John P. A. IoannidispersName (2005date). “Why Most Published Research Findings Are False.” PLOS Medicinetitle·j, IoanninaplaceName.
Object of study — The probabilityterm·key that a claimed research findingterm·dom is trueterm·key, as a function of a field's pre-study oddsterm·key, study powerterm·var, biasterm·dom and the number of teams competing on the question.
Research question — If a finding is published because it crossed p < 0.05, what is the chance it is actually trueterm·key - and what makes that chance rise or fall?
Contribution — A closed-form model of the post-study probabilityterm·key of truth, showing it falls with biasterm·dom and with the number of independent teams, and that for most realistic settings it is below one half.
phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text| phenomenon | false positive published research findings — “There is increasing concern that most current published research findings are false.” | |
| claim-type | critique — “It can be proven that most claimed research findings are false.” | |
| method — evidence | — “Simulations show that for most study designs and settings, it is more likely for a research claim to be false than true.” | |
| object of study — evidence | — “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.” | |
| research question — evidence | — “Several methodologists have pointed out [ 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.” | |
| contribution — evidence | — “It can be proven that most claimed research findings are false.” | |
| transfer | from probability / diagnostic testing (Bayesian predictive value): applying the positive-predictive-value / Bayesian framework from diagnostic testing to estimate the probability that a published research finding is true — “the post-study probability that it is true is the positive predictive value, PPV” | transfers[0] |
| mechanism | a findings truth probability (PPV) is a Bayesian function of pre-study odds, statistical power, bias, and the number of teams - so with low prior odds, underpowered studies and analytic flexibility, most published positive 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” | mechanisms[0] |
| mechanism | the field's own hypothesis space sets the ceiling: R, the ratio of true to null relationships among those tested, is a property of the field and not of the study — “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.” | mechanisms[1] |
| mechanism | bias is modelled as a rate, not a lapse: the proportion of analyses reported as findings that should not have been — “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.” | mechanisms[2] |
| mechanism | competition makes it worse rather than better - the more teams chase one question, the lower the chance that the team who reports a positive is right — “With increasing number of independent studies, PPV tends to decrease, unless 1 - β < a, i.e., typically 1 − β < 0.05.” | mechanisms[3] |
| mechanism | at high enough bias the published literature stops measuring the world and starts measuring the bias — “Moreover, for many current scientific fields, claimed research findings may often be simply accurate measures of the prevailing bias.” | mechanisms[4] |
| builds-on | prior positive-predictive-value / significance-testing framework — “the probability that a research finding is indeed true depends on the prior probability of it being true” | claim_relations[0] |
| builds-on | Wacholder et al. [10], the false positive report probability — “The PPV is also the complementary probability of what Wacholder et al. have called the false positive report probability [ 10 ].” | claim_relations[1] |
| builds-on | prior methodological work [9-11] on nonreplication and single-study significance testing — “Several methodologists have pointed out [ 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.” | claim_relations[2] |
| extends | the previously established dependence of a finding's truth on prior probability, power and significance level [10, 11] — “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.” | claim_relations[3] |
| builds-on | Wacholder et al. on the false positive report probability — “The PPV is also the complementary probability of what Wacholder et al. have called the false positive report probability [ 10 ].” | claim_relations[4] |
| contradicts | the practice of claiming a conclusive finding from a single study at p < 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.” | claim_relations[5] |
| contradicts | the practice of interpreting research experiments in isolation from other teams working the same question — “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.” | claim_relations[6] |
| sense | bias - as a rate of unwarranted positives produced by design, analysis and reporting choices; a property of how research is done — “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.” | senses[0] |
| sense | bias - explicitly NOT chance variability, which produces false findings even under a perfect design — “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.” | senses[1] |
| sense | negative - a term the paper calls a misnomer, because a study that fails to find a relationship is informative rather than empty — ““Negative” is actually a misnomer, and the misinterpretation is widespread.” | senses[2] |
| sense | pre-study probability - the probability that a relationship is true before testing, equal to R divided by R plus one — “The pre-study probability of a relationship being true is R /( R + 1).” | senses[3] |
| sense | Type II error rate - beta, whose complement is the power to find a true relationship — “The probability of a study finding a true relationship reflects the power 1 - β (one minus the Type II error rate).” | senses[4] |
| sense | Type I error rate - alpha, governing a claimed relationship when none exists — “The probability of claiming a relationship when none truly exists reflects the Type I error rate, α.” | senses[5] |
| sense | Proteus phenomenon - rapidly alternating extreme claims and extremely opposite refutations — “The term Proteus phenomenon has been coined to describe this phenomenon of rapidly alternating extreme research claims and extremely opposite refutations [ 29 ].” | senses[6] |
| sense | null field - a field with no true findings, where unbiased effects vary by chance around the null — “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.” | senses[7] |
| sense | data dredging - using data-mining procedures to yield statistically significant results — “Commercially available “data mining” packages actually are proud of their ability to yield statistically significant results through data dredging.” | senses[8] |
| sense | confirmatory designs - large phase III randomized trials or meta-analyses treated as more likely to yield true findings — “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.” | senses[9] |
| sense | hypothesis-generating experiments - exploratory designs contrasted with confirmatory designs on truth probability — “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.” | senses[10] |
| sense | upfront registration of studies - advance registration proposed for designs such as randomized trials — “In some research designs, efforts may also be more successful with upfront registration of studies, e.g., randomized trials [ 35 ].” | senses[11] |
| sense | selective outcome reporting - manipulation of reported outcomes and analyses, common even in randomized trials — “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 [ 25 ].” | senses[12] |
| control | simulations sweeping statistical power, the ratio of true to non-true relationships, and bias, across a range of study types (Table 4) — held — “In the described framework, a PPV exceeding 50% is quite difficult to get.” — rules out that the conclusion depends on one particular choice of power, pre-study odds or bias rather than holding across the parameter range — “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.” | controls[0] |
| evidence status note | prior positive-predictive-value / significance-testing framework — QUOTE REPAIRED: the extractor split a ligature and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. Update, 15 September 2026: CLEARED evidence status='quote-not-in-current-staged-text' - the quote now locates in the current staged text, so the condition the marker recorded no longer holds. — “the probability that a research finding is indeed true depends on the prior probability of it being true” | claim_relations[0] |
| edge | bias —contrasted-with→ reverse bias — “Conversely, true research findings may occasionally be annulled because of reverse bias.” | concept_edges[2] |
| effect direction | bias —causes→ PPV — reduces — “In the presence of bias ( Table 2 ), one gets PPV = ([1 - β] R + u β R )/( R + α − β R + u − u α + u β R ), and PPV decreases with increasing u , unless 1 − β ≤ α, i.e., 1 − β ≤ 0.05 for most situations. Thus, with increasing bias, the chances that a research finding is true diminish considerably” — “PPV decreases with increasing u” | concept_edges[4] |
| holds when | bias —causes→ PPV — except where the power is at or below the significance level, which the authors note is 1 - beta <= 0.05 in most situations — “In the presence of bias ( Table 2 ), one gets PPV = ([1 - β] R + u β R )/( R + α − β R + u − u α + u β R ), and PPV decreases with increasing u , unless 1 − β ≤ α, i.e., 1 − β ≤ 0.05 for most situations. Thus, with increasing bias, the chances that a research finding is true diminish considerably” — “unless 1 − β ≤ α” | concept_edges[4] |
| note | bias —causes→ PPV — the endpoint is the abbreviation THE SENTENCE USES; the concept carries normalised='positive predictive value' so the two names resolve to one node — “In the presence of bias ( Table 2 ), one gets PPV = ([1 - β] R + u β R )/( R + α − β R + u − u α + u β R ), and PPV decreases with increasing u , unless 1 − β ≤ α, i.e., 1 − β ≤ 0.05 for most situations. Thus, with increasing bias, the chances that a research finding is true diminish considerably” | concept_edges[4] |
| relation | bias —causes→ PPV — more bias lowers the post-study probability that a claimed finding is true — “In the presence of bias ( Table 2 ), one gets PPV = ([1 - β] R + u β R )/( R + α − β R + u − u α + u β R ), and PPV decreases with increasing u , unless 1 − β ≤ α, i.e., 1 − β ≤ 0.05 for most situations. Thus, with increasing bias, the chances that a research finding is true diminish considerably” — “PPV decreases with increasing u” | concept_edges[4] |
| note | confirmatory designs —contrasted-with→ hypothesis-generating experiments — The paper directly compares the two design families on the probability that their findings are true. — “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.” | concept_edges[5] |
| outcome | control — held — “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.” — “In the described framework, a PPV exceeding 50% is quite difficult to get.” | controls[0] |
| for which use | limitation — every number the framework produces: it assumes CIRCUMSCRIBED FIELDS WHERE EITHER THERE IS ONLY ONE TRUE RELATIONSHIP ... OR THE POWER IS SIMILAR, adopted FOR COMPUTATIONAL SIMPLICITY — “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.” | limitations[0] |
| for which use | limitation — the bias term throughout: WE MAY ASSUME THAT u DOES NOT DEPEND ON WHETHER A TRUE RELATIONSHIP EXISTS OR NOT — “We may assume that u does not depend on whether a true relationship exists or not.” | limitations[1] |
| for which use | limitation — the treatment of reverse bias: THERE IS NO GOOD LARGE-SCALE EMPIRICAL EVIDENCE ON HOW FREQUENTLY SUCH REVERSE BIAS MAY OCCUR — “There is no good large-scale empirical evidence on how frequently such reverse bias may occur across diverse research fields.” | limitations[2] |
| for which use | limitation — the entire notion of a false finding as used here: A MAJOR PROBLEM IS THAT IT IS IMPOSSIBLE TO KNOW WITH 100% CERTAINTY WHAT THE TRUTH IS IN ANY RESEARCH QUESTION - the standard against which false is defined is unobtainable — “A major problem is that it is impossible to know with 100% certainty what the truth is in any research question.” | limitations[3] |
| for which use | limitation — any applied use of the framework: EVEN THOUGH THESE ASSUMPTIONS WOULD BE CONSIDERABLY SUBJECTIVE, THEY WOULD STILL BE VERY USEFUL - the pre-study odds are supplied by judgement — “Even though these assumptions would be considerably subjective, they would still be very useful in interpreting research claims and putting them in context.” | limitations[4] |
| duplicate of | limitation — limitations[2] — “There is no good large-scale empirical evidence on how frequently such reverse bias may occur across diverse research fields.” | limitations[5] |
| for which use | limitation — the same scope as limitations[2] - reverse bias is acknowledged and left unmeasured — “There is no good large-scale empirical evidence on how frequently such reverse bias may occur across diverse research fields.” | limitations[5] |
| duplicate of | limitation — limitations[1] — “We may assume that u does not depend on whether a true relationship exists or not.” | limitations[6] |
| for which use | limitation — the same scope as limitations[1] - the bias rate is assumed independent of the truth of the relationship — “We may assume that u does not depend on whether a true relationship exists or not.” | limitations[6] |
| for which use | limitation — the empirical standing of the title claim: the argument is analytic and simulated, and no corpus of published findings is checked against it — “Simulations show that for most study designs and settings, it is more likely for a research claim to be false than true.” | limitations[7] |
| replication | untested | |
| no type for this | PPV → false positive report probability — one is the COMPLEMENTARY PROBABILITY of the other (PPV = 1 - FPRP). The schema has no type for complementarity: it is not sameness, not a contrast, not a cause - it is an exact arithmetic relation between two quantities, and bending it to 'distinct-from' would lose that they determine each other completely. — “The PPV is also the complementary probability of what Wacholder et al. have called the false positive report probability [ 10 ].” | unhoused_relations[0] |
| limitation | The framework simplifies fields to a single true relationship or uniform power across true relationships. — “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.” | limitations[0] |
| limitation | Bias u is assumed independent of whether a true relationship exists. — “We may assume that u does not depend on whether a true relationship exists or not.” | limitations[1] |
| limitation | There is no good empirical basis for estimating how often reverse bias operates. — “There is no good large-scale empirical evidence on how frequently such reverse bias may occur across diverse research fields.” | limitations[2] |
| limitation | The gold standard the whole framework is measured against is unobtainable. — “A major problem is that it is impossible to know with 100% certainty what the truth is in any research question.” | limitations[3] |
| limitation | Applying the framework requires considerably subjective assumptions about pre-study odds. — “Even though these assumptions would be considerably subjective, they would still be very useful in interpreting research claims and putting them in context.” | limitations[4] |
| limitation | Reverse bias - findings lost to noise, buried or missed - is acknowledged and then left unmeasured, with no evidence base. — “There is no good large-scale empirical evidence on how frequently such reverse bias may occur across diverse research fields.” | limitations[5] |
| limitation | The model assumes the bias rate is independent of whether a relationship is real, justified on the grounds that nobody can tell which are real. — “We may assume that u does not depend on whether a true relationship exists or not.” | limitations[6] |
| limitation | The argument is analytic and simulated; no corpus of published findings is checked against it. — “Simulations show that for most study designs and settings, it is more likely for a research claim to be false than true.” | limitations[7] |
finding · quantity · variable · definition · key-term — grounded in the full text| finding | Simulations show that for most study designs and settings a research claim is more likely to be false than true. — “Simulations show that for most study designs and settings, it is more likely for a research claim to be false than true.” | content_tags.findings[0] |
| finding | Findings are less likely to be true when studies are smaller, when effect sizes are smaller, and when more relationships are tested with less preselection. — “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” | content_tags.findings[1] |
| evidence status note | finding — QUOTE REPAIRED: the extractor split a ligature and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. | content_tags.findings[1] |
| finding | The high rate of nonreplication of research discoveries is a consequence of a convenient but ill-founded strategy of claiming them. — “the high rate of nonreplication (lack of confirmation) of research discoveries is a consequence of the convenient, yet ill-founded strategy of claiming” | content_tags.findings[2] |
| evidence status note | finding — QUOTE REPAIRED: the extractor split a ligature and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. | content_tags.findings[2] |
| finding | For most designs and settings a published claim is more likely false than true. — “Simulations show that for most study designs and settings, it is more likely for a research claim to be false than true.” | content_tags.findings[3] |
| finding | With increasing bias, the chance that a research finding is true diminishes considerably. — “Thus, with increasing bias, the chances that a research finding is true diminish considerably.” | content_tags.findings[4] |
| finding | With more independent studies on the same question, PPV tends to decrease, unless power is very low (typically 1 − β < 0.05). — “With increasing number of independent studies, PPV tends to decrease, unless 1 - β < a, i.e., typically 1 − β < 0.05.” | content_tags.findings[5] |
| finding | In many current fields, claimed research findings may often be simply accurate measures of the prevailing bias. — “Moreover, for many current scientific fields, claimed research findings may often be simply accurate measures of the prevailing bias.” | content_tags.findings[6] |
| quantity | EVIDENCE CORRECTED (RE-GROUNDED) · < 0.05 p-value — conventional threshold for declaring a research finding statistically significant — “Several methodologists have pointed out [ 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.” | content_tags.quantities[0] |
| retracted | quantity — RE-GROUNDED. The old span welded 'reaching formal statistical signifi cance' - from the sentence DEFINING a research finding - to ', typically for a p-value less than 0.05' from a different sentence 291 characters earlier, about an ill-founded strategy. The 'signifi cance' damage sat exactly on the join and explained the failed substring check well enough that nobody looked past it. | content_tags.quantities[0] |
| quantity | p < 0.05 — the single-study significance threshold the whole critique is aimed at — “Several methodologists have pointed out [ 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.” | content_tags.quantities[1] |
| variable | positive predictive value (dependent) — “the post-study probability that it is true is the positive predictive value, PPV” | content_tags.variables[1] |
| variable | study power (independent) — “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.” | content_tags.variables[4] |
| variable | bias (independent) — “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.” | content_tags.variables[5] |
| variable | power (independent) — “Small sample size means smaller power and, for all functions above, the PPV for a true research finding decreases as power decreases towards 1 − β = 0.05.” | content_tags.variables[6] |
| variable | sample size (independent) — “Small sample size means smaller power and, for all functions above, the PPV for a true research finding decreases as power decreases towards 1 − β = 0.05.” | content_tags.variables[7] |
| definition | positive predictive value — “the post-study probability that it is true is the positive predictive value, PPV” | content_tags.definitions[0] |
| definition | research finding — “Research findings are defined here as any relationship reaching formal statistical significance, e.g., effective interventions, informative predictors, risk factors, or associations.” | content_tags.definitions[2] |
| definition | 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.” | content_tags.definitions[3] |
| definition | R — “Let R be the ratio of the number of “true relationships” to “no relationships” among those tested in the field.” | content_tags.definitions[4] |
| key-terms | research, studies, power, bias, probability, true, false, relationships, PPV, positive predictive value, pre-study odds, statistical power, statistical significance, nonreplication, reverse bias, false positive report probability, research finding |
| concept | positive predictive value — “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.” | concepts[0] |
| concept | statistical power — “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 [ 10 , 11 ]” | concepts[1] |
| concept | false positive report probability — not defined in this paper's own words; Wacholder's name for the complement of the same quantity - one concept, two literatures' labels — “The PPV is also the complementary probability of what Wacholder et al. have called the false positive report probability [ 10 ].” | concepts[5] |
| concept | bias — not defined in this paper's own words; the rate at which design, analysis and reporting choices turn non-findings into reported findings - a property of practice, not of chance — “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.” | concepts[6] |
| concept | reverse bias — not defined in this paper's own words; the opposite failure - real relationships lost to measurement error, inefficiency or suppression — “Conversely, true research findings may occasionally be annulled because of reverse bias.” | concepts[7] |
| concept | research finding — not defined in this paper's own words; operationally, any relationship that reaches formal statistical significance - the definition that makes the whole argument computable — “Research findings are defined here as any relationship reaching formal statistical significance, e.g., effective interventions, informative predictors, risk factors, or associations.” | concepts[8] |
| concept | nonreplication — not defined in this paper's own words; failure of a finding to be confirmed by later work - the observed problem the model is built to explain — “Several methodologists have pointed out [ 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.” | concepts[9] |
| concept | PPV — “In the presence of bias ( Table 2 ), one gets PPV = ([1 - β] R + u β R )/( R + α − β R + u − u α + u β R ), and PPV decreases with increasing u , unless 1 − β ≤ α, i.e., 1 − β ≤ 0.05 for most situations. Thus, with increasing bias, the chances that a research finding is true diminish considerably” | concepts[10] |
| concept | pre-study probability — not defined in this paper's own words; the probability that a probed relationship is true before the study, expressed as R divided by R plus one — “The pre-study probability of a relationship being true is R /( R + 1).” | concepts[11] |
| concept | Type II error rate — not defined in this paper's own words; the error rate whose complement, one minus beta, is statistical power — “The probability of a study finding a true relationship reflects the power 1 - β (one minus the Type II error rate).” | concepts[12] |
| concept | Type I error rate — not defined in this paper's own words; the rate governing claims of a relationship when no relationship truly exists — “The probability of claiming a relationship when none truly exists reflects the Type I error rate, α.” | concepts[13] |
| concept | Proteus phenomenon — not defined in this paper's own words; rapid alternation between extreme research claims and extremely opposite refutations — “The term Proteus phenomenon has been coined to describe this phenomenon of rapidly alternating extreme research claims and extremely opposite refutations [ 29 ].” | concepts[14] |
| concept | null field — not defined in this paper's own words; a research field with no true findings to discover, in which unbiased observed effects should vary by chance around the null — “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.” | concepts[15] |
| concept | data dredging — not defined in this paper's own words; using data-mining procedures to produce statistically significant results — “Commercially available “data mining” packages actually are proud of their ability to yield statistically significant results through data dredging.” | concepts[16] |
| concept | confirmatory designs — not defined in this paper's own words; designs such as large phase III randomized trials or their meta-analyses, treated as more likely to yield true findings — “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.” | concepts[17] |
| concept | hypothesis-generating experiments — not defined in this paper's own words; exploratory experiments contrasted with confirmatory designs on the likelihood that their findings are true — “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.” | concepts[18] |
| concept | upfront registration of studies — not defined in this paper's own words; advance registration proposed as a way to improve research practice in designs such as randomized trials — “In some research designs, efforts may also be more successful with upfront registration of studies, e.g., randomized trials [ 35 ].” | concepts[19] |
| concept | selective outcome reporting — not defined in this paper's own words; manipulation of which outcomes and analyses are reported, described as common even in randomized trials — “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 [ 25 ].” | concepts[20] |
| Bayesian | as written: prior probabilit — “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” | content_tags.statistics[0] |
| evidence status note | Bayesian — QUOTE REPAIRED: the extractor split a unicode and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. | content_tags.statistics[0] |
| effect-size d | as written: effect sizes — “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” | content_tags.statistics[1] |
| evidence status note | effect-size — QUOTE REPAIRED: the extractor split a unicode and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. | content_tags.statistics[1] |
| false-discovery-rate FDR | as written: multiple testing — “Despite a large statistical literature for multiple testing corrections [ 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.” | content_tags.statistics[2] |
| odds-ratio OR | as written: odds ratios — “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.” | content_tags.statistics[5] |
| p-value p | — “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.” | content_tags.statistics[6] |
| sample-size n/N | — “Small sample size means smaller power and, for all functions above, the PPV for a true research finding decreases as power decreases towards 1 − β = 0.05.” | content_tags.statistics[7] |
| evidence status note | sample-size — QUOTE REPAIRED: the extractor split a unicode and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. | content_tags.statistics[7] |
| positive-predictive-value PPV | — “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.” | content_tags.statistics[9] |
| statistical-power 1-β | — “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 [ 10 , 11 ]” | content_tags.statistics[10] |
| statistical-significance α | — “Research findings are defined here as any relationship reaching formal statistical significance, e.g., effective interventions, informative predictors, risk factors, or associations.” | content_tags.statistics[11] |
| prior-probability R/(R+1) | — “Let R be the ratio of the number of “true relationships” to “no relationships” among those tested in the field.” | content_tags.statistics[12] |
| claim type | critique — a second reading reaching the same value; recorded: critique — “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.” | alternatives.claim_type |
| method | formal-model — a second reading DIFFERING from the recorded value; recorded: simulation — “Simulations show that for most study designs and settings, it is more likely for a research claim to be false than true.” | alternatives.method |
| phenomenon | the low probability that a published, statistically significant research finding is true — a second reading DIFFERING from the recorded value; recorded: false positive published research findings — “Simulations show that for most study designs and settings, it is more likely for a research claim to be false than true.” | alternatives.phenomenon |
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Abstract. Summary There is increasing concern that most current published research findingsterm·dom are falseterm·key. The probabilityterm·key that a researchterm·key claim is trueterm·key may depend on study powerterm·var and biasterm·dom, the number of other studiesterm·key on the same question, and, importantly, the ratio of trueterm·key to no relationshipsterm·key among the relationshipsterm·key probed in each scientific field. In this framework, a research findingterm·dom is less likely to be trueterm·key when the studiesterm·key conducted in a field are smaller; when effect sizesterm·stat are smaller; when there is a greater number and lesser preselection of tested relationshipsterm·key; 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 significanceterm·key. Simulationsterm·mth show that for most study designs and settings, it is more likely for a researchterm·key claim to be falseterm·key than trueterm·key. Moreover, for many current scientific fields, claimed research findingsterm·dom may often be simply accurate measures of the prevailing biasterm·dom. In this essay, I discuss the implications of these problems for the conduct and interpretation of researchterm·key. Published research findingsterm·dom are sometimes refuted by subsequent evidence, says IoannidispersName, with ensuing confusion and disappointment. Published research findingsterm·dom are sometimes refuted by subsequent evidence, with ensuing confusion and disappointment. Refutation and controversy is seen across the range of researchterm·key designs, from clinical trials and traditional epidemiological studiesterm·key [ 1–3 ] to the most modern molecular researchterm·key [ 4 , 5 ]. There is increasing concern that in modern researchterm·key, falseterm·key findings may be the majority or even the vast majority of published researchterm·key claims [ 6–8 ]. However, this should not be surprising. It can be proven that most claimed research findingsterm·dom are falseterm·key. Here I will examine the key factors that influence this problem and some corollaries thereof. Modeling the Framework for Falseterm·key Positive Findings Several methodologists have pointed out [ 9–11 ] that the high rate of nonreplicationterm·dom (lack of confirmation) of researchterm·key discoveries is a consequence of the convenient, yet ill-founded strategy of claiming conclusive research findingsterm·dom solely on the basis of a single study assessed by formal statistical significanceterm·key, typically for a p -value less than 0.05. Researchterm·key is not most appropriately represented and summarized by p -values, but, unfortunately, there is a widespread notion that medical researchterm·key articles should be interpreted based only on p -values. Research findingsterm·dom are defined here as any relationshipterm·key reaching formal statistical significanceterm·key, e.g., effective interventions, informative predictors, risk factors, or associations. “Negative” researchterm·key is also very useful. “Negative” is actually a misnomer, and the misinterpretation is widespread. However, here we will target relationshipsterm·key that investigators claim exist, rather than null findings. It can be proven that most claimed research findingsterm·dom are falseterm·key As has been shown previously, the probabilityterm·key that a research findingterm·dom is indeed trueterm·key depends on the prior probabilityterm·stat of it being trueterm·key (before doing the study), the statistical powerterm·mth of the study, and the level of statistical significanceterm·key [ 10 , 11 ]. Consider a 2 × 2 table in which research findingsterm·dom are compared against the gold standard of trueterm·key relationshipsterm·key in a scientific field. In a researchterm·key field both trueterm·key and falseterm·key hypotheses can be made about the presence of relationshipsterm·key. Let Rterm·def be the ratio of the number of “trueterm·key relationshipsterm·key” to “no relationshipsterm·key” among those tested in the field. Rterm·def is characteristic of the field and can vary a lot depending on whether the field targets highly likely relationshipsterm·key or searches for only one or a few trueterm·key relationshipsterm·key 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 trueterm·key relationshipterm·key (among many that can be hypothesized) or the powerterm·key is similar to find any of the several existing trueterm·key relationshipsterm·key. The pre-study probabilityterm of a relationshipterm·key being trueterm·key is Rterm·def /( Rterm·def + 1). The probabilityterm·key of a study finding a trueterm·key relationshipterm·key reflects the powerterm·key 1 - β (one minus the Type II error rateterm). The probabilityterm·key of claiming a relationshipterm·key when none truly exists reflects the Type I error rateterm, α. Assuming that c relationshipsterm·key are being probed in the field, the expected values of the 2 × 2 table are given in Table 1 . After a research findingterm·dom has been claimed based on achieving formal statistical significanceterm·key, the post-study probabilityterm·key that it is trueterm·key is the positive predictive valueterm·mth, PPVterm. The PPVterm is also the complementary probabilityterm·key of what Wacholder et al. have called the false positive report probabilityterm·mth [ 10 ]. According to the 2 × 2 table, one gets PPVterm = (1 - β) Rterm·def /( Rterm·def - βRterm·def + α). A research findingterm·dom is thus more likely trueterm·key than falseterm·key if (1 - β) Rterm·def > α. Since usually the vast majority of investigators depend on a = 0.05, this means that a research findingterm·dom is more likely trueterm·key than falseterm·key if (1 - β) Rterm·def > 0.05. Table 1 Research Findingsterm·dom and Trueterm·key Relationshipsterm·key What is less well appreciated is that biasterm·dom 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 findingsterm·dom being indeed trueterm·key. We will try to model these two factors in the context of similar 2 × 2 tables. Biasterm·dom First, let us define biasterm·dom as the combination of various design, data, analysis, and presentation factors that tend to produce research findingsterm·dom when they should not be produced. Let u be the proportion of probed analyses that would not have been “research findingsterm·dom,” but nevertheless end up presented and reported as such, because of biasterm·dom. Biasterm·dom should not be confused with chance variability that causes some findings to be falseterm·key by chance even though the study design, data, analysis, and presentation are perfect. Biasterm·dom can entail manipulation in the analysis or reporting of findings. Selective or distorted reporting is a typical form of such biasterm·dom. We may assume that u does not depend on whether a trueterm·key relationshipterm·key exists or not. This is not an unreasonable assumption, since typically it is impossible to know which relationshipsterm·key are indeed trueterm·key. In the presence of biasterm·dom ( Table 2 ), one gets PPVterm = ([1 - β] Rterm·def + u β Rterm·def )/( Rterm·def + α − β Rterm·def + u − u α + u β Rterm·def ), and PPVterm decreases with increasing u , unless 1 − β ≤ α, i.e., 1 − β ≤ 0.05 for most situations. Thus, with increasing biasterm·dom, the chances that a research findingterm·dom is trueterm·key diminish considerably. This is shown for different levels of powerterm·key and for different pre-study oddsterm·key in Figure 1 . Conversely, trueterm·key research findingsterm·dom may occasionally be annulled because of reverse biasterm·dom. For example, with large measurement errors relationshipsterm·key are lost in noise [ 12 ], or investigators use data inefficiently or fail to notice statistically significant relationshipsterm·key, or there may be conflicts of interest that tend to “bury” significant findings [ 13 ]. There is no good large-scale empirical evidence on how frequently such reverse biasterm·dom may occur across diverse researchterm·key fields. However, it is probably fair to say that reverse biasterm·dom 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 biasterm·dom may be modeled in the same way as biasterm·dom above. Also reverse biasterm·dom should not be confused with chance variability that may lead to missing a trueterm·key relationshipterm·key because of chance. Figure 1 PPVterm (Probabilityterm·key That a Research Findingterm·dom Is Trueterm·key) as a Function of the Pre-Study Oddsterm·key for Various Levels of Biasterm·dom, u Panels correspond to powerterm·key of 0.20, 0.50, and 0.80. Table 2 Research Findingsterm·dom and Trueterm·key Relationshipsterm·key in the Presence of Biasterm·dom Testing by Several Independent Teams Several independent teams may be addressing the same sets of researchterm·key questions. As researchterm·key efforts are globalized, it is practically the rule that several researchterm·key 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 researchterm·key experiments in isolation. An increasing number of questions have at least one study claiming a research findingterm·dom, and this receives unilateral attention. The probabilityterm·key that at least one study, among several done on the same question, claims a statistically significant research findingterm·dom is easy to estimate. For n independent studiesterm·key of equal powerterm·key, the 2 × 2 table is shown in Table 3 : PPVterm = Rterm·def (1 − β n )/( Rterm·def + 1 − [1 − α] n − Rterm·def β n ) (not considering biasterm·dom). With increasing number of independent studiesterm·key, PPVterm tends to decrease, unless 1 - β < a, i.e., typically 1 − β < 0.05. This is shown for different levels of powerterm·key and for different pre-study oddsterm·key in Figure 2 . For n studiesterm·key of different powerterm·key, the term β n is replaced by the product of the terms β i for i = 1 to n , but inferences are similar. Figure 2 PPVterm (Probabilityterm·key That a Research Findingterm·dom Is Trueterm·key) as a Function of the Pre-Study Oddsterm·key for Various Numbers of Conducted Studiesterm·key, n Panels correspond to powerterm·key of 0.20, 0.50, and 0.80. Table 3 Research Findingsterm·dom and Trueterm·key Relationshipsterm·key in the Presence of Multiple Studiesterm·key Corollaries A practical example is shown in Box 1 . Based on the above considerations, one may deduce several interesting corollaries about the probabilityterm·key that a research findingterm·dom is indeed trueterm·key. Box 1. An Example: Science at Low Pre-Study Oddsterm·key 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 ratiosterm·stat around 1.3 for the ten or so polymorphisms and with a fairly similar powerterm·key to identify any of them. Then Rterm·def = 10/100,000 = 10 −4 , and the pre-study probabilityterm for any polymorphism to be associated with schizophrenia is also Rterm·def /( Rterm·def + 1) = 10 −4 . Let us also suppose that the study has 60% powerterm·key to find an association with an odds ratioterm·stat of 1.3 at α = 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 probabilityterm·key that this is trueterm·key increases about 12-fold compared with the pre-study probabilityterm, 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 relationshipsterm·key 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 dredgingterm. In the presence of biasterm·dom with u = 0.10, the post-study probabilityterm·key that a research findingterm·dom is trueterm·key is only 4.4 × 10 −4 . Furthermore, even in the absence of any biasterm·dom, when ten independent researchterm·key teams perform similar experiments around the world, if one of them finds a formally statistically significant association, the probabilityterm·key that the research findingterm·dom is trueterm·key is only 1.5 × 10 −4 , hardly any higher than the probabilityterm·key we had before any of this extensive researchterm·key was undertaken! Corollary 1: The smaller the studiesterm·key conducted in a scientific field, the less likely the research findingsterm·dom are to be trueterm·key. Small sample sizeterm·var means smaller powerterm·key and, for all functions above, the PPVterm for a trueterm·key research findingterm·dom decreases as powerterm·key decreases towards 1 − β = 0.05. Thus, other factors being equal, research findingsterm·dom are more likely trueterm·key in scientific fields that undertake large studiesterm·key, such as randomized controlled trials in cardiology (several thousand subjects randomized) [ 14 ] than in scientific fields with small studiesterm·key, such as most researchterm·key of molecular predictors (sample sizesterm·var 100-fold smaller) [ 15 ]. Corollary 2: The smaller the effect sizesterm·stat in a scientific field, the less likely the research findingsterm·dom are to be trueterm·key. Powerterm·key is also related to the effect sizeterm·stat. Thus research findingsterm·dom are more likely trueterm·key 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) [ 7 ]. Modern epidemiology is increasingly obliged to target smaller effect sizesterm·stat [ 16 ]. Consequently, the proportion of trueterm·key research findingsterm·dom is expected to decrease. In the same line of thinking, if the trueterm·key effect sizesterm·stat are very small in a scientific field, this field is likely to be plagued by almost ubiquitous falseterm·key positive claims. For example, if the majority of trueterm·key 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 relationshipsterm·key in a scientific field, the less likely the research findingsterm·dom are to be trueterm·key. As shown above, the post-study probabilityterm·key that a finding is trueterm·key (PPVterm) depends a lot on the pre-study oddsterm·key (Rterm·def) . Thus, research findingsterm·dom are more likely trueterm·key in confirmatory designsterm, such as large phase III randomized controlled trials, or meta-analyses thereof, than in hypothesis-generating experimentsterm. Fields considered highly informative and creative given the wealth of the assembled and tested information, such as microarrays and other high-throughput discovery-oriented researchterm·key [ 4 , 8 , 17 ], should have extremely low PPVterm. Corollary 4: The greater the flexibility in designs, definitions, outcomes, and analytical modes in a scientific field, the less likely the research findingsterm·dom are to be trueterm·key. Flexibility increases the potential for transforming what would be “negative” results into “positive” results, i.e., biasterm·dom, u . For several researchterm·key designs, e.g., randomized controlled trials [ 18–20 ] or meta-analyses [ 21 , 22 ], there have been efforts to standardize their conduct and reporting. Adherence to common standards is likely to increase the proportion of trueterm·key findings. The same applies to outcomes. Trueterm·key 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) [ 23 ]. Similarly, fields that use commonly agreed, stereotyped analytical methods (e.g., Kaplan-Meier plots and the log-rank test) [ 24 ] may yield a larger proportion of trueterm·key 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 researchterm·key designs, biasterm·dom seems to be a major problem. For example, there is strong evidence that selective outcome reportingterm, 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 problem go away. Corollary 5: The greater the financial and other interests and prejudices in a scientific field, the less likely the research findingsterm·dom are to be trueterm·key. Conflicts of interest and prejudice may increase biasterm·dom, u . Conflicts of interest are very common in biomedical researchterm·key [ 26 ], and typically they are inadequately and sparsely reported [ 26 , 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 studiesterm·key 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 falseterm·key 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 findingsterm·dom are to be trueterm·key. This seemingly paradoxical corollary follows because, as stated above, the PPVterm 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 phenomenonterm has been coined to describe this phenomenon of rapidly alternating extreme researchterm·key 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 trueterm·key effect sizesterm·stat are perceived to be small may be more likely to perform large studiesterm·key than investigators working in fields where trueterm·key effect sizesterm·stat are perceived to be large. Or prejudice may prevail in a hot scientific field, further undermining the predictive value of its research findingsterm·dom. 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 studiesterm·key and improved standards of researchterm·key, enhancing the predictive value of its research findingsterm·dom. Or massive discovery-oriented testing may result in such a large yield of significant relationshipsterm·key that investigators have enough to report and search further and thus refrain from data dredgingterm and manipulation. Most Research Findingsterm·dom Are Falseterm·key for Most Researchterm·key Designs and for Most Fields In the described framework, a PPVterm exceeding 50% is quite difficult to get. Table 4 provides the results of simulationsterm·mth using the formulas developed for the influence of powerterm·key, ratio of trueterm·key to non-true relationshipsterm·key, and biasterm·dom, 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 trueterm·key about 85% of the time. A fairly similar performance is expected of a confirmatory meta-analysis of good-quality randomized trials: potential biasterm·dom probably increases, but powerterm·key and pre-test chances are higher compared to a single randomized trial. Conversely, a meta-analytic finding from inconclusive studiesterm·key where pooling is used to “correct” the low powerterm·key of single studiesterm·key, is probably falseterm·key if Rterm·def ≤ 1:3. Research findingsterm·dom from underpowered, early-phase clinical trials would be trueterm·key about one in four times, or even less frequently if biasterm·dom is present. Epidemiological studiesterm·key of an exploratory nature perform even worse, especially when underpowered, but even well-powered epidemiological studiesterm·key may have only a one in five chance being trueterm·key, if Rterm·def = 1:10. Finally, in discovery-oriented researchterm·key with massive testing, where tested relationshipsterm·key exceed trueterm·key ones 1,000-fold (e.g., 30,000 genes tested, of which 30 may be the trueterm·key culprits) [ 30 , 31 ], PPVterm for each claimed relationshipterm·key is extremely low, even with considerable standardization of laboratory and statistical methods, outcomes, and reporting thereof to minimize biasterm·dom. Table 4 PPVterm of Research Findingsterm·dom for Various Combinations of Powerterm·key (1 - ß), Ratio of Trueterm·key to Not-True Relationshipsterm·key (Rterm·def) , and Biasterm·dom (u) The estimated PPVsterm (positive predictive valuesterm·mth) are derived assuming a = 0.05 for a single study. RCT, randomized controlled trial. Claimed Research Findingsterm·dom May Often Be Simply Accurate Measures of the Prevailing Biasterm·dom As shown, the majority of modern biomedical researchterm·key is operating in areas with very low preand post-study probabilityterm·key for trueterm·key findings. Let us suppose that in a researchterm·key field there are no trueterm·key 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 trueterm·key scientific information, at least based on our current understanding. In such a “null fieldterm,” one would ideally expect all observed effect sizesterm·stat to vary by chance around the null in the absence of biasterm·dom. The extent that observed findings deviate from what is expected by chance alone would be simply a pure measure of the prevailing biasterm·dom. 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 sizesterm·stat are simply measuring nothing else but the net biasterm·dom that has been involved in the generation of this scientific literature. Claimed effect sizesterm·stat are in fact the most accurate estimates of the net biasterm·dom. It even follows that between “null fieldsterm,” the fields that claim stronger effects (often with accompanying claims of medical or public health importance) are simply those that have sustained the worst biasesterm·dom. For fields with very low PPVterm, the few trueterm·key relationshipsterm·key would not distort this overall picture much. Even if a few relationshipsterm·key are trueterm·key, the shape of the distribution of the observed effects would still yield a clear measure of the biasesterm·dom 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 biasterm·dom in most fields of modern researchterm·key. 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 fieldterm.” 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 biasterm·dom in one field may also be useful for obtaining insight into what might be the range of biasterm·dom 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 findingsterm·dom are falseterm·key, 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 researchterm·key question. In this regard, the pure “gold” standard is unattainable. However, there are several approaches to improve the post-study probabilityterm·key. Better powered evidence, e.g., large studiesterm·key or low-bias meta-analyses, may help, as it comes closer to the unknown “gold” standard. However, large studiesterm·key may still have biasesterm·dom and these should be acknowledged and avoided. Moreover, large-scale evidence is impossible to obtain for all of the millions and trillions of researchterm·key questions posed in current researchterm·key. Large-scale evidence should be targeted for researchterm·key questions where the pre-study probabilityterm is already considerably high, so that a significant research findingterm·dom will lead to a post-test probabilityterm·key 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 studiesterm·key based on narrow-minded criteria, such as the marketing promotion of a specific drug, is largely wasted researchterm·key. Moreover, one should be cautious that extremely large studiesterm·key may be more likely to find a formally statistical significant difference for a trivial effect that is not really meaningfully different from the null [ 32–34 ]. Second, most researchterm·key 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 biasterm·dom through enhanced researchterm·key 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 researchterm·key designs, efforts may also be more successful with upfront registration of studiesterm, e.g., randomized trials [ 35 ]. Registration would pose a challenge for hypothesis-generating researchterm·key. 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 experimentterm. Regardless, even if we do not see a great deal of progress with registration of studiesterm·key 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 significanceterm·key, we should improve our understanding of the range of Rterm·def values—the pre-study oddsterm·key—where researchterm·key efforts operate [ 10 ]. Before running an experiment, investigators should consider what they believe the chances are that they are testing a trueterm·key rather than a non-true relationshipterm·key. Speculated high Rterm·def values may sometimes then be ascertained. As described above, whenever ethically acceptable, large studiesterm·key with minimal biasterm·dom should be performed on research findingsterm·dom that are considered relatively established, to see how often they are indeed confirmed. I suspect several established “classics” will fail the test [ 36 ]. Nevertheless, most new discoveries will continue to stem from hypothesis-generating researchterm·key with low or very low pre-study oddsterm·key. We should then acknowledge that statistical significanceterm·key 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 testingterm·stat corrections [ 37 ], usually it is impossible to decipher how much data dredgingterm by the reporting authors or other researchterm·key teams has preceded a reported research findingterm·dom. Even if determining this were feasible, this would not inform us about the pre-study oddsterm·key. Thus, it is unavoidable that one should make approximate assumptions on how many relationshipsterm·key are expected to be trueterm·key among those probed across the relevant researchterm·key fields and researchterm·key designs. The wider field may yield some guidance for estimating this probabilityterm·key for the isolated researchterm·key project. Experiences from biasesterm·dom 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 researchterm·key claims and putting them in context.