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Why Most Published Research Findings Are False

• John P. A. Ioannidis

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• Published: August 30, 2005
• https://doi.org/ten.1371/journal.pmed.0020124

Figures

Abstract

Summary

In that location is increasing concern that virtually current published research findings are false. The probability that a research merits is truthful may depend on study power and bias, the number of other studies on the aforementioned question, and, importantly, the ratio of true to no relationships among the relationships probed in each scientific field. In this framework, a inquiry finding is less likely to exist truthful when the studies conducted in a field are smaller; when result sizes are smaller; when there is a greater number and lesser preselection of tested relationships; where there is greater flexibility in designs, definitions, outcomes, and analytical modes; when there is greater fiscal and other interest and prejudice; and when more teams are involved in a scientific field in chase of statistical significance. Simulations show that for most study designs and settings, it is more likely for a enquiry merits to be false than true. Moreover, for many current scientific fields, claimed research findings may often be simply accurate measures of the prevailing bias. In this essay, I discuss the implications of these issues for the bear and interpretation of research.

Citation: Ioannidis JPA (2005) Why Most Published Research Findings Are Fake. PLoS Med two(8): e124. https://doi.org/10.1371/journal.pmed.0020124

Published: Baronial 30, 2005

Copyright: © 2005 John P. A. Ioannidis. This is an open up-access commodity distributed under the terms of the Creative Eatables Attribution License, which permits unrestricted employ, distribution, and reproduction in any medium, provided the original work is properly cited.

Competing interests: The author has declared that no competing interests exist.

Abbreviation: PPV, positive predictive value

Published inquiry findings are sometimes refuted by subsequent evidence, with ensuing confusion and thwarting. Refutation and controversy is seen across the range of inquiry designs, from clinical trials and traditional epidemiological studies [1–3] to the virtually modern molecular research [4,5]. In that location is increasing concern that in modern research, false findings may exist the majority or even the vast bulk of published research claims [half-dozen–8]. However, this should not be surprising. It can be proven that nearly claimed inquiry findings are false. Here I volition examine the cardinal factors that influence this trouble and some corollaries thereof.

Modeling the Framework for False Positive Findings

Several methodologists have pointed out [9–11] that the high rate of nonreplication (lack of confirmation) of enquiry discoveries is a consequence of the convenient, however ill-founded strategy of claiming conclusive research findings solely on the basis of a single report assessed by formal statistical significance, typically for a p-value less than 0.05. Research is non most appropriately represented and summarized past p-values, but, unfortunately, there is a widespread notion that medical research articles should be interpreted based only on p-values. Enquiry findings are defined here as any relationship reaching formal statistical significance, due east.g., effective interventions, informative predictors, risk factors, or associations. "Negative" research is also very useful. "Negative" is actually a misnomer, and the misinterpretation is widespread. Yet, hither we volition target relationships that investigators claim exist, rather than goose egg findings.

It can be proven that virtually claimed research findings are imitation

As has been shown previously, the probability that a research finding is indeed truthful depends on the prior probability of it being true (earlier doing the written report), the statistical ability of the study, and the level of statistical significance [ten,11]. Consider a ii × 2 table in which inquiry findings are compared against the gold standard of true relationships in a scientific field. In a research field both true and faux hypotheses can be made about the presence of relationships. Allow R exist the ratio of the number of "truthful relationships" to "no relationships" amidst those tested in the field. R is characteristic of the field and tin vary a lot depending on whether the field targets highly probable relationships or searches for just one or a few truthful relationships amidst thousands and millions of hypotheses that may be postulated. Let us besides consider, for computational simplicity, confining fields where either there is only one true human relationship (among many that tin can be hypothesized) or the ability is similar to detect any of the several existing true relationships. The pre-study probability of a human relationship being true is R/(R + 1). The probability of a written report finding a true relationship reflects the power 1 - β (one minus the Blazon Two error charge per unit). The probability of challenge a relationship when none truly exists reflects the Blazon I fault rate, α. Assuming that c relationships are existence probed in the field, the expected values of the 2 × 2 table are given in Table i. Later on a research finding has been claimed based on achieving formal statistical significance, the post-study probability that it is true is the positive predictive value, PPV. The PPV is also the complementary probability of what Wacholder et al. have chosen the faux positive report probability [ten]. Co-ordinate to the 2 × 2 tabular array, one gets PPV = (1 - β)R/(R - βR + α). A research finding is thus more likely truthful than imitation if (1 - β)R > α. Since usually the vast majority of investigators depend on a = 0.05, this ways that a research finding is more than likely truthful than faux if (one - β)R > 0.05.

What is less well appreciated is that bias and the extent of repeated contained testing by different teams of investigators effectually the world may further distort this picture and may lead to even smaller probabilities of the research findings existence indeed true. Nosotros volition try to model these two factors in the context of like 2 × 2 tables.

Bias

Get-go, let us define bias as the combination of diverse design, data, analysis, and presentation factors that tend to produce research findings when they should not be produced. Let u exist the proportion of probed analyses that would not have been "research findings," but notwithstanding end up presented and reported every bit such, considering of bias. Bias should not exist confused with chance variability that causes some findings to exist simulated by chance even though the study design, information, analysis, and presentation are perfect. Bias can entail manipulation in the analysis or reporting of findings. Selective or distorted reporting is a typical form of such bias. We may assume that u does not depend on whether a truthful human relationship exists or non. This is non an unreasonable supposition, since typically it is impossible to know which relationships are indeed true. In the presence of bias (Tabular array two), one gets PPV = ([1 - β]R + uβR)/(R + α − βR + u − uα + uβR), and PPV decreases with increasing u, unless i − β ≤ α, i.e., 1 − β ≤ 0.05 for nigh situations. Thus, with increasing bias, the chances that a inquiry finding is true diminish considerably. This is shown for unlike levels of power and for different pre-study odds in Figure 1. Conversely, truthful research findings may occasionally be annulled because of reverse bias. For example, with big measurement errors relationships are lost in noise [12], or investigators use data inefficiently or fail to notice statistically significant relationships, or there may be conflicts of interest that tend to "bury" meaning findings [thirteen]. In that location is no skillful large-scale empirical show on how frequently such reverse bias may occur beyond diverse research fields. However, it is probably fair to say that opposite bias is not as common. Moreover measurement errors and inefficient use of data are probably becoming less frequent problems, since measurement fault has decreased with technological advances in the molecular era and investigators are becoming increasingly sophisticated about their data. Regardless, reverse bias may exist modeled in the aforementioned manner equally bias above. Likewise reverse bias should not exist confused with hazard variability that may pb to missing a true relationship because of run a risk.

Testing by Several Independent Teams

Several independent teams may be addressing the same sets of research questions. Every bit research efforts are globalized, it is practically the rule that several research teams, often dozens of them, may probe the same or similar questions. Unfortunately, in some areas, the prevailing mentality until now has been to focus on isolated discoveries by unmarried teams and interpret research experiments in isolation. An increasing number of questions have at least ane written report claiming a research finding, and this receives unilateral attending. The probability that at least one study, among several done on the same question, claims a statistically significant research finding is easy to estimate. For n independent studies of equal power, the two × 2 table is shown in Table three: PPV = R(1 − β ⁿ )/(R + 1 − [1 − α] ^north − Rβ ^{due north} ) (non considering bias). With increasing number of contained studies, PPV tends to decrease, unless 1 - β < a, i.e., typically 1 − β < 0.05. This is shown for dissimilar levels of power and for different pre-written report odds in Figure 2. For n studies of different ability, the term β ⁿ is replaced by the production of the terms β _i for i = 1 to north, but inferences are similar.

Corollaries

A practical example is shown in Box 1. Based on the above considerations, i may deduce several interesting corollaries nigh the probability that a inquiry finding is indeed true.

Box 1. An Example: Science at Low Pre-Written report Odds

Let us assume that a team of investigators performs a whole genome association study to examination whether whatever of 100,000 cistron polymorphisms are associated with susceptibility to schizophrenia. Based on what we know about the extent of heritability of the illness, it is reasonable to expect that probably around x factor polymorphisms among those tested would be truly associated with schizophrenia, with relatively similar odds ratios around 1.3 for the x or then polymorphisms and with a fairly similar power to place any of them. Then R = x/100,000 = x⁻⁴, and the pre-report probability for any polymorphism to exist associated with schizophrenia is also R/(R + one) = 10^−iv. Allow united states also suppose that the written report has 60% power to find an clan with an odds ratio of 1.3 at α = 0.05. So it can be estimated that if a statistically significant clan is constitute with the p-value barely crossing the 0.05 threshold, the post-study probability that this is truthful increases about 12-fold compared with the pre-written report probability, but information technology is however just 12 × ten^−four.

Now let u.s.a. suppose that the investigators dispense their pattern, analyses, and reporting then every bit to make more relationships cantankerous the p = 0.05 threshold even though this would not take been crossed with a perfectly adhered to blueprint and analysis and with perfect comprehensive reporting of the results, strictly according to the original study plan. Such manipulation could be done, for example, with serendipitous inclusion or exclusion of certain patients or controls, postal service hoc subgroup analyses, investigation of genetic contrasts that were non originally specified, changes in the disease or command definitions, and various combinations of selective or distorted reporting of the results. Commercially available "data mining" packages actually are proud of their ability to yield statistically meaning results through data dredging. In the presence of bias with u = 0.ten, the post-study probability that a inquiry finding is true is simply 4.4 × 10⁻⁴. Furthermore, even in the absence of whatever bias, when 10 contained research teams perform similar experiments effectually the world, if one of them finds a formally statistically significant association, the probability that the research finding is true is only i.v × ten⁻⁴, hardly whatever college than the probability nosotros had before any of this extensive research was undertaken!

Corollary 1: The smaller the studies conducted in a scientific field, the less probable the research findings are to exist true. Small sample size means smaller power and, for all functions higher up, the PPV for a true research finding decreases every bit power decreases towards 1 − β = 0.05. Thus, other factors being equal, research findings are more than likely true in scientific fields that undertake big studies, such equally randomized controlled trials in cardiology (several thousand subjects randomized) [xiv] than in scientific fields with pocket-size studies, such as nigh research of molecular predictors (sample sizes 100-fold smaller) [15].

Corollary 2: The smaller the outcome sizes in a scientific field, the less likely the research findings are to be true. Power is also related to the consequence size. Thus research findings are more likely truthful in scientific fields with large furnishings, such as the impact of smoking on cancer or cardiovascular disease (relative risks 3–20), than in scientific fields where postulated effects are pocket-sized, such as genetic risk factors for multigenetic diseases (relative risks i.1–ane.v) [vii]. Modern epidemiology is increasingly obliged to target smaller result sizes [16]. Consequently, the proportion of true research findings is expected to subtract. In the same line of thinking, if the truthful effect sizes are very small in a scientific field, this field is likely to be plagued by well-nigh ubiquitous false positive claims. For example, if the majority of true genetic or nutritional determinants of circuitous diseases confer relative risks less than 1.05, genetic or nutritional epidemiology would be largely utopian endeavors.

Corollary 3: The greater the number and the lesser the selection of tested relationships in a scientific field, the less likely the research findings are to be true. As shown to a higher place, the post-study probability that a finding is true (PPV) depends a lot on the pre-study odds (R). Thus, research findings are more likely true in confirmatory designs, such as large phase III randomized controlled trials, or meta-analyses thereof, than in hypothesis-generating experiments. Fields considered highly informative and creative given the wealth of the assembled and tested data, such as microarrays and other high-throughput discovery-oriented research [4,8,17], should accept extremely low PPV.

Corollary iv: The greater the flexibility in designs, definitions, outcomes, and analytical modes in a scientific field, the less likely the research findings are to be true. Flexibility increases the potential for transforming what would be "negative" results into "positive" results, i.e., bias, u. For several inquiry designs, e.g., randomized controlled trials [eighteen–20] or meta-analyses [21,22], there have been efforts to standardize their carry and reporting. Adherence to common standards is likely to increase the proportion of truthful findings. The aforementioned applies to outcomes. True findings may be more than mutual when outcomes are unequivocal and universally agreed (due east.1000., expiry) rather than when multifarious outcomes are devised (e.1000., scales for schizophrenia outcomes) [23]. Similarly, fields that employ unremarkably agreed, stereotyped analytical methods (e.g., Kaplan-Meier plots and the log-rank test) [24] may yield a larger proportion of true findings than fields where analytical methods are still under experimentation (east.grand., bogus intelligence methods) and only "best" results are reported. Regardless, fifty-fifty in the most stringent research designs, bias seems to be a major problem. For case, there is potent evidence that selective effect reporting, with manipulation of the outcomes and analyses reported, is a common problem fifty-fifty for randomized trails [25]. Just abolishing selective publication would not brand this problem go abroad.

Corollary five: The greater the financial and other interests and prejudices in a scientific field, the less likely the research findings are to be true. Conflicts of interest and prejudice may increase bias, u. Conflicts of interest are very mutual in biomedical inquiry [26], and typically they are inadequately and sparsely reported [26,27]. Prejudice may not necessarily accept financial roots. Scientists in a given field may be prejudiced purely because of their belief in a scientific theory or commitment to their ain findings. Many otherwise seemingly contained, university-based studies may be conducted for no other reason than to give physicians and researchers qualifications for promotion or tenure. Such nonfinancial conflicts may also lead to distorted reported results and interpretations. Prestigious investigators may suppress via the peer review procedure the advent and dissemination of findings that refute their findings, thus condemning their field to perpetuate imitation dogma. Empirical bear witness on expert opinion shows that it is extremely unreliable [28].

Corollary half dozen: The hotter a scientific field (with more scientific teams involved), the less likely the research findings are to be true. This seemingly paradoxical corollary follows because, every bit stated to a higher place, the PPV of isolated findings decreases when many teams of investigators are involved in the same field. This may explain why we occasionally see major excitement followed quickly by severe disappointments in fields that draw wide attending. With many teams working on the same field and with massive experimental data being produced, timing is of the essence in beating competition. Thus, each squad may prioritize on pursuing and disseminating its most impressive "positive" results. "Negative" results may get attractive for dissemination only if some other team has found a "positive" clan on the same question. In that instance, it may be attractive to refute a merits made in some prestigious journal. The term Proteus phenomenon has been coined to describe this phenomenon of chop-chop alternating extreme research claims and extremely opposite refutations [29]. Empirical evidence suggests that this sequence of extreme opposites is very mutual in molecular genetics [29].

These corollaries consider each factor separately, merely these factors often influence each other. For case, investigators working in fields where true upshot sizes are perceived to be pocket-sized may be more likely to perform big studies than investigators working in fields where truthful effect sizes are perceived to be large. Or prejudice may prevail in a hot scientific field, further undermining the predictive value of its research findings. Highly prejudiced stakeholders may even create a barrier that aborts efforts at obtaining and disseminating opposing results. Conversely, the fact that a field is hot or has strong invested interests may sometimes promote larger studies and improved standards of enquiry, enhancing the predictive value of its research findings. Or massive discovery-oriented testing may issue in such a large yield of significant relationships that investigators have enough to report and search further and thus refrain from information dredging and manipulation.

Most Inquiry Findings Are False for Most Research Designs and for About Fields

In the described framework, a PPV exceeding 50% is quite hard to go. Table 4 provides the results of simulations using the formulas developed for the influence of power, ratio of true to non-truthful relationships, and bias, for various types of situations that may exist characteristic of specific study designs and settings. A finding from a well-conducted, adequately powered randomized controlled trial starting with a 50% pre-study adventure that the intervention is effective is eventually true about 85% of the time. A fairly like performance is expected of a confirmatory meta-analysis of good-quality randomized trials: potential bias probably increases, but power and pre-test chances are higher compared to a single randomized trial. Conversely, a meta-analytic finding from inconclusive studies where pooling is used to "correct" the depression power of unmarried studies, is probably false if R ≤ 1:3. Research findings from underpowered, early-phase clinical trials would be truthful virtually one in four times, or fifty-fifty less often if bias is present. Epidemiological studies of an exploratory nature perform fifty-fifty worse, especially when underpowered, but even well-powered epidemiological studies may accept just a 1 in five take chances beingness true, if R = 1:ten. Finally, in discovery-oriented research with massive testing, where tested relationships exceed true ones i,000-fold (e.g., xxx,000 genes tested, of which 30 may exist the truthful culprits) [thirty,31], PPV for each claimed human relationship is extremely low, even with considerable standardization of laboratory and statistical methods, outcomes, and reporting thereof to minimize bias.

Claimed Research Findings May Often Be But Accurate Measures of the Prevailing Bias

As shown, the majority of modern biomedical inquiry is operating in areas with very low pre- and post-report probability for true findings. Let us suppose that in a research field there are no truthful findings at all to exist discovered. History of science teaches the states that scientific endeavor has ofttimes in the past wasted effort in fields with absolutely no yield of true scientific data, at least based on our current understanding. In such a "null field," one would ideally expect all observed effect sizes to vary by chance around the cipher in the absenteeism of bias. The extent that observed findings deviate from what is expected by risk solitary would be simply a pure measure of the prevailing bias.

For case, allow us suppose that no nutrients or dietary patterns are actually important determinants for the gamble of developing a specific tumor. Let us also suppose that the scientific literature has examined 60 nutrients and claims all of them to be related to the risk of developing this tumor with relative risks in the range of 1.two to 1.4 for the comparison of the upper to lower intake tertiles. So the claimed effect sizes are simply measuring nada else but the net bias that has been involved in the generation of this scientific literature. Claimed consequence sizes are in fact the well-nigh accurate estimates of the net bias. It even follows that betwixt "null fields," the fields that claim stronger effects (often with accompanying claims of medical or public wellness importance) are simply those that have sustained the worst biases.

For fields with very low PPV, the few true relationships would not distort this overall picture much. Even if a few relationships are true, the shape of the distribution of the observed furnishings would still yield a articulate measure of the biases involved in the field. This concept totally reverses the way we view scientific results. Traditionally, investigators have viewed large and highly significant effects with excitement, as signs of important discoveries. As well large and as well highly significant effects may actually be more probable to exist signs of large bias in most fields of modern research. They should lead investigators to careful critical thinking about what might accept gone wrong with their information, analyses, and results.

Of course, investigators working in whatsoever field are likely to resist accepting that the whole field in which they accept spent their careers is a "null field." Notwithstanding, other lines of evidence, or advances in technology and experimentation, may lead eventually to the dismantling of a scientific field. Obtaining measures of the net bias in ane field may also exist useful for obtaining insight into what might be the range of bias operating in other fields where like belittling methods, technologies, and conflicts may exist operating.

How Can We Improve the Situation?

Is information technology unavoidable that most inquiry findings are simulated, or can we improve the situation? A major problem is that it is incommunicable to know with 100% certainty what the truth is in whatsoever research question. In this regard, the pure "gold" standard is unattainable. However, there are several approaches to improve the post-study probability.

Better powered evidence, e.g., big studies or low-bias meta-analyses, may help, every bit it comes closer to the unknown "gold" standard. Even so, big studies may notwithstanding take biases and these should be acknowledged and avoided. Moreover, large-scale evidence is impossible to obtain for all of the millions and trillions of inquiry questions posed in current enquiry. Large-scale evidence should be targeted for inquiry questions where the pre-study probability is already considerably loftier, so that a pregnant enquiry finding will lead to a post-test probability that would be considered quite definitive. Large-calibration evidence is also particularly indicated when information technology can test major concepts rather than narrow, specific questions. A negative finding tin can so refute non only a specific proposed claim, but a whole field or considerable portion thereof. Selecting the performance of large-scale studies based on bigoted criteria, such every bit the marketing promotion of a specific drug, is largely wasted research. Moreover, i should be cautious that extremely large studies may be more likely to find a formally statistical significant difference for a footling effect that is non really meaningfully dissimilar from the goose egg [32–34].

Second, most inquiry questions are addressed by many teams, and it is misleading to emphasize the statistically significant findings of whatsoever single team. What matters is the totality of the evidence. Diminishing bias through enhanced research standards and curtailing of prejudices may also assist. However, this may crave a change in scientific mentality that might be difficult to accomplish. In some research designs, efforts may also be more successful with upfront registration of studies, e.k., randomized trials [35]. Registration would pose a challenge for hypothesis-generating research. Some kind of registration or networking of data collections or investigators within fields may exist more feasible than registration of each and every hypothesis-generating experiment. Regardless, fifty-fifty if nosotros exercise not see a great deal of progress with registration of studies in other fields, the principles of developing and adhering to a protocol could be more widely borrowed from randomized controlled trials.

Finally, instead of chasing statistical significance, nosotros should improve our agreement of the range of R values—the pre-report odds—where research efforts operate [10]. Before running an experiment, investigators should consider what they believe the chances are that they are testing a truthful rather than a non-true relationship. Speculated loftier R values may sometimes and then be ascertained. As described above, whenever ethically acceptable, large studies with minimal bias should be performed on inquiry findings that are considered relatively established, to encounter how ofttimes they are indeed confirmed. I doubtable several established "classics" volition fail the test [36].

Nevertheless, most new discoveries volition keep to stem from hypothesis-generating research with low or very low pre-study odds. Nosotros should so acknowledge that statistical significance testing in the report of a single study gives only a partial picture, without knowing how much testing has been done outside the report and in the relevant field at large. Despite a large statistical literature for multiple testing corrections [37], normally it is impossible to decipher how much data dredging by the reporting authors or other research teams has preceded a reported research finding. Even if determining this were feasible, this would not inform us about the pre-report odds. Thus, it is unavoidable that 1 should make judge assumptions on how many relationships are expected to be truthful among those probed across the relevant enquiry fields and research designs. The wider field may yield some guidance for estimating this probability for the isolated inquiry project. Experiences from biases detected in other neighboring fields would also exist useful to draw upon. Even though these assumptions would exist considerably subjective, they would even so exist very useful in interpreting research claims and putting them in context.

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