[Paleopsych] PLoS Medicine: Why Most Published Research Findings Are False
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PLoS Medicine: Why Most Published Research Findings Are False
http://medicine.plosjournals.org/perlserv/?request=get-document&doi=10%2E1371%2Fjournal%2Epmed%2E0020124
Volume 2 | Issue 8 | AUGUST 2005
John P. A. Ioannidis
Summary
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.
[33][table_thumb.gif]
[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.
Bias
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.
[37][10.1371_journal.pmed.0020124.g001-M.jpg]
[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.
[39][table_thumb.gif]
[40]Table 2. Research Findings and True Relationships in the Presence of
Bias
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.
[45][10.1371_journal.pmed.0020124.g002-M.jpg]
[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.
[47][table_thumb.gif]
[48]Table 3. Research Findings and True Relationships in the Presence of
Multiple Studies
Corollaries
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
Fields
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.
[72][table_thumb.gif]
[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
context.
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
undertaken!
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