An Odds Ratio Is Not a Risk Ratio — What the 'Times More Likely' Is a Multiple Of

A paper published two numbers side by side from the same data: 4.96 and 6.4.

The data came from randomized trials comparing two bariatric surgeries. One is laparoscopic sleeve gastrectomy, and the other is laparoscopic Roux-en-Y gastric bypass. The researchers compared the incidence of gastroesophageal reflux disease between the two surgeries at 5 years postoperatively. The period for finding the trials was 2015–2024. The two numbers above came from calculating the same comparison in two ways (PMID 42291164).

The 4.96 is a risk ratio. A risk ratio is the ratio of the proportions of people who got the disease between the two groups. The 6.4 is an odds ratio. An odds ratio is a ratio made from ingredients similar to that but different, and what those ingredients are is unpacked below. The data are the same and the direction is the same, but only the magnitudes differ.

Neither of the two is wrong. The two numbers are measuring different things.

Yet in the abstract, the numbers we encounter are usually only one of the two. Moreover, they come packed in a sentence like "the risk was several times higher." The reader takes that "several times" to mean that the number of people who get it has increased that much. It is talked about as if a disease that 20 out of 100 people used to get now affects 50 people.

This article establishes how to ask what that "several times" is a multiple of.

Stated in one line from the conclusion, it is this: If an outcome is rare, the two numbers almost overlap, and if it becomes common, they drift apart. And how far they drift apart can only be known if you know how common that outcome originally was.

The new terms to learn in this article are five, and each term is unpacked at its first appearance.

⚠️ The names of diseases, surgeries, and drugs appearing below all appear only as examples to show how to read numbers. They are not judgments on which treatment is good or bad, and each number has meaning only within the design and subjects of that study.

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The Question Before Whether It Is Reliable — How Many Times What of What

Two previous articles in the Numbers from Scratch series have each tackled a question attached to a single number. "What Does "Statistically Significant" Actually Say? — The p-Value, Explained with a Coin Toss" dealt with p<0.05 in an abstract. The p-value is the probability of getting a result as far apart as this or further, assuming there is no difference at all. "How Much Does a Number Counted Once Wobble? — The Two Numbers in the Parentheses, the Confidence Interval" dealt with the parentheses behind a number. A confidence interval is a range recording how much an estimate might wobble. Both tools answer how much that number can be trusted.

The question of this article is one step before that. What is that number how many times what of what in the first place? Neither the p-value nor the confidence interval answers this question. Even if an odds ratio of 6.4 comes with a very narrow confidence interval, that 6.4 does not mean 6.4 times the risk.

Even People Who Write Papers Frequently Get Confused

The mistake of reading an odds ratio as a risk ratio does not belong solely to readers who have not studied statistics. Authors writing papers make the same mistake.

The exact definitions of the two measures are given in the next section. For now, you only need to take away this much: A risk ratio is a comparison between "chances of getting it," while an odds ratio is a comparison between the ratio of "people who got it versus people who did not." Below is data on how often these two are actually switched in real papers.

In obstetrics and gynecology papers, about one in four interpreted the odds ratio as a risk ratio without giving a reason why that was okay. The subjects investigated were 151 papers published in two obstetrics and gynecology journals between 1998 and 1999 that used the term "odds ratio." The researchers extracted the core odds ratio from each paper and recalculated the risk ratio from the same data where possible. The number of papers that could be recalculated was 107.

There are two results. In 47 out of 107 papers (44%), the two values drifted apart by more than 20%. And 39 out of 151 papers (26%) interpreted the odds ratio as if it were a risk ratio without providing a reason why that was permissible. The authors also note in the results section that the odds ratio makes the effect look larger compared to the risk ratio. The authors' conclusion is straightforward — odds ratios are frequently used and frequently misunderstood (PMID 11576589).

The results of directly asking people who write papers are similar. An international survey was conducted by randomly selecting corresponding authors of papers indexed in PubMed and giving them four multiple-choice questions containing clinical scenarios. The completed responses numbered 315 (participation rate 39.4%). The percentage of people who got all four questions right was 10.5%, and those who got all of them wrong was 9.2%.

The correct answer rates by question are as follows.

It cannot be known from the abstract alone how similar the difficulty levels of the four questions were to one another. Clinicians answered more questions correctly than non-clinicians (mean 2.27±1.06 versus 1.83±1.14, p<0.001). The authors' recommendations are in two directions: authors should explicitly interpret their own results to prevent misunderstandings, and readers should continue to brush up on basic biostatistics (PMID 23326299). Since the results show that a considerable number of researchers misinterpret these terms, this gives readers a reason to check for themselves rather than blindly accepting the interpretation in the abstract.

Custom and practice also lean toward the odds ratio. To understand that practice, you must first know the term logistic regression. Logistic regression is a statistical method that analyzes an outcome divided into two branches of "present/absent" along with various conditions, and produces the result as an odds ratio.

In veterinary medicine papers, this method was almost everything. The subjects were papers dealing with "present/absent" outcomes using data surveyed at a single point in time, and the researchers reviewed them through a set procedure. Out of 62 papers found, 6 were excluded and 56 were analyzed. Regardless of how common the disease was, 96% of them used logistic regression and therefore produced odds ratios. This means that even in studies where the outcome was common, odds ratios were mostly produced.

In the same paper, the authors ran four alternative models that directly measure the ratio of proportions on bovine viral diarrhea data. The authors report that logistic regression inflated those direct estimates the most. The typical misreading singled out by the authors is a sentence familiar to us — "the risk is several times greater." The conclusion is that even though there are methods to measure directly, many studies do not use them and misinterpret odds ratios (PMID 29177157).

The inflation becomes especially large when the outcome is common. Logistic regression inflates the relative risk (which is the same term as the risk ratio) estimate, and the degree of inflation is particularly large when the outcome occurs in more than 10% of the population. This problem happens not only in observational studies but also in randomized clinical trials. There are also figures that give a sense of the scale. Meta-analyses have estimated that roughly 40% of relative risk estimates produced by logistic models in studies following people forward deviate significantly from the true value. However, this 40% is a figure reported by the aforementioned paper citing other studies, and the original source was not directly verified by this article. That paper offers modified Poisson regression as an alternative. It is another model that directly estimates the ratio of proportions (PMID 36428910).

Both of the above papers pointed out the problem and put forward alternative models that directly measure proportions in the same place. When this article cites such papers, it also notes their prescriptions alongside them.

Probability, Odds, and Two Ratios

To see whether a factor increases or decreases a disease, we compare the proportion of people who got the disease in the group with the factor to those without it. There are three ways to make this comparison: subtracting the two proportions, dividing the two proportions, and turning the proportions into odds before dividing them (PMID 40191901). To understand these three, you must first know two ingredients: probability and odds.

Probability is the proportion of people who got the disease among the total people. If 20 people out of 100 got it, the probability is 20 ÷ 100 = 0.20. In epidemiology, this probability is also called risk. In this article, you can simply read "risk" as "probability of getting the disease."

Odds is the value obtained by dividing the number of people who got the disease by the number of people who did not. If 20 people out of 100 got it, the odds are 20 ÷ 80 = 0.25. The difference from probability is just a single denominator. Probability divides by the total, while odds divide by the people who did not get it.

It sounds unfamiliar, but we already use these words. When we say "3 to 1" in horse racing or betting, that is the odds. There are three winning cases to one losing case, so the odds are 3. Translating this into probability gives 3 ÷ 4 = 0.75. It is the same fact told in two languages.

Lining up three numbers gives you a feel for it.

This table contains the main point of this article. When the probability is low, the odds are nearly equal to the probability, and as the probability grows, the odds grow much faster than the probability. This is because as the people who got the disease increase, the denominator of "people who did not get it" decreases along with them. Therefore, no matter how high the probability gets, it cannot exceed 1, but the odds have no ceiling.

Now, for the two ratios. Papers call the group with the factor the exposed group, and the group without it the unexposed group. Risk ratio is the risk of the exposed group divided by the risk of the unexposed group. It is also called relative risk, which is the same thing. Odds ratio is the odds of the exposed group divided by the odds of the unexposed group. The ingredients for the risk ratio are probabilities, and the ingredients for the odds ratio are odds. As seen in the table, since the two ingredients move differently, there is no reason for the two ratios to be the same.

Then Why Bother Using the Odds Ratio?

There is a reason to use the odds ratio. The risk ratio is easy to interpret and fits general intuition. However, the odds ratio has three advantages. In certain designs, only the odds ratio can be calculated. Calculations that simultaneously account for and adjust multiple conditions are easier on the odds ratio side. And the odds ratio responds without ambiguity even if you flip the labels of the outcome (whether you look at survival or death). The conclusion of an introductory paper summarizing these pros and cons is not taking the side of the odds ratio. Whether you read a study that used the odds ratio or one that used the risk ratio, the point is to read them knowing the limitations of each of the two metrics (PMID 11451349).

Among the three advantages, the first one is particularly large. A representative setting is the case-control study. A case-control study is a study where people who have a disease and people who do not are gathered first, and then the two groups are compared by looking backward at past factors. The reason the odds ratio is especially useful in this design is that when a disease is rare, the odds ratio approximates the risk ratio. Therefore, it provides valuable information even in situations where risk cannot be calculated directly (PMID 40191901). Why that design cannot directly measure risk is covered in "Some Studies Cannot Count Risk — The Design Picks the Measure, and Pooling the Strata Changes the Number".

Lastly, there is a common illusion about the relationship among the three metrics. It is the thought that if one among the difference of two proportions, the risk ratio, and the odds ratio is large, the others will be large as well. This thought does not hold. In the authors' phrasing, there is no logical relationship at all among the three metrics (shown through three mathematical theorems and examples). The authors' recommendation is to be very careful when combining the results of studies using different metrics or when implying relationships between the metrics (PMID 27688647). This means you cannot infer that just because the risk ratio is large, the odds ratio or the difference between the two proportions will also be large.

Why the Two Numbers Diverge as the Outcome Becomes Common

The baseline is this. The odds ratio always exaggerates the true relative risk to some degree. When the probability of disease is low (e.g., under 10%), the odds ratio approximates the true relative risk. The more common the event becomes, the greater the exaggeration, and past a certain point, the odds ratio ceases to be a useful proxy for relative risk (PMID 18238982).

The same 10% baseline appears in other literature. A paper addressing this problem with a real-world example from dermatological literature explains that the two values diverge when the event occurs in 10% or more of the sample. That paper also covers how to convert an odds ratio into a relative risk and why one should consider that conversion (PMID 16785380). "Some Studies Cannot Count Risk" covers what inputs the conversion takes and where its limits lie. The 10% condition from the logistic regression paper seen earlier points to the same spot (PMID 36428910).

Let us look directly at what this baseline means in terms of arithmetic.

Same Odds Ratio, Different Risk Ratio

Let us assume there are 100 people each in the exposed and unexposed groups. Here are three scenarios.

You can follow the calculation just by looking at the first row. The odds for the exposed group are 20 ÷ 80 = 0.25, and the odds for the unexposed group are 10 ÷ 90 ≈ 0.111. Thus, the odds ratio is 0.25 ÷ 0.111 ≈ 2.25. The risks are 0.20 and 0.10, so the risk ratio is 2.00. The bottom two rows were calculated in the same way. This table is an example constructed by purposely fixing the odds ratio at 2.25 and back-calculating the numbers on the exposed group side.

The odds ratio for all three rows is 2.25. However, the risk ratios differ as 2.00, 1.50, and 1.20.

In other words, from the single sentence "an odds ratio of 2.25," you cannot tell whether the risk doubles or becomes 1.2 times higher. To know that, one more thing is needed. How common the disease is originally.

Base Rate — Without Knowing How Common Something Originally Is, You Don't Know the Magnitude

The base rate is the rate at which an outcome occurs in the baseline group used for comparison. In the table above, the risk in the leftmost column, the unexposed group, is the base rate.

Translated into an everyday example, it is like this. Suppose you heard, "If you go to this cram school, your chances of passing double." If the original passing rate was 1%, it becomes 2%; if it was 40%, it becomes 80%. It is the same "double," but what it means is completely different. The odds ratio goes one step further here. Without knowing the original passing rate, even "how many times" larger it is cannot be determined.

Looking at the same table again, at a base rate of 10% the risk ratio is 2.00, at 40% it is 1.50, and at 70% it is 1.20. The odds ratio stays still at 2.25 throughout, while only the risk ratio moves.

The same verdict appears in the preventive medicine literature. The odds ratio is not a ratio of probabilities, but a ratio of odds. Yet it is frequently interpreted as if it meant the same thing as the risk ratio, and the authors judge that interpretation to be wrong both in data surveyed at a single point in time and in data that followed people over time. The core is the following sentence. In such analyses, if you do not know the base rate of the outcome event, there is no way to evaluate the magnitude of absolute and relative risk changes using only the odds ratio. When an outcome is not rare but common, misunderstanding the odds ratio as a risk ratio leads to overestimating the effect size. If it is a case-control analysis, whether the odds ratio can be read as a risk ratio depends on how the control group was chosen. The authors' recommendations are education, reviewer vigilance, and journal reporting standards (PMID 27639787).

So the practical rule is this. When you encounter an odds ratio, you must first look for the base rate of the outcome. If it is not in the abstract, look for it in the main text; if it is not in the main text either, the magnitude of that odds ratio cannot be interpreted.

Can We Rest Easy If It Is Rare?

You can mostly rest easy. It is confirmed through arithmetic as well that when something is rare, the two values almost overlap. If 1 person out of 100 becomes 2 people, the risk ratio is 2.00 and the odds ratio is (2/98) ÷ (1/99) ≈ 2.02. The difference is 1%. When the baseline rate is this low, the conclusion does not change even if you do not bother to distinguish between the two numbers.

However, there are known exceptions. Among them, what this article confirmed is when checking whether two factors change each other's effects. This phenomenon where the effect of one factor depends on another factor is called interaction.

When evaluating interactions, the odds ratio may not approximate the risk ratio even if the disease is rare. There are cases where an interaction appears when looking at the odds ratio, but does not appear or becomes weak when looking at the risk ratio. The authors call this phenomenon 'distributional interaction' and present a formula to quantify the difference between the two values. And they conclude like this. If the risk of the outcome is not negligible, distributional interaction is always possible, and this is true even when the disease is rare (less than 5% risk). Therefore, one must be careful when interpreting interactions on any scale (PMID 15745447).

How It Actually Appears in the Literature

① The ticks on the graph. Ratios like the odds ratio or hazard ratio are not symmetrical around 1. 0.5 and 2 are the same magnitude in opposite directions. This is because one has decreased by half and the other has doubled. Yet on a normal arithmetic scale, the doubled side is drawn twice as far from the baseline as the halved side. As a result, identical effect sizes look different in size. Using a logarithmic scale or a reciprocal (inverted) scale makes this asymmetry disappear.

Arithmetic scales were common even in figures from prestigious medical journals. Investigating papers presenting hazard ratios and odds ratios in figures across five high-impact general medical journals, researchers judged logarithmic and reciprocal scales as appropriate and arithmetic scales as inappropriate. In 2002–2003, 53 out of 101 papers (52%) used inappropriate scales. In 2007–2008, it was 58 out of 231 papers (25%). All five journals improved over the five years, but the problem persisted in one out of every four papers. The authors suggest that the International Committee of Medical Journal Editors should require the use of only logarithmic or reciprocal scales for figures of ratio data (PMID 20435436). Therefore, when looking at a paper's figures, there is a reason to check the scale.

② Authors may also choose the odds ratio side. The obesity surgery paper that opened this article does just that. The authors presented both a hazard ratio of 4.96 and an odds ratio of 6.4. They then wrote that while both values show a large effect size and strong association, the odds ratio demonstrates the strength of the association more persuasively. They thus concluded that predominantly using the odds ratio is the correct approach for this analysis (PMID 42291164).

Whether one agrees with this judgment is a separate matter. However, the intuition that "a larger number is more persuasive" makes its way into the actual concluding sentences of papers. This is why readers must directly question the true identity of "how many times."

Two Common Misconceptions

① "An Odds Ratio of 2.5 Means 2.5 Times the Risk"

This is the starting point of this article. An odds ratio is a ratio of odds, not a ratio of probabilities. When an outcome is not rare but common, this misconception leads to an overestimate of the effect size (PMID 27639787).

If you remember just one baseline, it is this: When the outcome is under 10%, the odds ratio is a workable approximation of the risk ratio, and the more common it gets, the larger the exaggeration (PMID 18238982, PMID 16785380).

② "The Odds Ratio Always Inflates"

Earlier, we shifted the baseline that the odds ratio "always exaggerates." This "exaggeration" means moving farther away from 1. It does not mean the value always increases. That benchmark spot of 1 is the value for "no effect," meaning no difference between the two groups.

A paper that algebraically solved the relationship between the two measures in data surveyed at a single point in time demonstrates this point. The relationship between the two metrics is not a straight line, but a curve whose degree of bending or turning of direction changes depending on how common the disease is and how common the factor is. However, in either case, the value on the odds side is always farther from 1—which signifies "no effect"—than the other side. And the divergence between the two values depends much more heavily on how common the disease is than on how common the factor is. The authors' conclusion is that the choice of measure should be made based on epidemiological rationale rather than what is easy to spit out in statistical software (PMID 9126523).

Let us verify this with arithmetic.

Suppose that 50 out of 100 people in the unexposed group and 30 out of 100 people in the exposed group got sick. The risk ratio is 0.30 ÷ 0.50 = 0.60. The odds ratio is (30/70) ÷ (50/50) ≈ 0.43. This time, the odds ratio is smaller than the risk ratio.

Therefore, if you read an odds ratio of 0.43 in a paper dealing with a protective effect as "risk was reduced by 57%," that too is an exaggeration. The actual risk reduction is 40%. On the side greater than 1, the odds ratio looks larger, and on the side smaller than 1, it looks smaller. Either way, it looks more dramatic than reality.

The Odds Ratio Is Still a Valid Measure

That very paper that wrote the sentence "always exaggerates" immediately adds: The odds ratio is always a valid measure of association. It just does not always make a good substitute for relative risk. The authors conclude that because the odds ratio is difficult to understand, it is better to limit its use to case-control studies and logistic regression. That is because in those two places, the odds ratio is the correct measure of association in the first place (PMID 18238982). The conclusion is not to discard the odds ratio, but to narrow the places where you use it.

To Go Deeper

When you encounter 'how many times' in an abstract, there are three things to ask.

1. What is the ratio of. Is it a ratio of probabilities (risk ratio) or an odds ratio? Papers usually write them as OR / RR.
2. Where is the base rate. Find what percentage that outcome was in the group that serves as the starting point for comparison. If that value is under 10%, the two metrics are nearly identical, and the exaggeration grows as it becomes more common (PMID 27639787, PMID 18238982). The direction of the exaggeration comes from the fact that the odds-side value is always farther from 1 (PMID 9126523).
3. What is the scale of the graph. If ratio data is on an arithmetic scale, opposite effects of the same size appear as different sizes (PMID 20435436).

If you are choosing what to read next, it is this.

• The definition once more, in simple words — risk, relative risk, odds, and odds ratios with examples, without technical terms (PMID 26231012). The relationship among three metrics—difference between two proportions, relative risk, and odds ratio—concisely (PMID 40191901).
• Try calculating it yourself — the procedure for calculating odds ratios and relative risks in Excel from a 2×2 table (PMID 29703623).
• Practice where intuition breaks — an article that gives the relative risks (1.67 and 1.42) or odds ratios (1.74 and 1.46) of two drugs in a hypothetical randomized trial and asks you to answer directly. The questions are "How much better is A than B" and "If B's absolute survival rate is 8.5%, what is A's." It shows with simple arithmetic why both readers and authors easily get it wrong, what the right answer is, and how to get it (PMID 37339361).

If you leave behind just one thing, it is this. The odds ratio is not a wrong number, but a number that measures something different from the risk ratio. And the size of that difference is not written inside the odds ratio. The base rate decides it.

There are also questions this article left blank. Why are only odds ratios calculated in certain designs? What happens to the odds ratio when you adjust for multiple conditions? And the still-ongoing debate: "So should we throw away the odds ratio?" These questions are handled by "Some Studies Cannot Count Risk — The Design Picks the Measure, and Pooling the Strata Changes the Number".

Next time you meet "how many times" in an abstract, you will start by looking at what kind of thing that fold is a multiple of.

Source Papers

The Reality of Misunderstanding — Literature and People

• "An odd measure of risk: use and misuse of the odds ratio." (2001) — PMID 11576589 — Survey study. Recalculated the risk ratio in 107 out of 151 papers using the 'odds ratio' in two obstetrics and gynecology journals from 1998 to 1999. A gap of more than 20% appeared in 47 papers (44%), and 39 papers (26%) interpreted it like a risk ratio without any basis. The results section contains the sentence, "The odds ratio makes the effect look larger compared to the risk ratio." The conclusion is that it is frequently used and frequently misunderstood.
• "Understanding of statistical terms routinely used in meta-analyses…" (2013) — PMID 23326299 — International survey. Four multiple-choice questions given to 315 corresponding authors (response rate 39.4%). All correct 10.5% and all incorrect 9.2%, with 51.1%, 71.4%, and 40.6% by question. Clinicians scored higher than non-clinicians. The recommendations are explicit interpretation by authors and foundational statistics learning by readers.
• "Odds Ratio or Prevalence Ratio? …Cross-sectional Studies… in Veterinary Medicine." (2017) — PMID 29177157 — Review + empirical study. 96% of 56 papers used logistic regression. Ran four alternative models on bovine viral diarrhea virus data to show that logistic regression has the largest inflation.
• "Overestimation of Relative Risk and Prevalence Ratio: Misuse of Logistic Modeling." (2022) — PMID 36428910 — Methodology paper. Pins down the condition where inflation becomes particularly large as when the occurrence of the outcome exceeds 10%, and notes that it happens not only in observational studies but also in randomized clinical trials. The figure of about 40% is what this paper reports from meta-analyses, and we could not verify the original source. The prescription is modified Poisson regression.

Definitions and Primer

• "[Key Measures in Epidemiology: Risk Difference, Relative Risk and Odds Ratio]." (2025) — PMID 40191901 — The definitions of the three measures and the meaning of odds. The source for the statement that "when a disease is rare, it approximates the relative risk, making it especially useful in case-control studies."
• "Making sense of odds and odds ratios." (2008) — PMID 18238982 — Primer paper. The definitions of odds and odds ratios, "always exaggerates to some degree," the 10% baseline. The authors' conclusion is not abandonment — that the odds ratio is always a valid measure of association, just not a good substitute for relative risk, and that it is better to restrict its use to case-control studies and logistic regression — with the added reason that in those two spots, the odds ratio is the right measure of association.
• "Understanding the odds ratio and the relative risk." (2001) — PMID 11451349 — Three reasons to use odds ratios (design constraints, ease of adjustment, label symmetry) and a table of pros and cons. The wrap-up is not taking sides with the odds ratio — whatever measure a study is summarized by, the point is to read it knowing the limitations of each of the two measures.
• "Relationships among three popular measures of differential risks…" (2016) — PMID 27688647 — Three theorems show that there is no monotonic relationship among risk difference, relative risk, and odds ratio. The recommendation is to be very careful when pooling studies with different measures.
• "Understanding relative risk, odds ratio, and related terms: as simple as it can get." (2015) — PMID 26231012 — A jargon-free example primer.
• "WASP (Write a Scientific Paper) using Excel - 12: Odds ratio and relative risk." (2018) — PMID 29703623 — How to calculate the two values in Excel from a 2×2 table.

The Divergence in Common Outcomes

• "Relationship between prevalence rate ratios and odds ratios in cross-sectional studies." (1997) — PMID 9126523 — An algebraic analysis paper. By solving the relationship between the two measures as a quadratic curve using data surveyed at a single point in time, it shows that the odds value is always farther from 1 and that the divergence depends much more on the disease frequency than on the factor frequency. The authors' conclusion is that the choice of measure should follow epidemiological reasoning rather than software convenience. (The original terms are prevalence ratio and prevalence odds ratio, and distinguishing them belongs to "Some Studies Cannot Count Risk".)
• "The (relative) risks of using odds ratios." (2006) — PMID 16785380 — Starting from a single odds ratio in dermatological literature, it covers why divergence happens when events occur in 10% or more of the sample, how to convert them, and why.
• "Distributional interaction: …incidence odds ratios to assess interaction." (2005) — PMID 15745447 — In evaluating interaction, approximation can break down even when the disease is rare (less than 5% risk). Along with formulas to quantify the difference, it concludes that one should be careful on any scale.
• "Assessing gastroesophageal reflux disease (GERD) threat 5 years following LVSG and LRYGB…" (2026) — PMID 42291164 — From the same data, a risk ratio of 4.96 and an odds ratio of 6.4. The authors concluded that using the odds ratio primarily is correct because the odds ratio side shows the strength of the association more persuasively. This piece does not take a side for or against that judgment.

Interpretation and Reporting

• "A Most Odd Ratio: Interpreting and Describing Odds Ratios." (2017) — PMID 27639787 — Core Citation. Whether data surveyed at a single point in time or data following people, without knowing the baseline rate, you cannot evaluate the magnitude of risk change with an odds ratio alone. In case-control studies, it depends on the selection of the control group. The recommendation is education, reviewer vigilance, and journal reporting standards.
• "Relative risk and odds ratio data are still portrayed with inappropriately scaled graphs…" (2010) — PMID 20435436 — 5 high-impact journals. Inappropriate arithmetic scales decreased from 53 out of 101 papers (52%) in 2002–03 to 58 out of 231 papers (25%) in 2007–08, but persisted in one out of four papers. The proposal is an editorial board requirement for scales.
• "Understanding Misunderstandings About the Relative Risk and Odds Ratio." (2023) — PMID 37339361 — A practical paper that has readers answer directly using the relative risk (1.67, 1.42) and odds ratio (1.74, 1.46) of a hypothetical trial. It shows why people get it wrong and the correct answers with simple arithmetic.