# NNT calculation in meta-analysis

Even the greatest have weaknesses. It is a reality that affects even the great NNT, the number needed to treat, without a doubt the king of the measures of absolute impact of the research methodology in clinical trials.

Of course, that is not an irreparable disgrace. We only have to be well aware of its strengths and weaknesses in order to take advantage of the former and try to mitigate and control the latter. And it is that the NNT depends on the baseline risks of the intervention and control groups, which can be inconsistent fellow travelers and be subjected to variation due to several factors.

As we all know, NNT is an absolute measure of effect that is used to estimate the efficacy or safety of an intervention. This parameter, just like a good marriage, is useful in good times and in bad, in sickness and in health.

Thus, on the good side we talk about NNT, which is the number of patients that have to be treated for one to present a result that we consider as good. By the way, on the dark side we have the number needed to harm (NNH), which indicates how many we have to treat in order for one to present an adverse event.

NNT was originally designed to describe the effect of the intervention relative to the control group in clinical trials, but its use was later extended to interpret the results of systematic reviews and meta-analyzes. And this is where the problem may arise since, sometimes, the way to calculate it in trials is generalized for meta-analyzes, which can lead to error.

## NNT calculation in meta-analyis

The simplest way to obtain the NNT is to calculate the inverse of the absolute risk reduction between the intervention and the control group. The problem is that this form is the one that is most likely to be biased by the presence of factors that can influence the value of the NNT. Although it is the king of absolute measures of impact, it also has its limitations, with various factors influencing its magnitude, not to mention its clinical significance.

One of these factors is the duration of the study follow-up period. This duration can influence the number of events, good or bad ones, that the study participants can present, which makes it incorrect to compare the NNTs of studies with follow-ups of different duration.

Another may be the baseline risk of presenting the event. Let’s think that the term “risk”, from a statistical point of view, does not always imply something bad. We can speak, for example, of risk of cure. If the baseline risk is higher, more events will likely occur and the NNT may be lower. The outcome variable used and the treatment alternative with which we compared the intervention should also be taken into account.

And third, to name a few more of these factors, the direction and size of the effect, the scale of measurement, and the precision of the NNT estimates, their confidence intervals, may influence its value.

## Controls event rate

And here the problem arises with systematic reviews and meta-analyzes. Even though we might want to, there will always be some heterogeneity among the primary studies in the review, so these factors we have discussed may differ among studies. At this point, it is easy to understand that the estimation of the global NNT based on the summary measures of risks between the two groups may not be the most suitable, since it is highly influenced by the variations in the baseline control event rate (CER).

For these situations, it is much more advisable to make other more robust estimates of the NNT, the most widely used being those that use other association measures such as the risk ratio (RR) or the odds ratio (OR), which are more robust in the face of variations in CER. In the attached figure I show you the formulas for the calculation of the NNT using the different measures of association and effect.

In any case, we must not lose sight of the recommendation of not to carry out a quantitative synthesis or calculation of summary measures if there is significant heterogeneity among primary studies, since then the global estimates will be unreliable, whatever we do.

But do not think that we have solved the problem. We cannot finish this post without mentioning that these alternative methods for calculating NNT also have their weaknesses. Those have to do with obtaining an overall CER summary value, which also varies among primary studies.

The simplest way would be to divide the sum of events in the control groups of the primary studies by the total number of participants in that group. This is usually possible simply by taking the data from the meta-analysis’ forest plot. However, this method is not recommended, as it completely ignores the variability among studies and possible differences in randomization.

Another more correct way would be to calculate the mean or median of the CER of all the primary studies and, even better, to calculate some weighted measure based on the variability of each study.

And even, if baseline risk variations among studies are very important, an estimate based on the investigator’s knowledge or other studies could be used, as well as using a range of possible CER values and comparing the differences among the different NNTs that could be obtained.

You have to be very careful with the variance weighting methods of the studies, since the CER has the bad habit of not following a normal distribution, but a binomial one. The problem with the binomial distribution is that its variance depends greatly on the mean of the distribution, being maximum in mean values around 0.5.

On the contrary, the variance decreases if the mean is close to 0 or 1, so all the variance-based weighting methods will assign a greater weight to the studies the more their mean separates from 0.5 (remember that CER can range from 0 to 1, like any other probability value). For this reason, it is necessary to carry out a transformation so that the values approach a normal instead of a binomial distribution and thus be able to carry out the weighting.

## We’re leaving…

And I think we will leave it here for today. We are not going to go into the methods to transform the CER, such as the double arcsine or the application of mixed generalized linear models, since that is for the most exclusive minds, among which my own’s is not included. Anyway, don’t get stuck with this. I advise you to calculate the NNT using statistical packages or calculators, such as Calcupedev. There are other uses of NNT that we could also comment on and that can be obtained with these tools, as is the case with NNT in survival studies. But that is another story…

# Critical appraisal of meta-analysis

Yes, I know that the saying goes just the opposite. But that is precisely the problem we have with so much new information technology. Today anyone can write and make public what goes through his head, reaching a lot of people, although what he says is bullshit (and no, I do not take this personally, not even my brother-in-law reads what I post!). The trouble is that much of what is written is not worth a bit, not to refer to any type of excreta. There is a lot of smoke and little fire, when we all would like the opposite to happen.

The same happens in medicine when we need information to make some of our clinical decisions. Anywhere the source we go, the volume of information will not only overwhelm us, but above all the majority of it will not serve us at all. Also, even if we find a well-done article it may not be enough to answer our question completely. That’s why we love so much the revisions of literature that some generous souls publish in medical journals. They save us the task of reviewing a lot of articles and summarizing the conclusions. Great, isn’t it? Well, sometimes it is, sometimes it is not. As when we read any type of medical literature’s study, we should always make a critical appraisal and not rely solely on the good know-how of its authors.

Revisions, of which we already know there are two types, also have their limitations, which we must know how to value. The simplest form of revision, our favorite when we are younger and ignorant, is what is known as a narrative review or author’s review. This type of review is usually done by an expert in the topic, who reviews the literature and analyzes what she finds as she believes that it is worth (for that she is an expert) and summarizes the qualitative synthesis with her expert’s conclusions. These types of reviews are good for getting a general idea about a topic, but they do not usually serve to answer specific questions. In addition, since it is not specified how the information search is done, we cannot reproduce it or verify that it includes everything important that has been written on the subject. With these revisions we can do little critical appraising, since there is no precise systematization of how these summaries have to be prepared, so we will have to trust unreliable aspects such as the prestige of the author or the impact of the journal where it is published.

As our knowledge of the general aspects of science increases, our interest is shifting towards other types of revisions that provide us with more specific information about aspects that escape our increasingly wide knowledge. This other type of review is the so-called systematic review (SR), which focuses on a specific question, follows a clearly specified methodology of searching and selection of information and performs a rigorous and critical analysis of the results found. Moreover, when the primary studies are sufficiently homogeneous, the SR goes beyond the qualitative synthesis, also performing a quantitative synthesis analysis, which has the nice name of meta-analysis. With these reviews we can do a critical appraising following an ordered and pre-established methodology, in a similar way as we do with other types of studies.

The prototype of SR is the one made by the Cochrane’s Collaboration, which has developed a specific methodology that you can consult in the manuals available on its website. But, if you want my advice, do not trust even the Cochrane’s and make a careful critical appraising even if the review has been done by them, not taking it for granted simply because of its origin. As one of my teachers in these disciplines says (I’m sure he’s smiling if he’s reading these lines), there is life after Cochrane’s. And, besides, there is lot of it, and good, I would add.

## Critical appraisal of meta-analyes

Although SRs and meta-analyzes impose a bit of respect at the beginning, do not worry, they can be critically evaluated in a simple way considering the main aspects of their methodology. And to do it, nothing better than to systematically review our three pillars: validity, relevance and applicability.

Regarding VALIDITY, we will try to determine whether or not the revision gives us some unbiased results and respond correctly to the question posed. As always, we will look for some primary validity criteria. If these are not fulfilled we will think if it is already time to walk the dog: we probably make better use of the time.

Has the aim of the review been clearly stated? All SRs should try to answer a specific question that is relevant from the clinical point of view, and that usually arises following the PICO scheme of a structured clinical question. It is preferable that the review try to answer only one question, since if it tries to respond to several ones there is a risk of not responding adequately to any of them. This question will also determine the type of studies that the review should include, so we must assess whether the appropriate type has been included. Although the most common is to find SRs of clinical trials, they can include other types of observational studies, diagnostic tests, etc. The authors of the review must specify the criteria for inclusion and exclusion of the studies, in addition to considering their aspects regarding the scope of realization, study groups, results, etc. Differences among the studies included in terms of (P) patients, (I) intervention or (O) outcomes make two SRs that ask the same question to reach to different conclusions.

If the answer to the two previous questions is affirmative, we will consider the secondary criteria and leave the dog’s walk for later. Have important studies that have to do with the subject been included? We must verify that a global and unbiased search of the literature has been carried out. It is frequent to do the electronic search including the most important databases (generally PubMed, Embase and the Cochrane’s Library), but this must be completed with a search strategy in other media to look for other works (references of the articles found, contact with well-known researchers, pharmaceutical industry, national and international registries, etc.), including the so-called gray literature (thesis, reports, etc.), since there may be important unpublished works. And that no one be surprised about the latter: it has been proven that the studies that obtain negative conclusions have more risk of not being published, so they do not appear in the SR. We must verify that the authors have ruled out the possibility of this publication bias. In general, this entire selection process is usually captured in a flow diagram that shows the evolution of all the studies assessed in the SR.

It is very important that enough has been done to assess the quality of the studies, looking for the existence of possible biases. For this, the authors can use an ad hoc designed tool or, more usually, resort to one that is already recognized and validated, such as the bias detection tool of the Cochrane’s Collaboration, in the case of reviews of clinical trials. This tool assesses five criteria of the primary studies to determine their risk of bias: adequate randomization sequence (prevents selection bias), adequate masking (prevents biases of realization and detection, both information biases), concealment of allocation (prevents selection bias), losses to follow-up (prevents attrition bias) and selective data information (prevents information bias). The studies are classified as high, low or indeterminate risk of bias according to the most important aspects of the design’s methodology (clinical trials in this case).

In addition, this must be done independently by two authors and, ideally, without knowing the authors of the study or the journals where the primary studies of the review were published. Finally, it should be recorded the degree of agreement between the two reviewers and what they did if they did not agree (the most common is to resort to a third party, which will probably be the boss of both).

To conclude with the internal or methodological validity, in case the results of the studies have been combined to draw common conclusions with a meta-analysis, we must ask ourselves if it was reasonable to combine the results of the primary studies. It is fundamental, in order to draw conclusions from combined data, that the studies are homogeneous and that the differences among them are due solely to chance. Although some variability of the studies increases the external validity of the conclusions, we cannot unify the data for the analysis if there are a lot of variability. There are numerous methods to assess the homogeneity about which we are not going to refer now, but we are going to insist on the need for the authors of the review to have studied it adequately.

In summary, the fundamental aspects that we will have to analyze to assess the validity of a SR will be: 1) that the aims of the review are well defined in terms of population, intervention and measurement of the result; 2) that the bibliographic search has been exhaustive; 3) that the criteria for inclusion and exclusion of primary studies in the review have been adequate; and 4) that the internal or methodological validity of the included studies has also been verified. In addition, if the SR includes a meta-analysis, we will review the methodological aspects that we saw in a previous post: the suitability of combining the studies to make a quantitative synthesis, the adequate evaluation of the heterogeneity of the primary studies and the use of a suitable mathematical model to combine the results of the primary studies (you know, that of the fixed effect and random effects models).

Regarding the RELEVANCE of the results we must consider what is the overall result of the review and if the interpretation has been made in a judicious manner. The SR should provide a global estimate of the effect of the intervention based on a weighted average of the included quality items. Most often, relative measures such as risk ratio or odds ratio are expressed, although ideally, they should be complemented with absolute measures such as absolute risk reduction or the number needed to treat (NNT). In addition, we must assess the accuracy of the results, for which we will use our beloved confidence intervals, which will give us an idea of ​​the accuracy of the estimation of the true magnitude of the effect in the population. As you can see, the way of assessing the importance of the results is practically the same as assessing the importance of the results of the primary studies. In this case we give examples of clinical trials, which is the type of study that we will see more frequently, but remember that there may be other types of studies that can better express the relevance of their results with other parameters. Of course, confidence intervals will always help us to assess the accuracy of the results.

The results of the meta-analyzes are usually represented in a standardized way, usually using the so-called forest plot. A graph is drawn with a vertical line of zero effect (in the one for relative risk and odds ratio and zero for means differences) and each study is represented as a mark (its result) in the middle of a segment (its confidence interval). Studies with results with statistical significance are those that do not cross the vertical line. Generally, the most powerful studies have narrower intervals and contribute more to the overall result, which is expressed as a diamond whose lateral ends represent its confidence interval. Only diamonds that do not cross the vertical line will have statistical significance. Also, the narrower the interval, the more accurate result. And, finally, the further away from the zero-effect line, the clearer the difference between the treatments or the comparative exposures will be.

If you want a more detailed explanation about the elements that make up a forest plot, you can go to the previous post where we explained it or to the online manuals of the Cochrane’s Collaboration.

We will conclude the critical appraising of the SR assessing the APPLICABILITY of the results to our environment. We will have to ask ourselves if we can apply the results to our patients and how they will influence the care we give them. We will have to see if the primary studies of the review describe the participants and if they resemble our patients. In addition, although we have already said that it is preferable that the SR is oriented to a specific question, it will be necessary to see if all the relevant results have been considered for the decision making in the problem under study, since sometimes it will be convenient to consider some other additional secondary variable. And, as always, we must assess the benefit-cost-risk ratio. The fact that the conclusion of the SR seems valid does not mean that we have to apply it in a compulsory way.

If you want to correctly evaluate a SR without forgetting any important aspect, I recommend you to use a checklist such as PRISMA’s or some of the tools available on the Internet, such as the grills that can be downloaded from the page, which are the ones we have used for everything we have said so far.

## PRISMA statement

The PRISMA statement (Preferred Reporting Items for Systematic reviews and Meta-Analyzes) consists of 27 items, classified in 7 sections that refer to the sections of title, summary, introduction, methods, results, discussion and financing:

1. Title: it must be identified as SR, meta-analysis or both. If it is specified, in addition, that it deals with clinical trials, priority will be given to other types of reviews.
2. Summary: it should be a structured summary that should include background, objectives, data sources, inclusion criteria, limitations, conclusions and implications. The registration number of the revision must also be included.
3. Introduction: includes two items, the justification of the study (what is known, controversies, etc) and the objectives (what question tries to answer in PICO terms of the structured clinical question).
4. Methods. It is the section with the largest number of items (12):

– Protocol and registration: indicate the registration number and its availability.

– Eligibility criteria: justification of the characteristics of the studies and the search criteria used.

– Sources of information: describe the sources used and the last search date.

– Search: complete electronic search strategy, so that it can be reproduced.

– Selection of studies: specify the selection process and inclusion’s and exclusion’s criteria.

– Data extraction process: describe the methods used to extract the data from the primary studies.

– Data list: define the variables used.

– Risk of bias in primary studies: describe the method used and how it has been used in the synthesis of results.

– Summary measures: specify the main summary measures used.

– Results synthesis: describe the methods used to combine the results.

– Risk of bias between studies: describe biases that may affect cumulative evidence, such as publication bias.

1. Results. Includes 7 items:

– Selection of studies: it is expressed through a flow chart that assesses the number of records in each stage (identification, screening, eligibility and inclusion).

– Characteristics of the studies: present the characteristics of the studies from which data were extracted and their bibliographic references.

– Risk of bias in the studies: communicate the risks in each study and any evaluation that is made about the bias in the results.

– Results of the individual studies: study data for each study or intervention group and estimation of the effect with their confidence interval. The ideal is to accompany it with a forest plot.

– Synthesis of the results: present the results of all the meta-analysis performed with the confidence intervals and the consistency measures.

– Risk of bias between the subjects: present any evaluation that is made of the risk of bias between the studies.

– Additional analyzes: if they have been carried out, provide the results of the same.

1. Discussion. Includes 3 items:

– Summary of the evidence: summarize the main findings with the strength of the evidence of each main result and the relevance from the clinical point of view or of the main interest groups (care providers, users, health decision-makers, etc.).

– Limitations: discuss the limitations of the results, the studies and the review.

– Conclusions: general interpretation of the results in context with other evidences and their implications for future research.

1. Financing: describe the sources of funding and the role they played in the realization of the SR.

As a third option to these two tools, you can also use the aforementioned Cochrane’s Handbook for Systematic Reviews of Interventions, available on its website and whose purpose is to help authors of Cochrane’s reviews to work explicitly and systematically.

## We’re leaving…

As you can see, we have not talked practically anything about meta-analysis, with all its statistical techniques to assess homogeneity and its fixed and random effects models. And is that the meta-analysis is a beast that must be eaten separately, so we have already devoted two post only about it that you can check when you want. But that is another story…

# Systematic review and meta-analysis

This is another of those famous quotes that are all over the place. Apparently, the first person to have this clever idea was Aristotle, who used it to summarize his holism general principle in his briefs on metaphysics. Who would have said that this tinny phrase contains so much wisdom?. Holism theory insists that everything must be considered in a comprehensive manner, because its components may act in a synergistic way, allowing the meaning of the whole to be greater than the meaning that each individual part contribute with.

Don’t be afraid, you are still on the blog about the brains and not on a blog about philosophy. Neither have I changed the topic of the blog, but this saying is just what I needed to introduce you to the wildest beast of scientific method, which is called meta-analysis.

## Introducing the topic

We live in the information age. Since the end of the 20th century, we have witnessed a true explosion of the available sources of information, accessible from multiple platforms. The end result is that we are overwhelmed every time we need information about a specific point, so we do not know where to look or how we can find what we want. For this reason, systems began to be developed to synthesize the information available to make it more accessible when needed.

## Narrative review

So, the first reviews come of the arid, the so-called narrative or author reviews. To write them, one or more authors, usually experts in a specific subject, made a general review on this topic, although without any strict criteria on the search strategy or selection of information. Following with total freedom, the authors analyzed the results as instructed by their will and ended up drawing their conclusions from a qualitative synthesis of the obtained results.

These narrative reviews are very useful for acquiring an overview of the topic, especially when one knows little about the subject, but they are not very useful for those who already know the topic and need answers to a more specific question. In addition, as the whole procedure is done according to authors´ wishes, the conclusions are not reproducible.

## Systematic review

For these reasons, a series of privileged minds invented the other type of review in which we will focus on this post: the systematic review. Instead of reviewing a general topic, systematic reviews do focus on a specific topic in order to solve specific doubts of clinical practice. In addition, they use a clearly specified search strategy and inclusion criteria for an explicit and rigorous work, which makes them highly reproducible if another group of authors comes up with a repeat review of the same topic. And, if that were not enough, whenever possible, they go beyond the analysis of qualitative synthesis, completing it with a quantitative synthesis that receives the funny name of meta-analysis.

The realization of a systematic review consists of six steps: formulation of the problem or question to be answered, search and selection of existing studies, evaluation of the quality of these studies, extraction of the data, analysis of the results and, finally, interpretation and conclusion. We are going to detail this whole process a little.

Any systematic review worth its salt should try to answer a specific question that must be relevant from the clinical point of view. The question will usually be asked in a structured way with the usual components of population, intervention, comparison and outcome (PICO), so that the analysis of these components will allow us to know if the review is of our interest.

In addition, the components of the structured clinical question will help us to search for the relevant studies that exist on the subject. This search must be global and not biased, so we avoid possible biases of source excluding sources by language, journal, etc. The usual is to use a minimum of two important electronic databases of general use, such as Pubmed, Embase or the Cochrane’s, together with the specific ones of the subject that is being treated. It is important that this search is complemented by a manual search in non-electronic registers and by consulting the bibliographic references of the papers found, in addition to other sources of the so-called gray literature, such as doctoral theses, and documents of congresses, as well as documents from funding agencies, registers and, even, establishing contact with other researchers to know if there are studies not yet published.

It is very important that this strategy is clearly specified in the methods section of the review, so that anyone can reproduce it later, if desired. In addition, it will be necessary to clearly specify the inclusion and exclusion criteria of the primary studies of the review, the type of design sought and its main components (again in reference to the PICO, the components of the structured clinical question).

## It is important to assess the quality of the studies included in the review

The third step is the evaluation of the quality of the studies found, which must be done by a minimum of two people independently, with the help of a third party (who will surely be the boss) to break the tie in cases where there is no consensus among the extractors. For this task, tools or checklists designed for this purpose are usually used; one of the most frequently used tool for bias control is the Cochrane Collaboration Tool. This tool assesses five criteria of the primary studies to determine their risk of bias: adequate randomization sequence (prevents selection bias), adequate masking (prevents biases of realization and detection, both information biases), concealment of allocation (prevents selection bias), losses to follow-up (prevents attrition bias) and selective data information (prevents information bias). The studies are classified as high, low or indeterminate risk of bias. It is common to use the colors of the traffic light, marking in green the studies with low risk of bias, in red those with high risk of bias and in yellow those who remain in no man’s land. The more green we see, the better the quality of the primary studies of the review will be.

Ad-hoc forms are usually designed for extraction of data, which usually collect data such as date, scope of the study, type of design, etc., as well as the components of the structured clinical question. As in the case of the previous step, it is convenient that this be done by more than one person, establishing the method to reach an agreement in cases where there is no consensus among the reviewers.

## And we come to meta-analysis

And here we enter the most interesting part of the review, the analysis of the results. The fundamental role of the authors will be to explain the differences that exist between the primary studies that are not due to chance, paying special attention to the variations in the design, study population, exposure or intervention and measured results. You can always make a qualitative synthesis analysis, although the real magic of the systematic review is that, when the characteristics of primary studies allow it, a quantitative synthesis, called meta-analysis, can also be performed.

A meta-analysis is a statistical analysis that combines the results of several independent studies that try to answer the same question. Although meta-analysis can be considered as a research project in its own right, it is usually part of a systematic review.

Primary studies can be combined using a statistical methodology developed for this purpose, which has a number of advantages. First, by combining all the results of the primary studies we can obtain a more complete global vision (you know, the whole is greater …). The second one, when studies are combined we increase the sample size, which increases the power of the study in comparison with that of the individual studies, improving the estimation of the effect we want to measure. Thirdly, when extracting the conclusions of a greater number of studies, its external validity increases, since having involved different populations it is easier to generalize the results. Finally, it can allow us to resolve controversies between the conclusions of the different primary studies of the review and, even, to answer questions that had not been raised in those studies.

Once the meta-analysis is done, a final synthesis must be made that integrates the results of the qualitative and quantitative synthesis in order to answer the question that motivated the systematic review or, when this is not possible, to propose the additional studies that must be carried out to be able to answer it.

But a meta-analysis will only deserve all our respect if it fulfills a series of requirements. As the systematic review to witch the meta-analysis belongs, it should aim to answer one specific question and it must be based on all relevant available information, avoiding publication bias and recovery bias. Also, primary studies must have been assessed to ensure its quality and its homogeneity before combining them. Of course, data must be analyzed and presented in an appropriate way. And, finally, it must make sense to combine the results in order to do it. The fact that we can combine results doesn’t always mean that we have to do it if it is not needed in our clinical setting.

## Methods for combining studies

And how do you combine the studies?, you could ask yourselves. Well, that’s the meta-analysis’ crux of the matter (crossings, really, there’re many), because there are several possible ways to do it.

Anyone could think that the easiest way would be a sort of Eurovision Contest. We account for the primary studies with a statistically significant positive effect and, if they are majority, we conclude that there’s consensus for positive result. This approach is quite simple but, you will not deny it, also quite sloppy. Also I can think about a number of disadvantages about its use. On one hand, it implies that lack of significance and lack of effect is synonymous, which does not always have to be true. On the other hand, it doesn’t take into account the direction and strength of effect in each study, nor the accuracy of estimators, neither the quality nor the characteristics of primary studies’ design. So, this type of approach is not very recommended, although nobody is going to fine us if we use it as an informal first approach before deciding which if the best way to combine the results.

Another possibility is to use a sort of sign test, similar to other non-parametric statistical techniques. We count the number of positive effects, we subtract the negatives and we have our conclusion. The truth is that this method also seems too simple. It ignores studies that don’t have statistical significance and also ignores the accuracy of studies’ estimators. So, this approach is not of much use, unless you only know the directions of the effects measured in the studies. We could also use it when primary studies are very heterogeneous to get an approximation of the global result, although I would not trust very much results obtained in this way.

The third method is to combine the different Ps of the studies (our beloved and sacrosanct Ps). This could come to our minds if we had a systematic review whose primary studies use different outcome measures, although all of them tried to answer the same question. For example, think about a study on osteoporosis where some studies use ultrasonic densitometry, others spine or femur DEXA, etc. The problem with this method is that it doesn’t take into account the intensities of effects, but only its directions and statistical significances, and we all know the deficiencies of our holy Ps. To be able to make this approach we’d need software that combines data that follow a Chi-square or Gaussian distribution, giving us an estimate and its confidence interval.

The fourth and final method that I know is also the most stylish: to make a weighted combination of the estimated effect in all the primary studies. To calculate the mean would be the easiest way, but we have not come this far to make fudge again. Arithmetic mean gives same emphasis to all studies, so if you have an outlier or imprecise study, results will be greatly distorted. Don’t forget that average always follow the tails of distributions and are heavily influenced by extreme values (which does not happen to her relative, the median).

This is why we have to weigh the different estimates. This can be done in two ways, taking into account the number of subjects in each study, or performing a weighting based on the inverses of the variances of each (you know, the squares of standard errors). The latter way is the more complex, so it is the one people preferred to do more often. Of course, as the maths needed are very hard, people usually use special software that can be external modules working in usual statistical programs such as Stata, SPSS, SAS or R, or specific software such as the famous Cochrane Collaboration’s RevMan.

## In summary

As you can see, I have not been short of calling the systematic review with meta-analysis as the wildest beast of epidemiological designs. However, it has its detractors. We all know someone who claims not to like systematic reviews because almost all of them end up in the same way: “more quality studies are needed to be able to make recommendations with a reasonable degree of evidence”. Of course, in these cases we cannot put the blame on the review, because we do not take enough care to perform our studies so the vast majority deserves to end up in the paper shredder.

Another controversy is that of those who debate about what is better, a good systematic review or a good clinical trial (reviews can be made on other types of designs, including observational studies). This debate reminds me of the controversy over whether one should do a calimocho mixing a good wine or if it is a sin to mix a good wine with Coca-Cola. Controversies aside, if you have to take a calimocho, I assure you that you will enjoy it more if you use a good wine, and something similar happens to reviews with the quality of their primary studies.

The problem of systematic reviews is that, to be really useful, you have to be very rigorous in its realization. So that we do not forget anything, there are lists of recommendations and verification that allow us to order the entire procedure of creation and dissemination of scientific works without making methodological errors or omissions in the procedure.

It all started with a program of the Health Service of the United Kingdom that ended with the founding of an international initiative to promote the transparency and precision of biomedical research works: the EQUATOR network (Enhancing the QUAlity and Transparency of health Research). This network consists of experts in methodology, communication and publication, so it includes professionals involved in the quality of the entire process of production and dissemination of research results. Among many other objectives, which you can consult on its website, one is to design a set of recommendations for the realization and publication of the different types of studies, which gives rise to different checklists or statements.

The checklist designed to apply to systematic reviews is the PRISMA statement (Preferred Reporting Items for Systematic reviews and Meta-Analyses), which comes to replace the QUOROM statement (QUality Of Reporting Of Meta-analyses). Based on the definition of systematic review of the Cochrane Collaboration, PRISMA helps us to select, identify and assess the studies included in a review. It also consists of a checklist and a flowchart that describes the passage of all the studies considered during the realization of the review. There is also a lesser-known statement for the assessment of meta-analyses of observational studies, the MOOSE statement (Meta-analyses of Observational Studies in Epidemiology).

The Cochrane Collaboration also has a very well structured and defined methodology, which you can consult on its website. This is the reason why they have so much prestige within the world of systematic reviews, because they are made by professionals who are dedicated to the task following a rigorous and contrasted methodology. Anyway, even Cochrane’s reviews should be critically read and not giving them anything for insured.

## We’re leaving…

And with this we have reached the end for today. I want to insist that meta-analysis should be done whenever possible and interesting, but making sure beforehand that it is correct to combine the results. If the studies are very heterogeneous we should not combine anything, since the results that we could obtain would have a much compromised validity. There is a whole series of methods and statistics to measure the homogeneity or heterogeneity of the primary studies, which also influence the way in which we analyze the combined data. But that is another story…