[Paleopsych] PLoS Medicine: Why Most Published Research Findings Are False

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PLoS Medicine: Why Most Published Research Findings Are False
Volume 2 | Issue 8 | AUGUST 2005

John P. A. Ioannidis


    There is increasing concern that most current published research
    findings are false. The probability that a research claim is true may
    depend on study power and bias, the number of other studies on the
    same question, and, importantly, the ratio of true 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 lesser preselection of
    tested relationships; where there is greater flexibility in designs,
    definitions, outcomes, and analytical modes; when there 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
    likely for a research claim 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 problems for the conduct and
    interpretation of research.

    John P. A. Ioannidis is in the Department of Hygiene and Epidemiology,
    University of Ioannina School of Medicine, Ioannina, Greece, and
    Institute for Clinical Research and Health Policy Studies, Department
    of Medicine, Tufts-New England Medical Center, Tufts University School
    of Medicine, Boston, Massachusetts, United States of America. E-mail:
    jioannid at cc.uoi.gr

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

    Published: August 30, 2005

    DOI: 10.1371/journal.pmed.0020124

    Abbreviation: PPV, positive predictive value

    Citation: Ioannidis JPA (2005) Why Most Published Research Findings
    Are False. PLoS Med 2(8): e124

    Published research findings are sometimes refuted by subsequent
    evidence, with ensuing confusion and disappointment. Refutation and
    controversy is seen across the range of research designs, from
    clinical trials and traditional epidemiological studies [[24]1-3] to
    the most modern molecular research [[25]4,[26]5]. There is increasing
    concern that in modern research, false findings may be the majority or
    even the vast majority of published research claims [[27]6-8].
    However, this should not be surprising. It can be proven that most
    claimed research findings are false. Here I will examine the key
    factors that influence this problem and some corollaries thereof.

Modeling the Framework for False Positive Findings

    Several methodologists have pointed out [[28]9-11] that the high rate
    of nonreplication (lack of confirmation) of research discoveries is a
    consequence of the convenient, 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 by p-values, but, unfortunately, there is a widespread
    notion that medical research articles should be interpreted based only
    on p-values. Research findings are defined here as any relationship
    reaching formal statistical significance, e.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. However, here we
    will target relationships that investigators claim exist, rather than
    null findings.

    It can be proven that most claimed research findings are false.

    As has been shown previously, the probability that a research finding
    is indeed true depends on the prior probability of it being true
    (before doing the study), the statistical power of the study, and the
    level of statistical significance [[29]10,[30]11]. Consider a 2 × 2
    table in which research findings are compared against the gold
    standard of true relationships in a scientific field. In a research
    field both true and false hypotheses can be made about the presence of
    relationships. Let R be the ratio of the number of "true
    relationships" to "no relationships" among those tested in the field.
    R is characteristic of the field and can vary a lot depending on
    whether the field targets highly likely relationships or searches for
    only one or a few true relationships among thousands and millions of
    hypotheses that may be postulated. Let us also consider, for
    computational simplicity, circumscribed fields where either there is
    only one true relationship (among many that can be hypothesized) or
    the power is similar to find any of the several existing true
    relationships. The pre-study probability of a relationship being true
    is R/(R + 1). The probability of a study finding a true relationship
    reflects the power 1 - b (one minus the Type II error rate). The
    probability of claiming a relationship when none truly exists reflects
    the Type I error rate, a. Assuming that c relationships are being
    probed in the field, the expected values of the 2 × 2 table are given
    in [31]Table 1. After 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 called the
    false positive report probability [[32]10]. According to the 2 × 2
    table, one gets PPV = (1 - b)R/(R - bR + a). A research finding is
    thus more likely true than false if (1 - b)R > a. Since usually the
    vast majority of investigators depend on a = 0.05, this means that a
    research finding is more likely true than false if (1 - b)R > 0.05.

[34]Table 1. Research Findings and True Relationships

    What is less well appreciated is that bias and the extent of repeated
    independent testing by different teams of investigators around the
    globe may further distort this picture and may lead to even smaller
    probabilities of the research findings being indeed true. We will try
    to model these two factors in the context of similar 2 × 2 tables.


    First, let us define bias as the combination of various design, data,
    analysis, 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 have been "research findings," but
    nevertheless end up presented and reported as such, because of bias.
    Bias should not be confused with chance variability that causes some
    findings to be false by chance 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 form of such bias. We may assume that u does
    not depend on whether a true relationship exists or not. This is not
    an unreasonable assumption, since typically it is impossible to know
    which relationships are indeed true. In the presence of bias
    ([35]Table 2), one gets PPV = ([1 - b]R + ubR)/(R + a - bR + u - ua +
    ubR), and PPV decreases with increasing u, unless 1 - b =< a, i.e., 1
    - b =< 0.05 for most 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 [36]Figure 1.

[38]Figure 1. PPV (Probability That a Research Finding Is True) as a
Function of the Pre-Study Odds for Various Levels of Bias, u

    Panels correspond to power of 0.20, 0.50, and 0.80.

[40]Table 2. Research Findings and True Relationships in the Presence of

    Conversely, true research findings may occasionally be annulled
    because of reverse bias. For example, with large measurement errors
    relationships are lost in noise [[41]12], or investigators use data
    inefficiently or fail to notice statistically significant
    relationships, or there may be conflicts of interest that tend to
    "bury" significant findings [[42]13]. There is no good large-scale
    empirical evidence on how frequently such reverse bias may occur
    across diverse research fields. However, it is probably fair to say
    that reverse bias is not as common. Moreover measurement errors and
    inefficient use of data are probably becoming less frequent problems,
    since measurement error has decreased with technological advances in
    the molecular era and investigators are becoming increasingly
    sophisticated about their data. Regardless, reverse bias may be
    modeled in the same way as bias above. Also reverse bias should not be
    confused with chance variability that may lead to missing a true
    relationship because of chance.

Testing by Several Independent Teams

    Several independent teams may be addressing the same sets of research
    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 have at least one study
    claiming a research finding, and this receives unilateral attention.
    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 2 × 2
    table is shown in [43]Table 3: PPV = R(1 - b^n)/(R + 1 - [1 - a]^n -
    Rb^n) (not considering bias). With increasing number of independent
    studies, PPV tends to decrease, unless 1 - b < a, i.e., typically 1 -
    b < 0.05. This is shown for different levels of power and for
    different pre-study odds in [44]Figure 2. For n studies of different
    power, the term b^n is replaced by the product of the terms b[i] for i
    = 1 to n, but inferences are similar.

[46]Figure 2. PPV (Probability That a Research Finding Is True) as a
Function of the Pre-Study Odds for Various Numbers of Conducted Studies, n

    Panels correspond to power of 0.20, 0.50, and 0.80.

[48]Table 3. Research Findings and True Relationships in the Presence of
Multiple Studies


    A practical example is shown in [49]Box 1. Based on the above
    considerations, one may deduce several interesting corollaries about
    the probability that a research finding is indeed true.

    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 above, the PPV for a
    true research finding decreases as power decreases towards 1 - b =
    0.05. Thus, other factors being equal, research findings are more
    likely true in scientific fields that undertake large studies, such as
    randomized controlled trials in cardiology (several thousand subjects
    randomized) [[50]14] than in scientific fields with small studies,
    such as most research of molecular predictors (sample sizes 100-fold
    smaller) [[51]15].

    Corollary 2: The smaller the effect sizes in a scientific field, the
    less likely the research findings are to be true. Power 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 small, such as
    genetic risk factors for multigenetic diseases (relative risks
    1.1-1.5) [[52]7]. Modern epidemiology is increasingly obliged to
    target smaller effect sizes [[53]16]. Consequently, the proportion of
    true research findings is expected to decrease. In the same line of
    thinking, if the true effect sizes are very small in a scientific
    field, this field is likely to be plagued by almost ubiquitous false
    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 likely the
    research findings are to be true. As shown above, 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 information, such as
    microarrays and other high-throughput discovery-oriented research
    [[54]4,[55]8,[56]17], should have extremely low 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 be true. Flexibility increases the
    potential for transforming what would be "negative" results into
    "positive" results, i.e., bias, u. For several research designs, e.g.,
    randomized controlled trials [[57]18-20] or meta-analyses
    [[58]21,[59]22], there have been efforts to standardize their conduct
    and reporting. Adherence to common standards is likely 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.g., scales for schizophrenia outcomes)
    [[60]23]. Similarly, fields that use commonly agreed, stereotyped
    analytical methods (e.g., Kaplan-Meier plots and the log-rank test)
    [[61]24] may yield a larger proportion of true findings than fields
    where analytical methods are still under experimentation (e.g.,
    artificial intelligence methods) and only "best" results are reported.
    Regardless, even in the most stringent research designs, bias seems to
    be a major problem. For example, there is strong evidence that
    selective outcome reporting, with manipulation of the outcomes and
    analyses reported, is a common problem even for randomized trails
    [[62]25]. Simply abolishing selective publication would not make this
    problem go away.

    Corollary 5: 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 common in biomedical
    research [[63]26], and typically they are inadequately and sparsely
    reported [[64]26,[65]27]. Prejudice may not necessarily have financial
    roots. Scientists in a given field may be prejudiced purely because of
    their belief in a scientific theory or commitment to their own
    findings. Many otherwise seemingly independent, 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 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 [[66]28].

    Corollary 6: 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, as 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
    see major excitement followed rapidly by severe disappointments in
    fields that draw wide attention. 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 team may prioritize on
    pursuing and disseminating its most impressive "positive" results.
    "Negative" results may become attractive for dissemination only if
    some other team has found a "positive" association on the same
    question. In that case, it may be attractive to refute a claim made in
    some prestigious journal. The term Proteus phenomenon has been coined
    to describe this phenomenon of rapidly alternating extreme research
    claims and extremely opposite refutations [[67]29]. Empirical evidence
    suggests that this sequence of extreme opposites is very common in
    molecular genetics [[68]29].

    These corollaries consider each factor separately, but these factors
    often influence each other. For example, investigators working in
    fields where true effect sizes are perceived to be small may be more
    likely to perform large studies than investigators working in fields
    where true 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 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 enough to report and search further and thus
    refrain from data dredging and manipulation.

Most Research Findings Are False for Most Research Designs and for Most

    In the described framework, a PPV exceeding 50% is quite difficult to
    get. [69]Table 4 provides the results of simulations using the
    formulas developed for the influence of power, ratio of true 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, adequately powered randomized
    controlled trial starting with a 50% pre-study chance that the
    intervention is effective is eventually true about 85% of the time. A
    fairly similar 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 low power
    of single studies, is probably false if R =< 1:3. Research findings
    from underpowered, early-phase clinical trials would be true about one
    in four times, or even less frequently if bias is present.
    Epidemiological studies of an exploratory nature perform even worse,
    especially when underpowered, but even well-powered epidemiological
    studies may have only a one in five chance being true, if R = 1:10.
    Finally, in discovery-oriented research with massive testing, where
    tested relationships exceed true ones 1,000-fold (e.g., 30,000 genes
    tested, of which 30 may be the true culprits) [[70]30,[71]31], PPV for
    each claimed relationship is extremely low, even with considerable
    standardization of laboratory and statistical methods, outcomes, and
    reporting thereof to minimize bias.

[73]Table 4. PPV of Research Findings for Various Combinations of Power (1 -
b), Ratio of True to Not-True Relationships (R), and Bias (u)

Claimed Research Findings May Often Be Simply 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 true findings.
    Let us suppose that in a research field there are no true findings at
    all to be discovered. History of science teaches us that scientific
    endeavor has often in the past wasted effort in fields with absolutely
    no yield of true scientific information, 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 null in the absence
    of bias. The extent that observed findings deviate from what is
    expected by chance alone would be simply a pure measure of the
    prevailing bias.

    For example, let 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 comparison of the upper to lower intake tertiles. 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 net bias. It even follows that between "null 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 picture much. Even if a few relationships are
    true, the shape of the distribution of the observed effects would
    still yield a clear 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. Too large
    and too highly significant effects may actually be more likely to be
    signs of large bias in most fields of modern research. They should
    lead investigators to careful critical thinking about what might have
    gone wrong with their data, analyses, and results.

    Of course, investigators working in any field are likely to resist
    accepting that the whole field in which they have spent their careers
    is a "null field." However, 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 one field
    may also be 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 it unavoidable that most research findings are false, or can we
    improve the situation? A major problem is that it is impossible to
    know with 100% certainty what the truth is in any 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., large studies or low-bias
    meta-analyses, may help, as it comes closer to the unknown "gold"
    standard. However, large studies may still have biases and these
    should be acknowledged and avoided. Moreover, large-scale evidence is
    impossible to obtain for all of the millions and trillions of research
    questions posed in current research. Large-scale evidence should be
    targeted for research questions where the pre-study probability is
    already considerably high, so that a significant research finding will
    lead to a post-test probability that would be considered quite
    definitive. Large-scale evidence is also particularly indicated when
    it can test major concepts rather than narrow, specific questions. A
    negative finding can then refute not only a specific proposed claim,
    but a whole field or considerable portion thereof. Selecting the
    performance of large-scale studies based on narrow-minded criteria,
    such as the marketing promotion of a specific drug, is largely wasted
    research. Moreover, one should be cautious that extremely large
    studies may be more likely to find a formally statistical significant
    difference for a trivial effect that is not really meaningfully
    different from the null [[74]32-34].

    Second, most research questions are addressed by many teams, and it is
    misleading to emphasize the statistically significant findings of any
    single team. What matters is the totality of the evidence. Diminishing
    bias through enhanced research standards and curtailing of prejudices
    may also help. However, this may require a change in scientific
    mentality that might be difficult to achieve. In some research
    designs, efforts may also be more successful with upfront registration
    of studies, e.g., randomized trials [[75]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 do 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, we should
    improve our understanding of the range of R values--the pre-study
    odds--where research efforts operate [[76]10]. Before running an
    experiment, investigators should consider what they believe the
    chances are that they are testing a true rather than a non-true
    relationship. Speculated high R values may sometimes then be
    ascertained. As described above, whenever ethically acceptable, large
    studies with minimal bias should be performed on research findings
    that are considered relatively established, to see how often they are
    indeed confirmed. I suspect several established "classics" will fail
    the test [[77]36].

    Nevertheless, most new discoveries will continue to stem from
    hypothesis-generating research with low or very low pre-study odds. We
    should then 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 [[78]37], usually 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-study odds.
    Thus, it is unavoidable that one should make approximate assumptions
    on how many relationships are expected to be true among those probed
    across the relevant research fields and research designs. The wider
    field may yield some guidance for estimating this probability for the
    isolated research project. Experiences from biases detected in other
    neighboring fields would also be useful to draw upon. Even though
    these assumptions would be considerably subjective, they would still
    be very useful in interpreting research claims and putting them in

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

    Let us assume that a team of investigators performs a whole genome
    association study 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 disease, it is reasonable
    to expect that probably around ten gene polymorphisms among those
    tested would be truly associated with schizophrenia, with relatively
    similar odds ratios around 1.3 for the ten or so polymorphisms and
    with a fairly similar power to identify any of them. Then R =
    10/100,000 = 10^ -4, and the pre-study probability for any
    polymorphism to be associated with schizophrenia is also R/(R + 1) =
    10^ -4. Let us also suppose that the study has 60% power to find an
    association with an odds ratio of 1.3 at a = 0.05. Then it can be
    estimated that if a statistically significant association is found
    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 it is still only 12 × 10^ -4.

    Now let us suppose that the investigators manipulate their design,
    analyses, and reporting so as to make more relationships cross the p =
    0.05 threshold even though this would not have 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 be done, for example,
    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 control 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 significant results through data dredging. In the
    presence of bias with u = 0.10, the post-study probability that a
    research finding is true is only 4.4 × 10^ -4. Furthermore, even in
    the absence of any 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 1.5 × 10^ -4, hardly any higher than
    the probability we had before any of this extensive research was


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