abstract: Why do we have so much trouble distinguishing life from non-life, and distinguishing our biology from another? When in doubt, one should count the "bits" of heritable information.
author: Gerald F. Joyce\* E-mail: <firstname.lastname@example.com>[^1]
date: 2012-05
institute: 1Department of Molecular Biology, Skaggs Institute for Chemical Biology, The Scripps Research Institute, La Jolla, California, United States of America; 2Department of Chemistry, The Scripps Research Institute, La Jolla, California, United States of America
references:
title: Bit by Bit: The Darwinian Basis of Life

Thanks to a combination of ground- and space-based astronomical observations, the number of confirmed extrasolar planets will soon exceed 1,000. An increasing number of these will be said to lie within the "habitable zone" and even be pronounced as "Earth-like." Within a decade there will be observational data regarding the atmospheric composition of some of those planets, and just maybe those data will indicate something funny going on—something well outside the state of chemical equilibrium—on a potentially hospitable planet. Perhaps our astronomy colleagues should be forgiven for their enthusiasm in declaring that humanity is on the brink of discovering alien life.

But haven't we heard this before? Didn't President Clinton announce in 1996 that a Martian meteorite recovered in Antarctica \[1\] "speaks of the possibility of life" on Mars? (No, it turned out to be mineralic artifacts.) Wasn't some "alien" arsenic-based life discovered recently in Mono Lake, California \[2\]? (No, it's a familiar proteobacterium struggling to survive in a toxic environment.) Didn't Craig Venter and his colleagues recently create a synthetic bacterial cell \[3\], "the first self-replicating species we've had on the planet whose parent is a computer"? (No, its parent is *Mycoplasma mycoides* and its genome was dutifully reconstructed through DNA synthesis and PCR amplification.)

Why are we so confused (or so lonely) that we have such trouble distinguishing life from non-life and distinguishing our biology from another? A key limitation is that we know of only one life form, causing us to regard life from that singular perspective (Figure 1). We see life as cellular, with a nucleic acid genome that is translated to a protein machinery. Life self-reproduces, transmits heritable information to its progeny, and undergoes Darwinian evolution based on natural selection. Life captures high-energy starting materials and converts them to lower-energy products to drive metabolic processes. Life exists on at least one temperate, rocky planet, where it has persisted for about four billion years. There are likely to be tens of thousands of "habitable" planets within a thousand light years of Earth, and more than a billion such planets in our galaxy, so *surely* (say the astronomers) we are not alone.

# Rolling the Dice

What, in fact, is the probability that a temperate, rocky planet will generate life? Science cannot say. That is because, based on the one known example of obscure origins, even a Bayesian would not want to assign a probability to such an event. The probability assessment would be more meaningful if there were even one more genuine example of life, whether discovered in space, on Earth, or in a test tube. If that entity had all of the properties of terrestrial life described above, then one would conclude that, indeed, we are not alone. But what if the entity had only some of those properties? What if it could self-reproduce, directing the assembly of progeny of identical composition, but could not evolve new functions? What if it consisted of complex chemical processes within a cellular compartment but had no basis for maintaining heritable genetic information? What if it had all of the properties of life but was descended from our own life form rather than derived from an independent origin?

When faced with such real or hypothetical situations regarding alternative life, it is useful to frame the question in terms of information: How many heritable bits are involved, and where did they come from? (Box 1) Biological systems are distinguishable from chemical systems because they contain components that have many potential alternative compositions but adopt a particular composition based on the history of the system. In this sense biological systems have a molecular memory (genotype), which is shaped by experience (selection) and maintained by self-reproduction. One can count the number of bits in this molecular memory, for example, up to two bits per base pair for a nucleic acid genome. The bits accrue as potential alternative compositions are excluded and specific compositions are adopted. More formally, the number of bits is calculated as log~2~ of the number of potential compositions divided by the number of realized compositions. One must count only those bits that accrue within the system, not those that were evolved elsewhere and bestowed upon the system for free.

## Box 1. Counting Bits

When evaluating potential examples of alternative life, one should look at the genetic material and ask the following questions regarding its information content. The aim is to determine how many heritable bits are involved, excluding those that did not arise within the genetic system.

**Q1.** How many different types of subunits (x) does the genetic material contain? For a binary polymer, x = 2; for a nucleic acid polymer, x = 4 (A, T/U, G, C).

**Q2.** What is the length (n) of the genetic material? Count only those positions that can potentially be occupied by different types of subunits.

**Q3.** Do all of the possible compositions have the same prior probability of occurrence? Some combinations may be less probable if one of the subunits is less abundant or less frequently incorporated into the genetic material. Some combinations may be disfavored for chemical or biochemical reasons (e.g., long runs of G residues in DNA).

The number of possible compositions is x^n^. If these are all equally probable, then each has a prior probability of occurrence of x^−n^, and the information content (number of bits) associated with a particular realized composition is log~2~(x^n^). This can also be expressed as 2^\#bits^ = x^n^. For a binary polymer, \#bits = n; for a nucleic acid polymer, \#bits = 2n.

If the various compositions do *not* have the same prior probability of occurrence, then the information content associated with a particular realized composition must be calculated based on its prior probability of occurrence (*p* ~k~), which ranges from 0 to 1. The information content (number of bits) associated with a particular realized composition is −log~2~(*p* ~k~).

**Q4.** Was a portion of the composition of the genetic material determined outside the genetic system? Some of the composition may have evolved in a different system and was merely available for the taking. Do not include preexisting information when counting bits because its prior probability of occurrence is 1, and therefore its information content with respect to the genetic system being considered is −log~2~(1) = 0.

Suppose one has a molecule that self-duplicates indefinitely, directing the ordered assembly of building blocks to produce additional copies of itself. That would be an interesting chemical process, but unless there is the opportunity for alternative compositions to arise and similarly reproduce—that is, for Darwinian evolution to occur—the bit content would be zero. Suppose one has a complex reaction cascade, perhaps even an autocatalytic cycle, contained within a growing and dividing physical compartment. That too would be an interesting chemical process, but it would not involve any heritable bits. Suppose one uses the genetic information from a preexisting biological organism to construct a facsimile that, going forward, can evolve alternative compositions. New bits could accrue within such a system, but all of the bits that were provided at the outset would have derived from the preexisting organism. To be considered a new life form, the majority of bits must be self-derived.

# Pathways to Life

In principle, there are two pathways by which a new life form can arise: either directly from chemistry or spun off from some other biology. If life arises from chemistry, as is thought to have occurred on the primitive Earth (Figure 2), then it begins with zero heritable bits and organizes into a bit-generating system. Following an era of prebiotic chemistry, perhaps reaching a high level of chemical complexity, molecular memory arises. Molecules of variable composition begin to replicate, mutate, and evolve in a Darwinian manner. If, instead, life arises from another life form, then it may have a privileged beginning, benefitting from a chemical environment that has been shaped by preexisting life. A new life form may grow on the spoils of prior life with no carryover of bits, or it may descend from prior life with some carryover of bits into a different genetic system. The latter type of transition is thought to have occurred during the early history of life on Earth when RNA-based life gave way to DNA/protein-based life \[4\]. That transition likely involved a substantial transfer of bits that had accrued within RNA and were ported over to DNA through what might be termed The Great Reverse Transcription. We see echoes of those ancestral bits in the sequences of ribosomal RNA, tRNA, and possibly other contemporary RNAs that are present across all three kingdoms of life.

It has been suggested that RNA-based life was preceded by yet another life form \[5\], perhaps based on a nucleic-acid-like genetic molecule such as threose nucleic acid (TNA) \[6\] or glycol nucleic acid (GNA) \[7\]. There does not appear to be any trace of pre-RNA life in contemporary biology, although maybe we do not know how to look. It is conceivable, for example, that some of the deeply conserved bits in contemporary RNAs are the double echo of information that was carried from pre-RNA life to RNA life and then to DNA/protein-based life. It also is possible that there was life on Earth prior to RNA but that it had no chemical resemblance to RNA. Information from such a pre-RNA genetic molecule could have been translated into RNA through a machinery analogous to the ribosome, but with RNA as the output rather than the input. Alternatively, pre-RNA life may have facilitated the emergence of RNA life, but with no transfer of information. Pre-RNA life may have generated RNA molecules as a metabolic product, and eventually the RNA molecules began replicating and evolving on their own.

# Getting Started

The above discussion emphasizes that there are many possible routes by which one life form can give rise to another, but it does not address the question of how an initial life form arises in the first place. A key question to ask is: What is the minimum number of bits it takes to provide a replicating, evolving system that has the ongoing capacity to accrue more bits? That will depend on the chemical nature of the first self-replicating molecules and the resources that are available in its environment. When astronomers speak of habitable zones they refer to a planetary orbit that is of appropriate distance from a star to maintain liquid water on the planetary surface. This may be too restrictive or too generous a definition, depending on your point of view \[8\]. Perhaps life can exist in a non-aqueous environment, although there is little data to support this conjecture. Conversely, even a temperate little pond of water, salts, and dilute organics may be insufficient for life to originate. The pond would need to accumulate heteropolymers of variable composition, including some that could replicate and provide the basis for molecular memory, and it is not clear whether this is a common or exceedingly rare occurrence.

In terms of bits, a binary heteropolymer that contains 10 subunits would have 1,024 potential compositions, and any particular composition would represent up to 10 bits of heritable information. It seems doubtful that there is any heteropolymer for which 10 bits is enough to get started. Now suppose that it is a quaternary heteropolymer (like RNA) that is assembled into chains of 40 subunits. Then there would be 10^24^ possible compositions, and any particular composition would represent up to 80 bits of heritable information. An RNA biochemist might argue (see below) that this is just enough to get started. However, to represent all of these combinations as even a single copy would require that the little pond contain 27 kilograms of RNA, which seems highly implausible. Finally, suppose there are millions of winning compositions of 40 subunits, any of which could self-replicate and initiate Darwinian evolution. Then even a lucky milligram of RNA might contain the seed of life.

In the laboratory one can prepare milligram quantities of random-sequence RNA molecules containing 40 or more subunits. One can provide an endless supply of activated nucleotide building blocks and control all aspects of the reaction conditions. Stacking the deck in this way, why haven't we witnessed the origin of RNA life experimentally? Because even a lucky milligram of RNA is insufficient. In order for a seed copy of replicating RNA to germinate, it must produce additional copies of itself faster than the existing copies become degraded, and it must operate with sufficient fidelity that the accurate copies are not overwhelmed by error copies \[9\]. The requisite rate and fidelity of replication might reasonably be achieved in a pure reaction system that contains only the replicator and its corresponding building blocks. However, in a complex mixture of almost entirely mismatched parts, what process singles out the rare matching components? Darwinian evolution can enrich one molecule in a milligram, but before the onset of Darwinian evolution there would be only chemistry, and the chemistry of complex mixtures of cross-interacting molecules is very messy.

One way to avoid complex mixtures would be for each replicating RNA, together with its corresponding building blocks, to be spatially isolated within a separate compartment. These compartments need not be "cells," but at least separate locales to avoid crosstalk among the replicators and to allow the fruits of their labor to accumulate locally for their own benefit. The need for compartments places additional restrictions on the nature of the environment, although at a minimum a "compartment" could be as simple as a non-covalent assemblage of the replicator and its components. Again it comes down to bits. How many bits of specific chemical organization are required to exclude the molecular riff-raff and allow a fledgling replicator to begin evolving? If 80 bits are required and there are a million such 80-bit combinations, then there would need to be 10^18^ separate locales of suitable composition to provide a reasonable opportunity for life to begin. If each suitable locale is a bubble in the sea, then the origin of life may not be a rare event, but if each is a different habitable planet in our galaxy, then even among a billion such planets, we may be very much alone.

# Second Life?

My laboratory recently described an example, outside of biology, of a chemical system that can undergo Darwinian evolution in a self-sustained manner \[10\]. "Self-sustained" in this context means that all of the bits necessary for the system to undergo Darwinian evolution are part of the system that is evolving. The chemical system involves pairs of RNA enzymes that catalyze each other's synthesis by joining together two oligonucleotide building blocks (Figure 3A). Each of the two building blocks can adopt thousands of potential alternative compositions and thus can be joined to form millions of different combinations. Each of the many possible combinations can self-replicate and transmit compositional information to its progeny. Variants that replicate most efficiently grow to dominate the population until new, more advantageous variants arise to supplant their predecessors in a never-ending Darwinian battle for survival.

The population of evolving RNA enzymes constitutes a synthetic genetic system, but it is limited in two important respects. First, the molecules contain only 24 bits (12 base pairs) of heritable information to encode function. Second, replication depends on 60 bits (30 defined nucleotides) that are provided at the outset and are not subject to mutation and selection (Figure 3B). Thus of the 84 total bits required for the system to replicate and evolve, only about one-fourth can be counted as part of the system's molecular memory. The synthetic genetic system is not a new life form because it operates mostly on borrowed bits.

# Prospects

Someday the threshold may be crossed in which an alternative genetic system contains more heritable bits than the number of bits required to initiate its operation. Crossing that threshold is a reasonable criterion for what would constitute a new form of life. A life form that arises directly from bit-free chemistry would be considered "new" from the outset, while one that derives from a biological cell would have a long way to go before reaching the threshold. Between these two extremes lie the possibilities of starting with a modest number of bits, whether by the luck of combinatorial chemistry or derived from preexisting life, then accruing enough bits within the system to be regarded as new life. Perhaps the first true alternative to terrestrial biology will be found on an extrasolar planet, in a rock from Mars, or within an extreme environment on Earth. More likely, it will be the handiwork of an intelligent species that has discovered the principles of Darwinian evolution and learned to devise chemical systems that have the capacity to generate bits on their own.

# References

## Abbreviations

GNA

:   glycol nucleic acid

TNA

:   threose nucleic acid

[^1]: Essays articulate a specific perspective on a topic of broad interest to scientists.


author: Ursula Neubauer; Gregor Kastl\*To whom correspondence should be addressed: Ursula Neubauer, Michael-Gaismair Strasse 11, 6020 Innsbruck, Austria, E-mail: <email@example.com>
date: 2010-04-22
institute: 1University of Innsbruck, student in medicine, Innsbruck, Austria
title: A student's perspective from the Medical University of Innsbruck

# Report

Innsbruck is known for its skiing resorts, the 'olden Dacherl'(golden roof) and the medical school, which recently has become a refuge for foreign students desperately seeking admission to medical education. However, the Medical University of Innsbruck is much more than a place of last resort for students; it is first and foremost an outstanding medical school which is held in high esteem internationally. It is well-renowned for its medical research and practice and its international reputation transcends the small size of Austria as a country. Numerous scientists such as Ignaz Semmelweis, Karl Landsteiner, Sigmund Freud and Konrad Lorenz gained international recognition for their significant contributions to the field of medicine.

Innsbruck therefore combines for students the spirit of a young city dominated by students and situated in the midst of famous skiing resorts with the heritage of a great tradition and the professional environment of a high ranking institution for education and training.

Today Austria has four medical universities: public universities at Vienna, Graz and Innsbruck and the private Paracelsus University at Salzburg.

As in most other countries, it is not easy to get into medical school as the number of applicants far exceeds the number of available places. Medical Universities have therefore adopted various admission procedures. In Vienna and Innsbruck, applicants take a general admissions test, the 'Eignungstest fuer das Medizinstudium' (EMS) (ability test for medical education), which tests skills and competencies like stereoscopic vision, concentration, knowledge of maths and the ability to understand scientific texts. The test is designed to be very exhausting and stressful. The tension is palpable when one enters the large examination hall where approximately 1800 applicants are gathered to compete for a mere 400 places at the medical school. During the test the level of pressure rises because the test is designed to be too long to complete in the short time allowed. Accordingly, there is a strong sense of discouragement among students after the test. Six weeks after the test, the results are published together with the list of the 400 candidates that are invited to start their studies in the upcoming semester.

From the very start the curriculum is quite challenging. To help students cope with their new situation they are guided during the first four weeks before the first exam by senior more experienced students acting as tutors.

The basic structure of the curricula of the three public medical universities in Austria is similar. The curriculum is divided into three parts: 'pre-clinical', 'middle-clinical' and 'clinical', consisting of modules, such as 'musculoskeletal system' or 'components of life'.

Despite the basic similarity, the curricula differ significantly because medical schools are free to design their own programme and determine their own concept and standards of academic excellence. Unfortunately, these differences are a barrier to students moving between universities and most students complete their studies at one medical school.

However, in order to offer students international experience, there are many scholarships enabling students to work in hospitals abroad during semester breaks.

The medical programme at Innsbruck Medical University comprises twelve semesters. From the first year to the tenth semester, students have to take an exam consisting of 800 multiple choice questions every second semester.

It is therefore important that these questions test students' basic medical knowledge. However, as teachers are required to produce new questions for the same topics every year, in practice questions tend to ask about details that may be overly specific and not adequately reflect basic medical knowledge. This system has come under strong criticism from both students and teachers.

Innsbruck has a long and established history in medical education and it is the seat of one of the oldest faculties of anatomy in Europe. Unlike other medical schools where students often do not have sufficient access to practical courses in anatomy, Innsbruck Medical University upholds its longstanding tradition of intensive dissection courses in the first two years. Groups of eight students are provided with one human body for anatomical observation and medical procedures. This offers students extensive practice in gross anatomy and gives them ample opportunity to develop their anatomical skills and knowledge.

The 11^th^ and 12^th^ semesters are designed as clinical clerkships ('Klinisch-Praktisches Jahr') in six disciplines. During this year students can also gain international experience. Because this practical year was only established fairly recently with the introduction of a new curriculum, there was no previous experience with this type of training and there has not been enough time for improvement. An important benefit of the new curriculum is the reduction in the size of student groups to maximize their work experience and enhance their learning.

Medical studies in Austria are a diploma study, which means that students have to write a diploma thesis to complete their studies. Strangely, this diploma thesis is the basis for the title of Medicinae Universalis Doctor (Dr. med. univ., Doctor of Medicine). However, it is not equivalent to a PhD degree. Consequently, students additionally have to earn a PhD degree in order to obtain a postgraduate lecture qualification.

After completing undergraduate medical studies students in Austria have to work as a 'Turnusarzt' in different medical disciplines for a minimum period of 36 months. Having successfully completed this period, graduates are awarded the *ius practicandi* (licence to practice). The 'Turnusarzt' system is subject to strong criticism because it is considered too time consuming and to delay specialty training until very late in a trainee's development. As a consequence, plans are in the offing to change this system fundamentally, or at least to shorten the required 36 months of working as a 'Turnusarzt'.

Another issue that should be mentioned is the relationship between German and Austrian students at Innsbruck. The population of Germany is ten times the size of the Austrian population and approximately 20% of medical students in Austria are from Germany. In Innsbruck, which is located just 30 km from the German border, this percentage is even higher. Unable to secure a place at a German medical school because of the "numerus clausus" (limited admission), many young Germans try to gain entrance to an Austrian Medical University by participating in the EMS test. This situation has aroused much heated debate in Austria. Presently, Austria is attempting to control the number of German students by allocating a maximum number places for foreign students from countries within the European Union. According to current regulations, at least 75% of students have to be Austrian citizens.

Overall there are several advantages to studying medicine at Innsbruck Medical University. From the first semester onwards, students benefit from a good education in clinical practical subjects. As early as the first weeks of the first semester students can take part in clinical training in the hospital where they can join nurses and doctors. Moreover, there are lectures by general practitioners in addition to lectures by professors specialized in anatomy or biochemistry. This enhances learning, since students are brought into contact with "real medical practice" from the very beginning of their training. The strong clinical orientation is the main reason for the good reputation that medical students from Innsbruck have in numerous hospitals across Europe. Many of our students undertaking clinical traineeships elsewhere have been complimented by doctors on the standard of their clinical knowledge, which even in the early semesters is very high compared to that of medical students from other universities.

The early clinical orientation makes it easy for students to stay highly motivated even during the preclinical phase. Obviously, there are also theoretical lectures but students additionally gain more in-depth experience by practical training in small student groups.

Another important aspect is that students are involved in almost every decision of the university concerning their education and take an important and proactive role in improving the curriculum.

The experience we have gained over the last seven semesters has convinced us that education at Innsbruck Medical University is highly competitive. Looking back we have not once regretted our decision to study at Innsbruck and we can definitely recommend it to all those considering Innsbruck Medical University for their medical studies.

# The authors

1\. Ursula Neubauer, 3th year student in medicine, University of Innsbruck.

2\. Gregor Kastl. 3th year student in medicine, University of Innsbruck.


abstract: The number of neuroimaging studies has grown exponentially in recent years and their results are not always consistent. Meta-analyses are helpful to summarize this vast literature and also offer insights that are not apparent from the individual studies. In this review, we describe the main methods used for meta-analyzing neuroimaging data, with special emphasis on their relative advantages and disadvantages. We describe and discuss meta-analytical methods for global brain volumes, methods based on regions of interest, label-based reviews, voxel-based meta-analytic methods and online databases. Regions of interest-based methods allow for optimal statistical analyses but are affected by a limited and potentially biased inclusion of brain regions, whilst voxel-based methods benefit from a more exhaustive and unbiased inclusion of studies but are statistically more limited. There are also relevant differences between the different available voxel-based meta-analytic methods, and the field is rapidly evolving to develop more accurate and robust methods. We suggest that in any meta-analysis of neuroimaging data, authors should aim to: only include studies exploring the whole brain; ensure that the same threshold throughout the whole brain is used within each included study; and explore the robustness of the findings via complementary analyses to minimize the risk of false positives.
author: Joaquim Radua; David Mataix-Cols
date: 2012
institute: 1Institute of Psychiatry, King's College London, De Crespigny Park, London, UK; 2Research Unit, FIDMAG-CIBERSAM, Sant Boi de Llobregat, Barcelona, Spain
references:
title: Meta-analytic methods for neuroimaging data explained

# Introduction

The number of neuroimaging studies has grown exponentially in recent years. However, findings from different studies may sometimes be difficult to integrate into a coherent picture. Inconsistent results are not uncommon. Furthermore, a few influential studies might often eclipse robust findings from other studies. In other words, we may at times not see the forest for the trees. In this context, meta-analyses are helpful to combine and summarize the data of interest and potentially offer insights that are not immediately apparent from the individual studies.

The present paper aims to describe the main methods which have been used for the meta-analysis of neuroimaging data, as well as their advantages and drawbacks, with some examples of application to mood and anxiety disorders. The first section of the paper introduces how a standard meta-analysis is conducted, that is, when there is only one variable of interest, with an example from a meta-analysis of global brain volumes. This is important for a better appreciation of the pros and cons of the meta-analytic methods that we review later. The second section of the paper describes the meta-analyses of neuroimaging studies based on regions of interest (ROI) and their particular issues. The third section introduces the various available voxel-based meta-analytic methods, which aim to overcome some of the limitations of the ROI-based methods but have, in turn, their own limitations. The similarities and differences between the various voxel-based methods are also discussed in depth. Finally, we describe the available online databases of neuroimaging studies. This paper is meant to be accessible for the applied researcher in the fields of psychiatry, neurology and allied disciplines. Other excellent, more technical, reviews of meta-analytical methods can be found elsewhere \[1,2\].

## Standard meta-analyses

Prior to any meta-analytic calculation, researchers conduct an exhaustive and critical literature search, often including contact with the authors of the original studies in order to retrieve important pieces of missing information. Then, researchers conduct a mathematical summary of the findings of the included studies (that is, the meta-analysis proper). Finally, researchers apply a series of tests, plots and subgroup analyses to assess the heterogeneity and robustness of the results. The latter step, along with the exhaustive and critical inclusion of studies, is of utmost importance in order to obtain unbiased meta-analytic conclusions.

With the aim of introducing the reader to the logics of a standard meta-analysis, in this section we will use as an example a meta-analysis of global gray matter volumes in patients with obsessive-compulsive disorder (OCD) (see Table 1). The included studies correspond to seven publications reporting global gray matter volume, which were included in a published meta-analysis of voxel-based morphometry studies in OCD \[3\].

Global gray matter volumes reported in seven studies on obsessive-compulsive disorder

|  | Reference | Patients |  | Controls |  | Patients + controls |  | Difference |  | Effect size |  |
|----|----|----|----|----|----|----|----|----|----|----|----|
|  |  |  |  |  |  |  |  |  |  |  |  |
|  |  | Number | Volume ± SD | Number | Volume ± SD | N | Variance | Estimate | Variance | Estimate | Variance |
| Study 1 | \[46\] | 18 | 773 ± 56 | 18 | 822 ± 56 | 36 | 3,114 | -49 | 346 | -0.854 | 0.122 |
| Study 2 | \[47\] | 55 | 685 ± 74 | 50 | 708 ± 72 | 105 | 5,323 | -23 | 203 | -0.313 | 0.039 |
| Study 3 | \[48\] | 25 | 850 ± 83 | 25 | 834 ± 71 | 50 | 5,997 | +16 | 480 | 0.196 | 0.080 |
| Study 4 | \[49\] | 72 | 739 ± 82 | 72 | 763 ± 78 | 144 | 6,404 | -24 | 178 | -0.298 | 0.028 |
| Study 5 | \[50\] | 37 | 776 ± 69 | 26 | 747 ± 68 | 63 | 4,680 | +29 | 307 | 0.418 | 0.067 |
| Study 6 | \[51\] | 19 | 827 ± 44 | 15 | 836 ± 63 | 34 | 3,041 | -9 | 363 | -0.179 | 0.120 |
| Study 7 | \[52\] | 71 | 740 ± 66 | 71 | 738 ± 63 | 142 | 4,119 | +2 | 116 | 0.035 | 0.028 |

All volumes are in milliliters. SD: standard deviation.

### Weighting of the studies

In order to summarize these seven studies, a simple meta-analysis could consist of calculating the mean difference in global gray matter volume between patients and controls as reported in the original studies \[4\]. Thus, we could summarize Table 1 by saying that the mean global gray matter volume is 8.4 mL inferior in patients than in healthy controls-this number is just the arithmetic mean of the differences shown in the table.

The use of the arithmetic mean, however, may be too simplistic, because the different studies should have different weights. For example, the number of patients in study 4 is four times larger than the number of patients in study 1. Clearly, we cannot give the same weight to both studies and should give more weight to study 4. Probably, we should give it about four times more weight, as it includes four times as many patients.

Including all the studies in Table 1 and weighting the mean difference by the sample sizes of the studies, we would conclude now that the mean global gray matter volume is 8.8 mL inferior in patients than in controls. Note that when we previously calculated the mean difference as the simple arithmetic mean, we were indeed assuming that all the studies had the same sample size. This erroneous assumption had only a minor effect here (we thought that the difference was about 5% smaller than what we think now), but it could have important effects in other meta-analyses, especially if studies with smaller sample sizes inexplicably find more differences than studies with larger sample sizes-we will introduce how to detect this kind of bias later.

Unfortunately, weighting the calculations only by sample size would still be too simplistic, because the weight of a study should also include its precision. For example, study 1 included fewer patients than study 4, but its volume estimates seem much more precise, as its sample variance is approximately the half than that in study 4 (see Patients + controls column in Table 1). We do not know the reason for this higher precision (maybe the sample was more homogenous; maybe the technical procedures were cleaner; maybe it was just chance); however, we must take this precision into account by weighting by the inverse of the variance of the difference-which also includes the sample size.

Including all the studies in Table 1 and weighting by the inverse of the variance of the difference, we would conclude that the mean global gray matter volume is 8.9 mL inferior in patients than in controls (z-value = -1.55, *P* = 0.121). When previously we did not weight by sample variance we were assuming that all the studies had the same variance, though in this case this assumption was acceptable because the variance of the studies is rather homogeneous.

However, as explained in the next section, weighting the calculations only by the inverse of the variance of the difference may still be too simplistic.

### Heterogeneity in the studies

Healthy individuals have different global gray matter volumes, that is, some have larger brains, some have thicker cortices, and so on. When conducting an analysis with original data, we are usually able to explain or model a part of this variability, but there is also a part of this variability that remains unexplained. This residual error may be due to unobserved variables, etiological heterogeneity within particular diagnoses, poor model fitting, or maybe just pure chance. This individual-based within-study variability cause the sample means to be variable, so that different studies obtain different results.

However, within-study variability is not the only source of the between-study variability or heterogeneity. Given the relatively small amount of robust findings in neuroimaging, it would be highly desirable that all researchers conducted their studies using the exact same inclusion criteria and methods so that all between-study variability was only related to the within-study variability. However, the fact is that clinical and methodological differences between studies are often substantial.

On the one hand, patients included in the individual studies may have been sampled from clinically different populations; for example, one study of major depressive disorder may include outpatients with mild reactive depressive episodes while another study may be focused on inpatients suffering from severe endogenous depressions with melancholic symptoms. Similarly, patients in different studies may be receiving different treatments, or be in different phases of the disorder (for example, having a first episode or having a history of multiple episodes).

On the other hand, researchers may have been investigated similar but still different aspects of a disorder; for example, one study may have described the blood oxygen level-dependent (BOLD) brain response to a task involving a high memory load, while another study may be interest in the BOLD response to a task related to decision-making. Or even if studying the same particular cognitive function, each study may employ a particular statistical package, and its large set of associated assumptions.

Finally, there may be a relevant part of the between-study heterogeneity which can be neither related to the within-study variability, nor explained by clinical or methodological differences between studies. This is called residual heterogeneity.

It is highly recommended to study the between-study variability or heterogeneity in any meta-analysis. For example, if the main analysis detects differences between patients and controls, it may be of interest to explore whether these differences depend on the severity of the disorder, or if they are related to special subtypes of the disorder. These questions may be assessed with meta-regressions. But even if the meta-analysis does not aim to explore the modulating effects of clinical variables on the main outcomes, heterogeneity should still be taken into account.

Indeed, there is agreement on always including the residual heterogeneity in the weighting of the calculations \[5-8\]. Meta-analyses conducted this way are said to follow random-effects models, in opposition to the fixed-effects models that we saw in the previous point, which did not include heterogeneity. In the example of Table 1 the use of a random-effects model would lead us to conclude that the mean global gray matter volume is 9.0 mL inferior in patients than in controls (z-value = -0.98, *P* = 0.328; see Figure 1, left). Note the increase of *P*-value in the random-effects model (from 0.121 to 0.328), thus better controlling the false positive rate.

### Other complementary analyses

The above meta-analysis of global gray matter volumes in OCD was only aimed to help interpret the findings of a regional voxel-based meta-analysis, for which no other tests beyond a correctly weighted random-effects model would probably be required. However, if global gray matter volumes were the main outcome of a meta-analysis, some complementary plots and tests would be recommended to help the reader assess the reliability and robustness of the findings \[9\].

On the one hand, the meta-regressions described above may be useful for assessing if the findings are predominantly (or only) present in one group of patients, for example, in those with more severe forms of OCD. In this regard, specific meta-analyses of subgroups of patients may further confirm these hypotheses or, also important, may state that the abnormalities are present in all subgroups of patients, increasing the robustness of the findings. Similarly, sensitivity analyses consisting of repeating the meta-analysis many times, each time with a different combination of studies, may be useful to assess whether the findings are driven by one or few studies. Finally, funnel plots (see Figure 1, right) may be useful for appraising whether studies with small samples report more statistically significant findings than studies with larger samples. This is typical of subjects with publication bias, where studies with small samples are only published if their results match *a priori* hypotheses.

It is important to note that these kinds of tests and graphical aids are necessary but do not provide conclusive information, and should only be interpreted in the context of the field under investigation. A symmetrical funnel plot, for example, is not an amulet against publication bias, especially in some types of meta-analysis. ROI-based studies, for instance, may be more prone to be affected by publication biases, as the authors may decide which brain regions are reported and which are not. Conversely, an asymmetrical funnel plot would not necessarily invalidate a meta-analysis if publication bias appears unlikely. This may be the case of voxel-based studies, where the whole brain is included in the analysis.

### Use of effect sizes

Most meta-analyses do not use the raw volume differences as we exemplified in the previous points, but rather, they use standardized volume differences, that is, effect sizes \[10\]. Briefly, a raw difference is the difference in milliliters between patients' and controls' global gray matter volume, while a standardized difference is the difference is standard deviations-usually corrected for small sample size bias.

This subtle difference has a series of consequences. First, the unit of measure (milliliters, in this case) is lost, which makes the interpretation of the findings less straightforward but indeed more comparable with other measures, for example, an effect size of d = 0.5 is considered 'medium' independently of whether it refers to a difference in gray matter volume, in BOLD response or in a questionnaire score. Using the data from Table 1, the effect size of the difference in global gray matter volume between patients and controls is d = -0.122 (z-value = -0.93, *P* = 0.354; Figure 2), which is below the conventional range of 'small' effect (0.2 to 0.3) \[11\]. Second, a study reporting a larger difference may be found to have a smaller effect size, or vice versa, depending on the sample variance. For instance in Table 1, the raw difference is slightly larger in study 4 than in study 3, whilst the effect size is slightly larger in study 3 than in study 4. Third, and very important, effect size can be directly derived from many statistics like a *t*-value or a *P*-value, which are much more often reported than sample statistics; that is, we can often know the effect size but not the raw difference. This advantage usually allows a much more exhaustive inclusion of studies, thus clearly justifying the use of effect sizes in many meta-analyses.

## Meta-analyses based on regions of interest

A ROI is a part of the brain that the authors of the study wish to investigate, usually based on *a priori* hypotheses. ROI-based studies usually select a set of few ROIs and manually delimitate them on the raw images. Researchers then analyze the volume of these ROIs, their mean BOLD response to a stimulus, their positron emission tomography ligand volume of distribution, or any other measure of interest.

### Region of interest-based meta-analyses

A typical ROI-based meta-analysis can be viewed as a set of different meta-analyses, each of them applied to a different ROI. These meta-analyses can usually be optimally conducted with all appropriate weightings and complementary analyses, as seen for example in the meta-analysis of regional brain volumes in OCD conducted by Rotge *et al.* \[12\], in which the analyses are based on effect sizes and random-effects models and complemented with explicit assessments of the heterogeneity, several sensitivity analyses, funnel plots and meta-regressions. Unfortunately, each original study included in this meta-analysis only investigated a small set of brain regions, causing the meta-analyses to include only a very small number of studies for each brain region. Indeed, only three or four studies could be included for highly relevant regions such as the putamen or the anterior cingulate cortex, both of which were found as abnormal in subsequent voxel-based meta-analyses \[3,13\]. Other brain regions could not be meta-analyzed because they had been investigated by too few or no studies. Needless to say, this would not be the case for those ROI studies reporting whole brain results in online supplements or similar, but this is seldom the case.

Moreover, it must be noted that some brain regions are more frequently studied than others, which causes the statistical power to differ depending on the brain region under study. In the example, while data from five studies or more were available for the orbitofrontal cortex, the thalamus and the caudate nuclei, some brain regions could not be meta-analyzed at all.

Ultimately, the authors of the original studies have a set of *a priori* hypotheses which influence their decision to investigate differences in a given brain region at the expense of other regions. These decisions determine the number of studies investigating that brain region, and thus the statistical power to detect that brain region as significantly different between patients and controls in a ROI-based meta-analysis. Publication bias is also a problem as studies failing to report statistically significant differences on hypothesized ROIs may be less likely to ever be become publicly available. A recent analysis of more than 450 ROI-based neuroimaging studies in psychiatry illustrates this point well \[14\]. The author demonstrated that the number of studies reporting significant results was nearly the double than expected, suggesting strong publication biases in the ROI literature.

Another consideration is the heterogeneous definition or the boundaries of the ROIs, which may differ from one study to the other \[12\]. However, this variability might have a relatively small impact on effect sizes, as boundary definitions are the same for the patients and controls included in a study. Furthermore, the spatial error may probably be counteracted by the higher anatomical accuracy achieved by the manual delimitation of the ROIs in the original studies \[15,16\].

### Label-based reviews

Some authors have used a simplified type of ROI-based meta-analysis, consisting of just counting how many times a particular ROI is detected as significantly abnormal in patients versus healthy controls. This procedure has been called label-based review \[17\]. For example, in their functional neuroimaging meta-analysis of the brain's response to emotional tasks, Phan *et al.* \[18\] represented each activation peak as a dot in an atlas of the brain. They then divided the brain into 20 ROIs and counted how many studies had one or more activation peak in each ROI.

A fictitious example of such approach is shown in Figure 3A. Here, the studies would have reported that the patients with mood or anxiety disorders have increases of gray matter volume in the basal ganglia, extending to the anterior part of the right insula, as well as decreases of gray matter volume in the anterior cingulate and insular cortices. The authors of a label-based review would have first plotted the peaks of the clusters of significant increase (red) or decrease (blue) of gray matter volume in a brain template. Then, they would divide the brain into several regions, for example, anterior cingulate gyrus, left and right inferior frontal gyri, insulas, superior temporal gyri, caudate nuclei, putamen nuclei, and so on. Finally, they would have counted how many peaks lay within each of these regions.

This method may be useful when other approaches are not feasible, for example when not enough information is available for conducting a ROI-based or a voxel-based meta-analysis. Its simplicity, however, may conceal a series of important drawbacks which must be taken into account. First, no weighting of the studies is performed, which means that all studies are assumed to have the same sample size and precision. This is a strong and unrealistic assumption which may be violated in most meta-analysis. Fortunately, sample size information is always available, and so label-based meta-analyses should at least be weighted by sample size. Second, the findings of the studies are binarized (significant versus not-significant), leading to a loss of information on the magnitude of the raw differences or on the effect sizes. Third, it is not clear whether studies reporting opposite findings in a particular ROI (for example, volume decrease in some studies and volume increase in others) are adequately dealt with. Finally, they may be also affected by the particular issues of ROI-based meta-analyses described above.

## Voxel-based meta-analyses

Scanner three-dimensional images are composed of thousands of tiny cubes (or rectangular cuboids) called voxels, in the same way that digital photographs are composed of thousands of tiny squares called pixels. Voxel-based methods consist of conducting the meta-analytic calculations separately in each voxel of the brain, thus freeing the meta-analysis from aprioristic anatomical definitions. There are different types of voxel-based meta-analyses, including image-based, coordinate-based and mixed image- and coordinate-based meta-analyses.

### Image-based meta-analyses

An image-based meta-analysis should be understood as a voxel-based version of the standard meta-analysis, that is, it consists of thousands of standard meta-analyses, each of them applied to a different voxel \[2,19\]. The data of each study is retrieved from its statistical parametric maps (the three-dimensional images resulting from the comparison between patients and controls), and thus include the whole brain. This technique shares some limitations with any voxel-based analysis, mainly relating to the massive number of statistical tests (that is, one test for each voxel). The correction of multiple comparisons is an unsolved issue, with current methods being either too liberal or too conservative \[19\]. For this reason, thresholds based on uncorrected *P*-values and cluster-size are usually preferred \[1,19,20\]. Also, such massive-scale testing prevents a careful visual inspection of the analyses (for example, to describe relevant non-significant trends).

However, the biggest drawback of image-based meta-analyses is that the statistical parametric maps of the original studies are seldom available, therefore seriously limiting the inclusion of studies.

### Coordinate-based meta-analyses

Given the poor availability of statistical parametric maps, early meta-analyses of voxel-based studies consisted of label-based (rather than image-based) reviews, as discussed earlier. These methods quickly evolved to coordinate-based meta-analyses, which in their simplest form consisted of counting, for each voxel, how many activation peaks had been reported within its surroundings \[21\]. In the fictitious example, the dots of the label-based review (Figure 3A) would be replaced with spheres (Figure 3B, C), and the brain would not be divided into conventional regions but rather the number of spheres surrounding each voxel would be counted, thus obtaining a count for each voxel. It must be noted that calculations in activation likelihood estimation (ALE) \[22\] are not exactly based on counting the number of spheres but on computing the probability of a union, though in practice, the latter behaves like the former.

The use of voxels rather than conventional divisions of the brain improved the anatomical localization of the findings. However, the first available methods, namely ALE and kernel density analysis (KDA) \[21\], had some additional issues which enlarged the list of drawbacks of label-based reviews. Specifically, they only counted the total number of peaks, independently of whether they came from the same or different studies, and thus the analysis could not be weighted by sample size and a single study reporting many peaks in close proximity could drive the findings of the whole analysis.

These drawbacks led to the creation of a second generation of coordinate-based meta-analytic methods, mainly evolved versions of KDA, such as multilevel KDA \[23\] and parametric voxel-based meta-analysis \[24\]; evolved versions of ALE \[25,26\]; and signed differential mapping (SDM) \[3,27-30\] (Figure 3D, E), which overcame these limitations by separating the peaks of each study. Moreover, some of these new methods weighted the studies by their sample size and included a series of complementary analyses to assess the reliability and robustness of the findings. One of the methods, SDM, also addressed between-study heterogeneity by reconstructing positive and negative maps in the same image, thus counteracting the effects of studies reporting findings in opposite directions \[31\] and incorporating meta-regression methods. Finally, SDM included templates for white matter \[32\], allowing multimodal meta-analyses which were not possible with previous methods \[33\]. However, these methods still did not employ the standard statistical methods of the ROI-based meta-analyses, for example, they did not weight by the precision of each study.

Several of these methods have recently been applied to mood and anxiety disorders. One such was a meta-analysis of studies investigating bipolar disorder \[34\] using SDM, which found patients to have gray matter reductions in the left medial frontal and/or anterior cingulate cortex (MF/ACC) and bilateral anterior insula, with complementary analyses showing findings in the left ACC and right insula to be robust, and left MF/ACC volume to be higher in samples where patients were being treated with lithium. An SDM meta-analysis of studies investigating major depressive disorder also found patients to have gray matter reductions in the MF/ACC \[35\], and complementary analyses showed this finding to be robust and more severe in multiple-episode samples. Recent SDM meta-analyses of studies investigating anxiety disorders have also found patients to have gray matter reduction in the MF/ACC \[13\], along with abnormalities in the basal ganglia. Specifically, patients with OCD were found to have increased gray matter volume in the bilateral putamen and caudate nuclei \[3\], with complementary analyses showing findings in the MF/ACC and left basal ganglia to be robust, and bilateral increases of basal ganglia volume to be higher in samples including patients with higher symptom severity. Conversely, patients with anxiety disorders other than OCD were found to have decreased gray matter volume in the left putamen nucleus \[13\].

An example of the use of these methods in functional neuroimaging is the recent study by Delvecchio *et al.* \[36\], which meta-analyzed the functional brain response to emotional faces using ALE. They found that both patients with bipolar disorder and patients with unipolar depression displayed limbic hyperactivations. However, only patients with bipolar disorder showed a set of hypoactivations in the prefrontal cortex and hyperactivations in the thalamus and basal ganglia. Conversely, only patients with major depressive disorder showed hypoactivations in the sensorimotor cortices. Another example from the anxiety disorders literature is a multilevel KDA meta-analysis, which found that patients showed hyperactivations in the amygdala and insula \[37\]. Interestingly, these hyperactivations were more observed in phobias, whilst patients with post-traumatic stress disorder displayed a hypoactivation of the MF/ACC. Finally, an ALE meta-analysis of functional differences in patients with OCD detected that symptom provocation was possibly associated with activation of the orbitofrontal cortex, prefrontal cortex, anterior cingulate cortex, precuneus, premotor cortex, superior temporal gyrus, basal ganglia, hippocampus and uncus \[38\].

These methods may also be applied to functional connectivity studies \[39,40\]. Laird *et al*., for instance, studied the default mode network by first creating ALE maps, and then deriving meta-analytic co-activation maps \[40\]. With this approach, they could identify an affective sub-network component. This approach is promising, given the increasing interest in functional connectivity studies in various mood and anxiety disorders.

### Mixed image- and coordinate-based meta-analyses

Recently, effect size SDM (ES-SDM) was designed to allow the combination of studies from which images (statistical parametric maps) are available with studies from which only peak coordinates are reported, thus allowing a more exhaustive inclusion of studies, as well as more accurate estimations \[19\].

This is achieved by first using peak coordinates and their statistical values to recreate the statistical parametric maps, and then conducting an image-based meta-analysis. Thus, this method has some statistical advantages as compared to previous coordinate-based methods, namely the use of standard statistical methods (for example, weighting the calculations by both sample size and study precision, use of effect sizes, inclusion and assessment of residual heterogeneity, and so on).

In a meta-analysis of the BOLD response to emotional facial stimuli \[19\], the sensitivity to detect real activations (that is, the number of actually activated voxels appearing as significant in the meta-analysis, divided by the total number of actually activated voxels) was similar between ES-SDM (55%) and SDM (51%) when only using peak coordinates. However, the inclusion of the statistical parametric maps led to a gradual and substantial increase of the sensitivity of ES-SDM (73% when the statistical parametric map of one study was included, 87% when the statistical parametric maps of two studies were included, 93% when the statistical parametric maps of three studies were included, and so on). Therefore, given the potential of this new method, we would encourage authors to make their statistical parametric maps widely available to the community on their laboratory websites or via other means.

## Online databases

In parallel with the development of new meta-analytical methods, several freely-available website-based databases of neuroimaging data have been made available. These online databases may be classified in three groups, namely: sets of original data (for example, the raw scanner images from several samples of individuals); summary statistics from the studies included in one meta-analysis (for example, the mean ± standard deviation ROI volumes); and sets of summary statistics of virtually all published studies.

The online sets of original data are composed of the raw and/or pre-processed brain images, along with the demographic and clinical characteristics of each of the many anonymous participants. These databases may be used by researchers to conduct their studies, thus being a useful resource for highly accurate data analyses. It must be noted, however, that analyses derived from these datasets should not be strictly considered meta-analyses, as they do not necessarily exhaustively include all available data. Examples of these datasets are BRAINNet (<http://www.brainnet.net>), the fMRI Data Center (<http://www.fmridc.org>) and OpenfMRI (<http://www.openfmri.org>).

Online databases containing the summary statistics from the studies included in particular meta-analyses represent a more interactive (and often complete) alternative to the traditional 'supplementary materials' that accompany published meta-analyses. Importantly, these online data may be used by other researchers to conduct updated or secondary analyses. Examples of this type of databases are the Bipolar Disorder Neuroimaging Database (<http://www.bipolardatabase.org>) and the Major Depressive Disorder Neuroimaging Database (<http://www.depressiondatabase.org>) by Kempton and colleagues \[41,42\], as well as the series of peak-coordinate databases from SDM meta-analyses (<http://www.sdmproject.com/database>).

Finally, many sets of summary statistics of virtually all published neuroimaging studies exist, allowing a rapid retrieval of specific data in order to facilitate the meta-analytic process. The developers of BrainMap (<http://www.brainmap.org>), for instance, have been building and updating an impressive database of neuroimaging findings since 1987 \[43\]. Other available databases are the AMAT toolbox (<http://www.antoniahamilton.com/amat.html>), the Brede Database (<http://neuro.imm.dtu.dk/services/brededatabase>) \[44\], the Internet Brain Volume Database (<http://www.cma.mgh.harvard.edu/ibvd>) and the Surface Management System Database (<http://sumsdb.wustl.edu/sums/index.jsp>).

Another recent and promising online development called NeuroSynth (<http://www.neurosynth.org>) \[45\] deserves mentioning. NeuroSynth contains a set of summary statistics together with online functions aimed to conduct real-time meta-analyses online. Unfortunately, extraction of coordinates from publications is not manually verified, which may bias the results towards those regions that the authors of the original articles wanted to emphasize in the tables of the manuscripts. However, when the researcher's goal is to obtain a very fast and preliminary meta-analysis of the literature, NeuroSynth may be one of the first options.

# Conclusions

In this paper we have reviewed the main types of meta-analytic methods available for neuroimaging studies, using examples from the mood and anxiety disorder literature to illustrate these methods.

ROI- and voxel-based methods each have advantages and disadvantages, which are summarized in Table 2. Specifically, ROI-based meta-analyses use optimal statistical methods, but they usually have a limited and likely biased inclusion of studies \[14\]. Conversely, voxel-based meta-analyses usually have a more exhaustive and unbiased inclusion of studies, but their statistical methods are less accurate. There are also relevant differences between the different available voxel-based meta-analytic methods. Fortunately, the field is rapidly evolving to develop more accurate and robust methods.

Comparison of the main meta-analytic methods for neuroimaging studies comparing patients and controls

|  |  |  |  |  |  |
|----|----|----|----|----|----|
|  | **ROI-based meta-analyses** | **Voxel-based meta-analyses** |  |  |  |
|  |  |  |  |  |  |
|  |  | **KDA/old ALE** | **Multilevel KDA/new ALE** | **SDM** | **ES-SDM** |
|  |  |  |  |  |  |
| **Selection of studies** |  |  |  |  |  |
|  Exhaustive inclusion of studies | Limited, as information for a given brain region is present in few or no studies | Probable, as far as the included studies investigate the whole brain and not only some ROIs (in which case should be discarded) |  |  | More probable, because statistical parametric maps can also be included |
|  Unbiased inclusion of studies | Limited, as information is only available for regions hypothesized *a priori*, ignoring the rest of the brain | Probable, as far as the included studies do not use different statistical thresholds for different parts of the brain (this is a strict inclusion criterion in SDM and ES-SDM) |  |  |  |
| **Statistical analyses** |  |  |  |  |  |
|  Weighting of the studies | Complete (sample size and study precision) | None | Partial (only sample size) |  | Complete (sample size and study precision) |
|  Control of the heterogeneity | Residual heterogeneity is correctly included in the analyses | Residual heterogeneity is not controlled, and increases and decreases are not counteracted, potentially leading to voxels being detected as increased and decreased at the same time |  | Residual heterogeneity is not included in the weightings, but increases and decreases are counteracted | Residual heterogeneity is correctly included in the weightings |
|  Study of the heterogeneity | Possible, by means of meta-regressions and subgroup analyses | Limited to subgroup analyses |  | Possible, by means of meta-regressions and subgroup analyses |  |
|  Correction for multiple comparisons | Possible | Not possible, questionable or limited to conventional voxel-thresholded cluster-based methods |  |  |  |
|  Description of the effect sizes | Possible | Not possible | Possible though limited to pseudo-effect sizes based on the proportion of studies reporting significant findings |  | Possible |
|  Description of relevant non-significant trends | Possible, as the number of ROIs is manageable | Not possible, or limited to the visual inspection of liberally thresholded maps, as the number of voxels is too massive for a more accurate individual inspection |  |  |  |

Please see text for further details. ALE: activation likelihood estimation; ES: effect size; KDA: kernel density analysis; ROI: region of interest; SDM: signed differential mapping.

Although voxel-based meta-analyses minimize the effects of selectively reporting certain ROI, they are not totally immune to publication biases, as negative results may still be less likely to be published (what is known as the file drawer problem). Authors of the original papers are strongly encouraged to publish their results even if they perceive them as being disappointing or they do not find differences between patients and controls.

Finally, we suggest that in any meta-analysis of neuroimaging data, independently of the chosen method, authors should aim to: only include studies which explored the whole brain; ensure that the same threshold throughout the whole brain was used within each included study; and explore the robustness of the findings with several complementary analyses, for example, sensitivity analyses, quantification of the ROI- or voxel-based between-study heterogeneity \[19\], funnel plots of the values extracted from the meta-analytic clusters or their peaks, and so on, just like in any standard meta-analysis.

# Competing interests

The authors declare that they have no competing interests.

# Authors' contributions

All authors drafted, read and approved the final manuscript.