Where Did 0.05 Come From? — Counting How Many Patients a Finding Rests On

Let us imagine there is a clinical trial with 100 participants. Two treatments were compared and the result was p = 0.006. The p-value is a number that shows how often a difference this large or larger would happen by chance if there were no effect at all. This value is well below 0.05, which is commonly used as the cutoff. The paper states that "there was a significant difference," and anyone who sees this number feels the conclusion is quite solid.

However, if an event had occurred in just 4 patients to whom nothing happened in this trial, the p-value would exceed 0.05. This means that even if the results of just 4 patients had been different, "significance" would vanish. The minimum number of people whose changed outcomes make significance disappear in this way is the first term of this article, the fragility index.

This trial is not a real trial. It is a hypothetical example created by a paper to make the calculation visible. And that paper created this example to criticize how this number is used (PMID 38777001). That criticism is covered later in the article. This article stands inside the debate from the start.

The p-value answers only one question, and that question is not "the probability that the result is due to chance." This story was covered in "What Does "Statistically Significant" Actually Say? — The p-Value, Explained with a Coin Toss". This article deals with the two subsequent questions. Why of all things 0.05? And how many people are those results that crossed that line actually resting on?

The new terms you will learn in this article are five, and each term is explained where it first appears.

⚠️ The names of diseases and procedures that appear below are name tags that tell us how many trials in which fields were counted. They are not judgments on whether a treatment is good or bad.

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0.05 is Not a Value Derived from Calculation

0.05 is not a constant of nature, nor is it a value derived from solving an equation. It is a custom that solidified because people kept using it. One review briefly summarizing the history of the p-value describes the process like this: practitioners very quickly found a simple method that worked well for them, and statisticians saw no particular reason to suppress that enthusiasm because everyone seemed to agree (PMID 41748420).

The same review calls 0.05 an "arbitrary yet sacred" threshold. And it summarizes the pitfalls of the p<0.05 convention into five points: a dichotomy that forces results into black and white, the likelihood of claiming an effect exists when it does not, the failure to indicate how large the effect is, the failure to indicate whether the difference is meaningful to patients, and the use of the result divorced from context. The conclusion of the review is not to discard the p-value. What should be discarded is the threshold of 0.05 and the term "statistical significance" (PMID 41748420).

The first pitfall, the dichotomy, leads to the second term of this article. Dichotomization is the act of cutting continuous numbers at a certain line to make two compartments. It is like measuring height and dividing people into "170 cm and taller" and "shorter than that." In the p-value, the cutting line is 0.05, and the names of the two compartments are "significant" and "not significant." Once cut, 0.049 and 0.051 fall into different compartments, while 0.049 and 0.001 fall into the same compartment.

Those who want to eliminate the threshold place special emphasis on a single number. To read that number, a third term is needed. Statistical power is the probability of catching an effect as "significant" when it truly exists. When designing a test, 80% is often set as the target. This means that if you run the same test five times, you will catch the effect four times.

Even at that favorable 80%, it is common for the results of two studies to conflict. There is a one-in-three chance that a true effect exists, yet one study is significant and the other is not (PMID 28698825). This means that even if you measure the same effect twice, one out of three times it will split into "present" and "absent."

The conclusion of this paper is to eliminate the fixed threshold. Instead, it suggests reading the p-value as a continuous scale. What that scale represents is how strong the evidence is against the assumption that "there is no difference." In statistics, this assumption is called the null hypothesis. The authors write that this reading aligns with the recommendation of the late Ronald Fisher (PMID 28698825).

The same paper reviews opposing arguments side by side. There are three opposing arguments: that decision rules should instead be made stricter, that eliminating the threshold could reduce sample sizes, and that it is better to discard the p-value altogether. After reviewing these three, the authors do not choose which method is right. The authors' conclusion is that no matter what inference method is used, dichotomous threshold thinking must yield to human judgment (PMID 28698825). The earlier review, which argued for discarding 0.05, also puts "stricter thresholds" on its list of alternatives (PMID 41748420).

There is also a review that directly defends maintaining the threshold. The argument is that clinical research needs dichotomous answers to guide decision-making, and this is especially true in diagnostic imaging and interventional procedures. It opposes the proposal to lower the threshold to 0.005. The reason is that doing so would increase research costs and could reduce grant-free, investigator-initiated research (PMID 32157489).

This review suggests leaving 0.05 as it is. It argues that the false discoveries and replication failures accompanying that threshold are better reduced by other methods rather than lowering the threshold. Those methods are secondary evidence such as systematic reviews and meta-analyses, data sharing, and cost-effectiveness analyses. And it adds that when reporting p-values, one should write the actual value rather than just "p < 0.05" (PMID 32157489).

Actual proposals diverge like this. One side argues for abolishing the threshold altogether (PMID 28698825, PMID 41748420). The other side argues for adding other criteria rather than erasing the threshold where decisions are at stake. An example of the latter is a proof-of-concept trial in new drug development. A proof-of-concept trial is a test to determine whether to continue or stop the development of a new drug. A paper addressing this problem considers it inappropriate to establish criteria based solely on significance testing in such settings. Therefore, it restructures the criteria within a Bayesian framework and proposes a dual criterion that requires both being better than the control group and having an effect size large enough to be meaningful (PMID 30222466).

This article does not say that "0.05 must be discarded." 0.05 is an agreed-upon convention, and whether to maintain that convention is still debated today. There is also something that both camps demand in common. The abolitionist side suggests reading the magnitude of the effect and its plausible range together, instead of two compartments: significant and non-significant (PMID 41748420, PMID 28698825). The retentionist side demands that one write the actual value, not just "p<0.05" (PMID 32157489).

The Fragility Index — How Many People Make Significance Disappear?

It is hard to get a feel for how different p=0.04 and p=0.06 are by just looking at the numbers. The fragility index was created to translate this difference into a number of people. The fragility index is the minimum number of participants in one group whose outcome must change from "no event" to "event" for the statistical significance of the result to disappear. The smaller the number, the more the conclusion rests on just a few people. In the earlier example of 100 people, this value was 4.

What this index counts is the number of people it takes for significance to disappear. It is not the number of people it takes for the conclusion to flip in the opposite direction. Once p goes over 0.05, the label "significant" simply falls off; the direction of the effect does not reverse.

This value has a narrow range of usable settings. In trials that divide two groups in half and count outcomes as either present or absent, it can only be calculated for results that fit those criteria (PMID 31822121). There were 407 randomized trials cited by the acute coronary syndrome clinical guidelines. Among them, 132 trials (32.4%) met this condition and also had significant results (P < 0.05), allowing this value to be calculated (PMID 36882068). At least within the evidence base for these guidelines, the fragility index was applicable to only about a third of the trials.

The paper that coined the name "fragility index" produced the central numbers for this article. This paper reviewed 399 randomized controlled trials from heavily cited major medical journals that reported at least one significant result in their abstract. The median fragility index was 8, with a range of 0 to 109. One-quarter had a value of 3 or less. This means that in one out of four studies, "significance" would have vanished even if the outcomes of just three patients had been different.

The same paper noted one more thing. People who lose touch with researchers during a study and whose outcomes become unknown are called loss to follow-up. In 53% of all trials, the fragility index was smaller than the number of participants lost to follow-up (PMID 24508144). This means there were more people with unknown outcomes than the number of people needed to erase statistical significance. However, placing these two numbers side by side for a direct comparison is currently criticized as inappropriate. That criticism is covered later in the article.

How Much Does It Vary by Field?

This calculation has spread to several fields. The table below reports the values from the trials collected by each study. Since each study reviewed a different number of trials, a study looking at 6 papers cannot be given the same weight as one looking at 1,007 papers. And these values inherently apply only to trials that yielded a significant result. The numbers in parentheses are the ranges spanned by the middle half when the trials are lined up in order of their index.

† The ischemic stroke row is a case where the authors interpreted their own value as relatively robust. The authors noted that the median of 7 was higher than the 2.5 of other clinical fields, and concluded with "many trials in this field possess a level of robustness that is respectable compared to other fields" (PMID 30765294).

There is also one row omitted from the table. A study reviewing 13 shoulder arthroplasty papers described a median of 6 as "a value higher than other orthopedic subspecialties." However, that value was calculated using individual outcomes rather than individual trials as the unit, and 89.7% of those outcomes were non-significant to begin with. Because the unit differed, it was excluded from the table (PMID 33271323).

The numbers in the table are the reported values of each study, and how those values should be read varies from paper to paper. The patent foramen ovale closure row is a case read in the opposite direction of the ischemic stroke row. Based on this value, the authors concluded that "recent positive results should be interpreted with caution due to their fragile nature, and individualized decision-making is important" (PMID 30890394).

It Is Getting Better

The median of 12 in the top row of the table is a significantly improved value compared to 8 in the same journals 10 years ago (p<0.001). However, the lower end of the middle half remains unchanged at 3. Even now, a quarter of the trials have their significance hanging on 3 or fewer events (PMID 35820586).

The same paper also conducted an umbrella review. An umbrella review is a review that gathers multiple systematic reviews back together. This umbrella review gathered 57 systematic reviews across 15 medical specialties, with each specialty containing between 10 and 692 trials. Across all specialties, the median fragility index was between 2 and 4 (PMID 35820586).

There is one property of the fragility index to know in advance. The fragility index is strongly intertwined with the p-value. In 66 trials on preterm infants, the correlation coefficient between the index and the p-value was −0.857 (PMID 35615631). This means that trials with smaller p-values tended to have larger fragility indices. This entanglement is the starting point for the criticisms that follow.

"No difference" also depends on how many people

The same calculation can be run in the reverse direction. The reverse-fragility index is the minimum number of people needed to turn a non-significant result into a significant one. The math and meaning are the same, just in reverse, so the name is flipped too.

There is a study that looked at 40 randomized trials in plastic surgery that reported no difference. The primary outcomes of these trials—meaning the outcomes the researchers predetermined as most important—numbered 65. The median sample size was 76 people, and the median number of events was 10. The median reverse-fragility index was 4. This means half of the results would have become "significant" even if just four participants' event statuses had been different (PMID 39850534).

An additional fact pointed out by the same study is more important. Out of the 40 trials, 21 did not perform a power analysis at all. A power analysis is the work of calculating in advance how many people are needed to match the statistical power we looked at earlier to a target level. The authors' conclusion is that these "no differences" rest on a small number of events, and that this metric complements the p-value (PMID 39850534).

In trials using steroids and antivirals together for Bell's palsy, you can see both directions side by side. Across 11 trials, there were 57 recovery-related outcomes. Among them, 7 outcomes were significant, and their mean fragility index was 2.714. Fifty outcomes were non-significant, and their mean reverse-fragility index was 5.960. The authors' conclusion is that the evidence for this combination therapy shows mixed effects and high fragility, especially on the side that was significant, and therefore more robust studies are needed (PMID 40741786).

A low fragility index means "this data alone is not enough to say anything firmly on either side." It does not mean "that treatment does not work."

But the Fragility Index Itself Is Under Debate

Literature criticizing the fragility index also exists side by side, and some target the calculation method cited above itself. The largest-scale criticism came from a simulation. It is a study that created and analyzed 300,000 virtual randomized trials by computer within common trial condition ranges. The result is twofold.

First, a single p-value explained 79.8% of the reason why fragility indices differ from trial to trial (71.9% in the reverse-fragility index). This means that whether the index is large or small comes mostly from the largeness or smallness of the p-value. The authors' conclusion is that the fragility metric is a mathematical reflection of sample size, event count, and p-value, not an independent measure of robustness.

Second is the comparison with loss to follow-up. When calculating how many people are needed to actually lose significance by putting people who lost contact back into the data, that number was larger than the index in 84.9% of cases. In the reverse direction, it was 95.5%. This means it cannot be seen that significance disappears simply because the number of lost-to-follow-up individuals is greater than the index. Therefore, the authors conclude that directly comparing the fragility index and the number of lost-to-follow-up individuals is statistically inappropriate and should be avoided in the future (PMID 42605132).

The same point came out in a literature audit. A literature audit is a study that gathers and checks the descriptions of already published papers. There were 39 studies that used this index in orthopedics. Among them, 37 (95%) directly compared the index with the number of lost-to-follow-up individuals, and among those, 22 (59%) had inaccurate or misleading statements (PMID 38777001).

The hypothetical trial of 100 people that opened this article came from this audit. In that trial with p=0.006 and an index of 4, for significance to actually disappear, 7 lost-to-follow-up patients had to be put back in. It is almost twice the index. This is because flipping the result of an existing patient and newly bringing in a patient who lost contact do not move the p-value by the same magnitude (PMID 38777001).

The conclusion of this paper is as follows. The claim that "if the number of lost-to-follow-up individuals exceeds the fragility index, the trial may lose significance" is frequently inaccurate, and such claims are rampant in orthopedics. Trials may not be as fragile as previous fragility reviews claimed. However, the authors immediately add: the value of any individual trial can only be judged by a holistic approach that looks at the context in which the trial was performed, potential biases, and results together (PMID 38777001).

There Are Also Robust Trials

There are fields with large fragility indices. In the pain outcomes of 30 randomized trials of spinal cord stimulation, the median was 5.45, and the authors concluded that the majority were robust trials (PMID 41376548).

How to use this metric is well illustrated by two heart failure trials. The participants were heart failure patients whose heart's pumping strength was preserved or only slightly reduced, and the trials are EMPEROR-Preserved and DELIVER, which used SGLT2 inhibitors. The authors of the study reviewing these trials first wrote this in the background: This drug reduces cardiovascular death and heart failure hospitalization across all heart failure types. However, in these two types, the magnitude and robustness of the benefit are not large (PMID 41314931).

The numbers are as follows. In the combined outcome of heart failure hospitalization and cardiovascular death, the fragility indices were 37 and 41. For heart failure hospitalization alone, they were 37 and 46. Both are robust values. However, in the same trials, the values for mortality were 10 or lower. Even within the same trial, robustness diverges like this depending on which outcome you look at. The authors' conclusion is that while this drug consistently reduces heart failure hospitalization, the robustness of the mortality benefit in these two groups remains uncertain (PMID 41314931).

Going a step further, a proposal has also emerged to place evidence side by side along three axes. The three axes are the p-value, fragility, and robustness. Here, robustness means how far the result is from "no effect." This proposal gathered 129 two-group trials with yes/no outcomes across 15 medical specialties, and compared them against 720,000 simulated trials. Among these, 77 trials were significant. Of those, 30 trials (39.0%) passed all three criteria, and 61.0% (47 trials) were fragile (PMID 41480455).

A qualifier is attached to this result. These simulated trials are randomly generated without factoring in publication bias or selective reporting. And the authors also explicitly state that this framework only grades the evidence and does not prove whether it is true, causal, or reproducible (PMID 41480455).

This proposal did not eliminate 0.05. It left p ≤ 0.05 as one of the three criteria, and erected two more criteria beside it.

So How Should We Use It?

After hearing all the criticisms, the place for this tool actually becomes clearer. The fragility index provides no new information about robustness. Most of its value is calculated from the p-value, sample size, and event counts (PMID 42605132). The common interpretation of comparing the index as if it were the number of lost-to-follow-up patients is also frequently inaccurate. According to the authors, the two are not the same (PMID 38777001).

What the fragility index does is translate the same information into units that humans can intuitively grasp. We have no intuition for "p=0.04," but we do for "three patients." That is also why studies calculating this metric write that it should be "reported alongside the p-value" (PMID 24508144, PMID 35820586). The reason this article brought up this index is the same. Not to judge, but to make visible just how thin a surface the sentence p<0.05 can stand on.

Common Misconceptions: Two

① "0.049 and 0.051 Belong to Different Worlds"

This misconception stems from the dichotomization we saw earlier. Once cut, the two values fall into different boxes, but there is no cliff between them. The rationale for abolishing thresholds also comes from here. If statistical power is not ideal, the effect size of a result that turns out significant is inflated far beyond reality. Interpreting only that inflated result while ignoring nonsignificant findings leads to false conclusions (PMID 28698825).

Therefore, this paper also outlines how to read large p-values. Even a large p-value is some evidence against the assumption that "there is no difference." Thus, a large p-value cannot be flipped into grounds supporting that assumption to conclude that "there is no effect" (PMID 28698825).

Here the fourth term appears. Replication is the act of re-running the same study. Let us lay out the numbers from earlier again. Even at 80% power, the probability that two studies will disagree is one-third. Therefore, one cannot interpret a re-run study as a failure of replication simply because it is nonsignificant (PMID 28698825).

② "A Single Significant Result Is the Truth"

Because the literature in this section refutes one another, reading just one side leads to the exact opposite conclusion. The starting point is a famous paper. This paper established a framework where the probability that a research claim is true depends on several factors. These are statistical power, bias, the number of other studies addressing the same question, and above all, the proportion of true relationships among those tested in the field (PMID 16060722).

According to this framework, several conditions lower the probability of being true. The smaller the study, the smaller the effect size, the more relationships tested and the less pre-selection, the more so. The greater the flexibility in design, definitions, outcomes, and analytical methods, and the greater the financial and other interests, the more so. Based on simulations, this essay concludes that under most designs and circumstances, a research claim is more likely false than true (PMID 16060722). The rebuttals that follow are aimed directly at this conclusion.

The practice introduced to reduce the "flexibility" in that list is the fifth term. Preregistration is the act of recording in advance in a public place what will be measured and how it will be analyzed, before looking at the data. Recording it in advance makes it difficult to choose analyses after seeing the results.

That paper was the beginning of a debate, and the debate has continued ever since. The same author later shifted the topic to "how to make more published research true" (PMID 25334033). An attempt to calculate what percentage of published papers are false findings met with a direct rebuttal. The rebuttal argued that all three levels—sampling, calculation, and conclusion—were flawed (PMID 24068251).

The rationale of this rebuttal touches upon the theme of this article. It argues that the p-values reported in paper abstracts are a severely distorted selected sample. Besides selective reporting, several causes make non-existent effects appear real. Especially in observational studies, unmeasured alternative causes shaking up the results is one such case. The gist of the rebuttal is that such calculations ignore these causes (PMID 24068251).

There is also an opposing camp. A paper directly rebutting medical nihilism argues that the proposition that "most published research findings are false" and the nihilistic discussion following it rest on an untenable account of the nature of facts. Any knowledge can be wrong, and knowledge finds its footing through verification by many people. Properly factoring these two things in leads first to the question: why on earth would anyone expect a single quantitative study to be irrefutably true in the first place? (PMID 33218468)

These authors agree with the flaws in the research system pointed out by the earlier paper and call for reforms. At the same time, they conclude that nihilism is not a natural consequence of the current state of research (PMID 33218468).

The lesson left by this section is that a single p-value is a single coin toss. This does not mean one should not trust papers.

Honest Unresolved Questions

① Should we eliminate the threshold? This article does not answer this question. We laid out the arguments for those who say to eliminate it (PMID 28698825, PMID 41748420) and those who say to keep it (PMID 32157489) side by side in front of you. In between them are proposals to add axes (PMID 41480455) and proposals to redraw decision rules (PMID 30222466). Neither side has won yet.

② New tools are also misunderstood. The fragility index is a case in point. An index created to translate into units humans can perceive spread through improper comparisons against the number of lost-to-follow-up participants. That is why two methodological papers emerged saying "do not make this comparison" (PMID 42605132, PMID 38777001). This means changing the tool may not be the problem that solves it. What we hold in our hands right now is not a verdict, but an auxiliary scale.

To Go Deeper

There are three things to ask when you encounter "there was a significant difference" in a paper.

1. Are the exact p-value and the size of the effect written down. Just having "p<0.05" written is different from having "p=0.048" written (PMID 32157489). How large the effect is and its plausible range cannot be known from the p-value alone (PMID 41748420, PMID 28698825).
2. How many events were there. Even without a fragility index, the number of events and sample size are usually written, and when events are few, the conclusion is thin (PMID 24508144, PMID 35820586). However, there is criticism that comparing those values 1:1 with lost-to-follow-up numbers is inappropriate (PMID 38777001, PMID 42605132).
3. Is it one paper, or multiple papers. A single p-value is a single table. There is a separate way to group and look at multiple papers. You can also look together at whether that study wrote down in advance what and how it would look (pre-registration).

If you leave behind just one thing — 0.05 is not a line set by nature, but a line agreed upon by people. The fact that it crossed that line makes sense only when read together with how many events the result stands on. The fragility index is merely one way to count those "several events," not a verdict.

Source Papers

The 0.05 Threshold and Its Debate

• "Goodbye P<0.05." (2026) — PMID 41748420 — A short review. What is being thrown away is not the p-value, but the threshold and the term "statistical significance," and the list of alternatives also includes "stricter thresholds."
• "The earth is flat (p > 0.05)." (2017) — PMID 28698825 — Review and argument. The authors directly list three counterarguments against removing the threshold, and the final conclusion is that regardless of the inference method used, dichotomous threshold thinking must yield to human judgment.
• "Statistical significance: p value, 0.05 threshold… reasons for a conservative approach." (2020) — PMID 32157489 — An overview of the threshold-maintenance position. The alternative is not threshold adjustment, but secondary evidence, data sharing, and cost-effectiveness analysis. It demands that actual p-values be written down.
• "Bayesian Design of Proof-of-Concept Trials." (2015) — PMID 30222466 — A methodology paper (applied to 2 cases of cystic fibrosis and psoriasis). It redesigns GO/NO-GO criteria within a Bayesian framework.

The Prototype, Scope of Application, and Field-Specific Measurements of the Fragility Index

• "…a case for a Fragility Index." (2014) — PMID 24508144 — The original methodological paper. The targets are 399 randomized trials in high-impact journals that reported at least one significant binary or survival outcome in the abstract. The conclusion is "It complements P values."
• "Statistical robustness … has improved but was low across medical specialties." (2022) — PMID 35820586 — Out of 2,544 papers, only the 643 that reported significant binary superiority outcomes were calculated. The umbrella review covers 57 literature reviews across 15 medical specialties.
• "Fragility Index in Cardiovascular RCTs." (2019) — PMID 31822121 — 123 papers with samples exceeding 500 people. It specifies that it can only be used for outcomes counted as present/absent.
• "…RCTs supporting clinical practice guidelines for acute coronary syndrome." (2023) — PMID 36882068 — 132 papers meeting the calculation conditions (two groups, 1:1 allocation, binary outcome, P<0.05). The conclusion is that it can be useful for evaluating the robustness of trials supporting guidelines.
• "Fragility Index in RCTs of Ischemic Stroke." (2019) — PMID 30765294 — 25 papers. The conclusion is that many trials in this field have a decent level of robustness compared to other fields.
• "Statistical fragility of RCTs in shoulder arthroplasty." (2021) — PMID 33271323 — 13 papers. Outcome unit aggregation, 74.4% of outcomes had an index < loss to follow-up, and 89.7% were non-significant to begin with. The conclusion is a similar level of robustness. Excluded from the table because the units differ.
• "The Fragility Index of RCTs for Preterm Neonates." (2022) — PMID 35615631 — 66 papers. The correlation between the index and the p-value is −0.857.
• "Predictors of Increased Fragility Index Scores…: An Umbrella Review." (2023) — PMID 36719446 — 1,007 papers reported by 50 reviews. It specifies that the value is "based on a limited sample" and urges design improvements.
• "…for Patent Foramen Ovale Closure in Cryptogenic Stroke." (2019) — PMID 30890394 — 6 papers. The conclusion is to interpret positive results cautiously and make individualized decisions.

The Reverse Direction — The Vulnerability of "No Difference"

• "Reverse Fragility Index in Plastic Surgery RCTs." (2025) — PMID 39850534 — 40 non-significant papers and 65 primary outcomes. The conclusion is that this index complements the p-value.
• "Statistical Fragility of Steroid-Antiviral Therapy for Bell's Palsy." (2025) — PMID 40741786 — 11 papers and 57 outcomes. The conclusion is that the evidence is mixed and that the significant side in particular is fragile.

Criticisms Aimed at the Fragility Index

• "…A Simulation Analysis of 300,000 Randomized Controlled Trials." (2026) — PMID 42605132 — 300,000 simulated trials. The conclusion is that the fragility index is not an independent measure of robustness and that direct comparisons with loss to follow-up are inappropriate.
• "The Number of Patients Lost to Follow-Up May Exceed the Fragility Index…" (2025) — PMID 38777001 — A literature audit of 39 papers plus a virtual trial model. The conclusion is that they may not be as fragile as previously portrayed, but that the value of an individual trial can only be judged through a holistic approach that considers context, bias, and results together.

Measurement of the Robustness Side and Suggested Uses

• "…RCTs of Spinal Cord Stimulation for Pain…" (2026) — PMID 41376548 — 30 papers, concluding that the vast majority are robust.
• "Robustness of RCT evidence for SGLT2 inhibitors in heart failure with preserved and mildly reduced ejection fraction." (2026) — PMID 41314931 — EMPEROR-Preserved and DELIVER (ejection fraction of 40% or higher). The background notes that this drug reduces cardiovascular death and heart failure hospitalization across all heart failure subtypes, and considers the absolute benefit and robustness to be small only in these two subtypes. Hazard ratios of 0.79 and 0.82, numbers needed to treat of 30 and 32.
• "Significance, Fragility, and Robustness in Clinical Trials." (2025) — PMID 41480455 — 129 papers plus 720,000 simulation trials. Author qualifiers: This only divides evidence grades and does not prove truth, causality, or reproducibility; publication bias and selective reporting were not included in the simulations; and extension to other data types has not been verified.

How to Read a Single Significant Result

• "Why most published research findings are false." (2005) — PMID 16060722 — An essay. Concludes that under most designs and settings, it is more likely for a research claim to be false than true.
• "How to make more published research true." (2014) — PMID 25334033 — A follow-up piece by the same author ("How to improve it").
• "Discussion: Why 'An estimate of the science-wise false discovery rate…' is false." (2014) — PMID 24068251 — A commentary. Critiques attempts to estimate the false discovery rate across three layers: sampling, calculation, and conclusion. (The abstract does not state who the author is.)
• "Countering medical nihilism by reconnecting facts and values." (2020) — PMID 33218468 — An argument. Agrees with flaws in the research system and calls for reform, but concludes that nihilism is not a natural consequence.