis when only the median survival times are known: a comparison with individual patient data results. Int J Technol Assess Health Care. 2005 Winter;21(1):119-25. http://www.ncbi.nlm.nih.gov/pubmed/15736523
6. Zang J, Xiang C, He J. Synthesis of median survival time in meta-analysis. Epidemiology. 2013 Mar;24(2):337-8. DOI 10.1097/EDE.0b013e318282a66c
7. Thorlund K, Walter SD, Johnston BC, Furukawa TA, Guyatt GH. Pooling health-related quality of life outcomes in meta-analysis—a tutorial and review of methods for enhancing interpretability. Research Synthesis Methods. 2011; 2(3): 188–203. DOI 10.1002/jrsm.46
8. Lewis S, Clarke M. Forest plots: trying to see the wood and the trees. BMJ 2001;322:1479. DOI 10.1136/bmj.322.7300.1479
9. Riley RD, Price MJ, Jackson D, Wardle M, Gueyffier F, Wang J, Staessen JA, White IR. Multivariate meta-analysis using individual participant data. Research Synthesis Methods. 2015; 6(2): 157–174. DOI 10.1002/jrsm.1129
10. Thompson SG, Higgins JPT. How should meta-regression analyses be undertaken and interpreted? Stat Med. 2002 Jun 15;21(11):1559-73. DOI 10.1002/sim.1187

• The PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) statement indicates what you should include as a minimum in a systematic review or meta-analysis. There are a number of extensions to the PRISMA statement. These can be useful for certain studies.
• The Cochrane Handbook for Systematic Reviews of Interventions provides extensive information on carrying out a meta-analysis.
• Cochrane Netherlands supports authors of Cochrane reviews, produces commissioned systematic reviews, provides methodological advice, offers training, and conducts scientific research into the methods of evidence-based medicine and systematic reviews. This organization also provides overviews of appraisal forms for different types of studies and of frequently asked questions.
• Wikipedia has an extensive article on meta-analyses.

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