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Why Nigh Published Research Findings Are Faux

• John P. A. Ioannidis

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• Published: August 30, 2005
• https://doi.org/x.1371/periodical.pmed.0020124

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Abstruse

Summary

There is increasing concern that nearly current published research findings are false. The probability that a inquiry claim is truthful may depend on report power and bias, the number of other studies on the same question, and, importantly, the ratio of truthful to no relationships among the relationships probed in each scientific field. In this framework, a research finding is less likely to be true when the studies conducted in a field are smaller; when effect sizes are smaller; when there is a greater number and bottom preselection of tested relationships; where in that location is greater flexibility in designs, definitions, outcomes, and analytical modes; when in that location is greater financial 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 probable for a enquiry claim to be false than true. Moreover, for many current scientific fields, claimed enquiry findings may often be just accurate measures of the prevailing bias. In this essay, I discuss the implications of these bug for the conduct and interpretation of enquiry.

Citation: Ioannidis JPA (2005) Why Most Published Inquiry Findings Are False. PLoS Med 2(8): e124. https://doi.org/10.1371/periodical.pmed.0020124

Published: Baronial thirty, 2005

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

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

Abridgement: PPV, positive predictive value

Published research findings are sometimes refuted past subsequent show, with ensuing defoliation and disappointment. Refutation and controversy is seen across the range of research designs, from clinical trials and traditional epidemiological studies [one–3] to the about mod molecular research [4,5]. There is increasing concern that in modernistic research, fake findings may be the majority or even the vast majority of published inquiry claims [half dozen–8]. Yet, this should non exist surprising. It can be proven that virtually claimed enquiry findings are false. Hither I will examine the key factors that influence this trouble and some corollaries thereof.

Modeling the Framework for False Positive Findings

Several methodologists have pointed out [nine–eleven] that the loftier rate of nonreplication (lack of confirmation) of enquiry discoveries is a event of the user-friendly, yet ill-founded strategy of claiming conclusive research findings solely on the basis of a single study assessed by formal statistical significance, typically for a p-value less than 0.05. Research is not most appropriately represented and summarized past p-values, but, unfortunately, there is a widespread notion that medical research articles should exist interpreted based just on p-values. Inquiry findings are defined here as any relationship reaching formal statistical significance, e.grand., effective interventions, informative predictors, risk factors, or associations. "Negative" enquiry is too very useful. "Negative" is actually a misnomer, and the misinterpretation is widespread. Even so, here we will target relationships that investigators claim be, rather than null findings.

It tin be proven that most claimed research findings are false

As has been shown previously, the probability that a inquiry finding is indeed true depends on the prior probability of it being true (earlier doing the study), the statistical power of the report, and the level of statistical significance [10,11]. Consider a ii × 2 table in which research findings are compared confronting the gold standard of true relationships in a scientific field. In a research field both truthful and false hypotheses can be made well-nigh the presence of relationships. Let R exist the ratio of the number of "true relationships" to "no relationships" among those tested in the field. R is feature of the field and can vary a lot depending on whether the field targets highly likely relationships or searches for only ane or a few true relationships amongst thousands and millions of hypotheses that may be postulated. Let us as well consider, for computational simplicity, circumscribed fields where either there is only one true relationship (among many that can be hypothesized) or the ability is similar to find any of the several existing true relationships. The pre-study probability of a relationship existence true is R/(R + 1). The probability of a written report finding a true relationship reflects the power ane - β (i minus the Type Two error charge per unit). The probability of claiming a relationship when none truly exists reflects the Blazon I fault charge per unit, α. Assuming that c relationships are being probed in the field, the expected values of the 2 × 2 tabular array are given in Table ane. Afterwards a enquiry finding has been claimed based on achieving formal statistical significance, the mail-study probability that it is true is the positive predictive value, PPV. The PPV is besides the complementary probability of what Wacholder et al. have called the false positive report probability [10]. According to the ii × two table, one gets PPV = (1 - β)R/(R - βR + α). A research finding is thus more likely true than false if (1 - β)R > α. Since usually the vast bulk of investigators depend on a = 0.05, this ways that a research finding is more than likely true than false if (1 - β)R > 0.05.

What is less well appreciated is that bias and the extent of repeated contained testing past different teams of investigators effectually the globe may farther distort this picture and may lead to even smaller probabilities of the research findings being indeed truthful. Nosotros will try to model these two factors in the context of similar ii × ii tables.

Bias

First, let us define bias as the combination of various blueprint, information, assay, and presentation factors that tend to produce research findings when they should not be produced. Let u be the proportion of probed analyses that would not accept been "enquiry findings," only notwithstanding end upward presented and reported as such, because of bias. Bias should not exist confused with chance variability that causes some findings to be simulated by adventure even though the study design, data, analysis, and presentation are perfect. Bias can entail manipulation in the analysis or reporting of findings. Selective or distorted reporting is a typical grade of such bias. We may assume that u does not depend on whether a true relationship exists or not. This is not an unreasonable supposition, since typically information technology is impossible to know which relationships are indeed truthful. In the presence of bias (Table 2), one gets PPV = ([1 - β]R + uβR)/(R + α − βR + u − uα + uβR), and PPV decreases with increasing u, unless 1 − β ≤ α, i.e., 1 − β ≤ 0.05 for nearly situations. Thus, with increasing bias, the chances that a research finding is true diminish considerably. This is shown for different levels of power and for different pre-study odds in Figure 1. Conversely, true enquiry findings may occasionally be annulled because of reverse bias. For example, with big measurement errors relationships are lost in dissonance [12], or investigators apply data inefficiently or fail to find statistically significant relationships, or at that place may be conflicts of interest that tend to "bury" meaning findings [13]. There is no expert large-scale empirical evidence on how frequently such reverse bias may occur across diverse research fields. However, it is probably fair to say that opposite bias is not as common. Moreover measurement errors and inefficient apply of data are probably becoming less frequent issues, since measurement fault has decreased with technological advances in the molecular era and investigators are condign increasingly sophisticated about their data. Regardless, opposite bias may be modeled in the same style equally bias above. Besides opposite bias should non exist confused with chance variability that may lead to missing a true relationship considering of hazard.

Testing by Several Independent Teams

Several independent teams may be addressing the same sets of enquiry questions. As 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 single teams and interpret research experiments in isolation. An increasing number of questions accept at least one written report claiming a research finding, and this receives unilateral attention. The probability that at least one study, amid several done on the aforementioned question, claims a statistically significant research finding is easy to judge. For north independent studies of equal power, the two × 2 table is shown in Table three: PPV = R(1 − β ^north )/(R + 1 − [ane − α] ⁿ − Rβ ⁿ ) (not considering bias). With increasing number of independent studies, PPV tends to decrease, unless 1 - β < a, i.e., typically 1 − β < 0.05. This is shown for different levels of power and for unlike pre-written report odds in Effigy two. For n studies of different power, the term β ⁿ is replaced by the product of the terms β _i for i = 1 to northward, merely inferences are similar.

Corollaries

A practical example is shown in Box one. Based on the above considerations, one may deduce several interesting corollaries about the probability that a enquiry finding is indeed truthful.

Box 1. An Instance: Science at Depression Pre-Study Odds

Allow us presume that a team of investigators performs a whole genome clan written report to test whether any of 100,000 gene polymorphisms are associated with susceptibility to schizophrenia. Based on what we know about the extent of heritability of the illness, information technology is reasonable to await that probably around ten factor polymorphisms amid those tested would be truly associated with schizophrenia, with relatively like odds ratios around ane.3 for the ten or so polymorphisms and with a adequately similar power to identify any of them. Then R = x/100,000 = 10⁻⁴, and the pre-written report probability for any polymorphism to be associated with schizophrenia is also R/(R + ane) = 10⁻⁴. Allow us also suppose that the study has threescore% power to notice an association with an odds ratio of 1.3 at α = 0.05. Then it can be estimated that if a statistically significant clan is plant with the p-value barely crossing the 0.05 threshold, the post-study probability that this is true increases about 12-fold compared with the pre-study probability, but information technology is still only 12 × x⁻⁴.

Now let us suppose that the investigators manipulate their design, analyses, and reporting and so as to make more relationships cross the p = 0.05 threshold even though this would not accept been crossed with a perfectly adhered to design and analysis and with perfect comprehensive reporting of the results, strictly according to the original study plan. Such manipulation could exist done, for instance, with serendipitous inclusion or exclusion of certain patients or controls, post hoc subgroup analyses, investigation of genetic contrasts that were not originally specified, changes in the disease or command definitions, and various combinations of selective or distorted reporting of the results. Commercially available "information mining" packages actually are proud of their ability to yield statistically significant results through data dredging. In the presence of bias with u = 0.ten, the post-study probability that a research finding is true is only 4.iv × ten^−four. Furthermore, even in the absenteeism of whatsoever bias, when ten independent research teams perform similar experiments around the world, if one of them finds a formally statistically significant association, the probability that the research finding is true is only ane.5 × 10⁻⁴, inappreciably whatsoever higher 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 likely the research findings are to be true. Small sample size means smaller power and, for all functions to a higher place, the PPV for a true enquiry finding decreases as power decreases towards 1 − β = 0.05. Thus, other factors being equal, research findings are more likely truthful in scientific fields that undertake large studies, such as randomized controlled trials in cardiology (several thousand subjects randomized) [xiv] than in scientific fields with small studies, such as nearly research of molecular predictors (sample sizes 100-fold smaller) [15].

Corollary ii: The smaller the effect sizes in a scientific field, the less likely the research findings are to be true. Ability is also related to the effect size. Thus research findings are more likely true in scientific fields with large effects, such as the impact of smoking on cancer or cardiovascular disease (relative risks 3–20), than in scientific fields where postulated effects are minor, such as genetic gamble factors for multigenetic diseases (relative risks 1.1–i.five) [vii]. Mod epidemiology is increasingly obliged to target smaller upshot sizes [16]. Consequently, the proportion of true research findings is expected to decrease. In the same line of thinking, if the truthful consequence sizes are very small in a scientific field, this field is probable to be plagued by virtually ubiquitous simulated positive claims. For example, if the majority of true genetic or nutritional determinants of complex 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 probable the research findings are to exist true. As shown above, the mail-written report probability that a finding is true (PPV) depends a lot on the pre-written report odds (R). Thus, research findings are more likely true in confirmatory designs, such every bit big 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 information, such as microarrays and other loftier-throughput discovery-oriented inquiry [4,8,17], should have extremely depression PPV.

Corollary 4: The greater the flexibility in designs, definitions, outcomes, and analytical modes in a scientific field, the less likely the research findings are to exist true. Flexibility increases the potential for transforming what would be "negative" results into "positive" results, i.east., bias, u. For several research designs, due east.k., randomized controlled trials [18–20] or meta-analyses [21,22], there have been efforts to standardize their carry and reporting. Adherence to mutual standards is probable to increase the proportion of true findings. The same applies to outcomes. True findings may be more common when outcomes are unequivocal and universally agreed (e.g., death) rather than when multifarious outcomes are devised (e.one thousand., scales for schizophrenia outcomes) [23]. Similarly, fields that employ unremarkably agreed, stereotyped analytical methods (eastward.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 nether experimentation (e.thou., bogus intelligence methods) and only "best" results are reported. Regardless, fifty-fifty in the near stringent research designs, bias seems to be a major problem. For example, there is strong evidence that selective issue reporting, with manipulation of the outcomes and analyses reported, is a common problem even for randomized trails [25]. Simply abolishing selective publication would not make this trouble get abroad.

Corollary five: The greater the financial and other interests and prejudices in a scientific field, the less likely the research findings are to exist truthful. Conflicts of interest and prejudice may increase bias, u. Conflicts of involvement are very mutual in biomedical research [26], and typically they are inadequately and sparsely reported [26,27]. Prejudice may non 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 exist conducted for no other reason than to requite physicians and researchers qualifications for promotion or tenure. Such nonfinancial conflicts may besides atomic number 82 to distorted reported results and interpretations. Prestigious investigators may suppress via the peer review process the appearance and dissemination of findings that refute their findings, thus condemning their field to perpetuate false dogma. Empirical evidence on expert opinion shows that it is extremely unreliable [28].

Corollary 6: The hotter a scientific field (with more scientific teams involved), the less likely the research findings are to exist true. This seemingly paradoxical corollary follows because, equally stated above, the PPV of isolated findings decreases when many teams of investigators are involved in the same field. This may explain why we occasionally run across major excitement followed quickly by severe disappointments in fields that draw broad 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 about impressive "positive" results. "Negative" results may become attractive for broadcasting merely if another team has plant a "positive" association on the same question. In that case, it may exist attractive to refute a merits made in some prestigious journal. The term Proteus phenomenon has been coined to describe this phenomenon of rapidly alternating extreme enquiry claims and extremely opposite refutations [29]. Empirical evidence suggests that this sequence of extreme opposites is very common in molecular genetics [29].

These corollaries consider each factor separately, but these factors often influence each other. For example, investigators working in fields where true event sizes are perceived to exist minor may be more likely to perform large studies than investigators working in fields where truthful effect sizes are perceived to exist big. Or prejudice may prevail in a hot scientific field, farther 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 stiff invested interests may sometimes promote larger studies and improved standards of research, enhancing the predictive value of its research findings. Or massive discovery-oriented testing may result in such a large yield of significant relationships that investigators have plenty to study and search farther and thus refrain from data dredging and manipulation.

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

In the described framework, a PPV exceeding l% is quite difficult to get. Tabular array 4 provides the results of simulations using the formulas developed for the influence of power, ratio of truthful to non-true relationships, and bias, for various types of situations that may be characteristic of specific study designs and settings. A finding from a well-conducted, fairly powered randomized controlled trial starting with a 50% pre-report take a chance that the intervention is constructive is eventually truthful about 85% of the fourth dimension. A fairly similar performance is expected of a confirmatory meta-analysis of proficient-quality randomized trials: potential bias probably increases, but ability and pre-exam 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 single studies, is probably simulated if R ≤ 1:3. Research findings from underpowered, early-stage clinical trials would be true about one in 4 times, or fifty-fifty less ofttimes if bias is nowadays. Epidemiological studies of an exploratory nature perform even worse, especially when underpowered, but even well-powered epidemiological studies may have only a one in v gamble being true, if R = ane:10. Finally, in discovery-oriented research with massive testing, where tested relationships exceed true ones 1,000-fold (e.g., xxx,000 genes tested, of which 30 may be the true culprits) [30,31], PPV for each claimed relationship is extremely depression, 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 research is operating in areas with very low pre- and post-study probability for truthful findings. Let united states of america suppose that in a research field there are no true findings at all to exist discovered. History of science teaches us that scientific attempt has ofttimes in the past wasted effort in fields with absolutely no yield of true scientific data, at to the lowest degree based on our current agreement. In such a "null field," one would ideally expect all observed event sizes to vary by adventure around the null in the absence of bias. The extent that observed findings deviate from what is expected by chance alone would be only a pure mensurate of the prevailing bias.

For example, allow us suppose that no nutrients or dietary patterns are actually important determinants for the risk 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 1.2 to 1.4 for the comparing of the upper to lower intake tertiles. And then the claimed effect sizes are simply measuring nothing else but the net bias that has been involved in the generation of this scientific literature. Claimed effect sizes are in fact the most accurate estimates of the internet bias. It even follows that between "nix fields," the fields that claim stronger effects (often with accompanying claims of medical or public health 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 moving picture much. Even if a few relationships are true, the shape of the distribution of the observed furnishings would even so yield a clear measure of the biases involved in the field. This concept totally reverses the mode we view scientific results. Traditionally, investigators have viewed big and highly significant effects with excitement, equally signs of of import discoveries. Too large and as well highly significant effects may actually exist more likely to exist signs of large bias in most fields of modern research. They should lead investigators to careful critical thinking about what might have gone incorrect with their data, analyses, and results.

Of grade, investigators working in whatever field are likely to resist accepting that the whole field in which they take spent their careers is a "cypher field." However, other lines of evidence, or advances in applied science and experimentation, may lead eventually to the dismantling of a scientific field. Obtaining measures of the net bias in 1 field may also exist useful for obtaining insight into what might be the range of bias operating in other fields where similar analytical methods, technologies, and conflicts may be operating.

How Can We Improve the Situation?

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

Better powered evidence, e.g., large studies or low-bias meta-analyses, may help, as information technology comes closer to the unknown "gold" standard. Nevertheless, big studies may yet have biases and these should be best-selling and avoided. Moreover, big-scale evidence is impossible to obtain for all of the millions and trillions of inquiry questions posed in current research. Large-calibration evidence should be targeted for enquiry questions where the pre-study probability is already considerably high, and so that a significant inquiry finding will lead to a mail-test probability that would be considered quite definitive. Big-scale evidence is likewise peculiarly indicated when it can exam major concepts rather than narrow, specific questions. A negative finding tin can then refute not only a specific proposed claim, only a whole field or considerable portion thereof. Selecting the performance of large-scale studies based on narrow-minded criteria, such equally the marketing promotion of a specific drug, is largely wasted enquiry. Moreover, i should be cautious that extremely large studies may be more than probable to find a formally statistical pregnant difference for a trivial effect that is non really meaningfully different from the aught [32–34].

Second, near research questions are addressed past many teams, and information technology is misleading to emphasize the statistically pregnant findings of any unmarried team. What matters is the totality of the show. Diminishing bias through enhanced inquiry standards and curtailing of prejudices may too assist. However, this may crave a alter in scientific mentality that might be hard to achieve. In some research designs, efforts may also be more successful with upfront registration of studies, due east.g., 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 be more feasible than registration of each and every hypothesis-generating experiment. Regardless, even if we practise not meet a groovy 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 ameliorate our understanding of the range of R values—the pre-study odds—where research efforts operate [ten]. Before running an experiment, investigators should consider what they believe the chances are that they are testing a truthful rather than a not-true relationship. Speculated loftier R values may sometimes so 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 see how often they are indeed confirmed. I doubtable several established "classics" will fail the test [36].

Nevertheless, nearly new discoveries will continue to stem from hypothesis-generating inquiry with depression or very depression pre-study odds. Nosotros should and so admit that statistical significance testing in the report of a unmarried study gives only a fractional picture, without knowing how much testing has been washed outside the written report and in the relevant field at big. Despite a large statistical literature for multiple testing corrections [37], usually information technology 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-written report odds. Thus, it is unavoidable that one should make estimate assumptions on how many relationships are expected to be truthful amidst those probed across the relevant inquiry fields and research designs. The wider field may yield some guidance for estimating this probability for the isolated inquiry projection. Experiences from biases detected in other neighboring fields would as well be useful to depict upon. Even though these assumptions would be considerably subjective, they would still exist very useful in interpreting inquiry claims and putting them in context.

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