If the Risk Was Cut in Half, How Many Fewer People Got Sick? — Relative and Absolute Risk

The Headline "50% Lower Risk"

"People who took this drug had their heart disease risk reduced by 50%." You have probably seen a sentence like this once or twice in a newspaper headline or broadcast news. Since it is half, it sounds like a big deal.

The same result can also be written like this. Among 100 people who did not take the preventative drug, 2 fell ill over the course of a year, and among 100 people who took the preventative drug, 1 fell ill. Since 2 people became 1 person, it is true that it decreased by half. And the difference in the number of people who fell ill out of 100 is one person.

"The risk was cut in half" and "The number dropped from 2 in 100 to 1" are two ways of writing the same result, and both are true. The first sentence sounds large and the second sentence sounds small. This article covers where that difference comes from, and what you should ask when you encounter a single headline.

This 100-person example is a number made up to help understanding, and is not the result of any study. We will carry this example with us to the end of the article. Drug names from actual studies appear a few times later on, but they are merely examples showing how numbers are written and are not judgments on whether to use those drugs or not.

Relative by Division, Absolute by Subtraction

We return to our two groups of 100 people. In the group that did not take the preventive drug, 2 people fell ill over the course of 1 year; in the group that did, 1 person did.

Absolute risk is the proportion of people in each group to whom the event actually happened. Here, "the event" is getting sick. The absolute risk is 2% for the group that did not take the drug, and 1% for the group that took it. Literally, it is "how many out of 100 people." A time period is always attached to this, which in this example is "over the course of 1 year."

There are two kinds of arithmetic we can do with these two numbers, 2% and 1%. They are division and subtraction.

Relative risk is the division of the two absolute risks. We divide the absolute risk of the group that took the drug by the absolute risk of the group that did not take it. 1% ÷ 2% = 0.5, which means the risk for the group that took the preventive drug is half that of the group that did not. A relative risk of 1 means the risk is the same in both groups.

Relative risk reduction is this 0.5 rephrased as "how much it decreased." Relative risk reduction is 1 minus the relative risk. It is a calculation measuring how far down we have come from 1, the point where both groups are the same. 1 − 0.5 = 0.5, or 50%. "A 50% reduction in risk" comes from this number.

Absolute risk reduction is the subtraction of the two absolute risks. 2% − 1% = 1 percentage point. Because it is the difference obtained by subtracting percentages from each other, we write "% point." Translated into a number of people, it is 1 out of 100 people, and "from 2 out of 100 people to 1" comes from this number.

Dividing the same two numbers yields relative numbers, and subtracting them yields absolute numbers. In this article, "relative numbers" refers to numbers obtained by division, such as relative risk and relative risk reduction, while "absolute numbers" refers to numbers read as "how out of 100 people," such as absolute risk and absolute risk reduction. Risk can be defined in these two ways, and you need to know what both expressions represent to accurately read research results (PMID 26952180).

Relative numbers have an appeal. They summarize the risks of two groups—that is, two numbers—into one. Yet that very property is also their greatest weakness. Once you are given the single number 0.5, there is no way to recover whether it went from 2% to 1% or from 40% to 20%. The absolute risk that lay underneath is obscured, and people who are told about an effect through relative expressions tend to overestimate the effect (PMID 28339913).

The impression you receive also changes depending on which number is used. Recommendations therefore state that both relative and absolute numbers should be reported, alongside how uncertain each is (PMID 12201860, PMID 28339913).

In actual papers, both expressions appear side by side. A study tracking people diagnosed with type 2 diabetes in the UK for 10 years is one such example. These were people aged 25 to 84 with no history of heart and blood vessel disease who were diagnosed between 2005 and 2016. The researchers compared people who started taking statins, which are cholesterol-lowering drugs, with those who did not, by matching similar individuals.

Let us look at those among them whose risk of developing major heart and blood vessel disease over the next 10 years was predicted to be less than 10%. The comparison outcome is whether major heart and blood vessel disease developed. Dividing the risk in the side that started statins by the side that did not give 0.78. Subtracting them showed that the side that started statins was 0.83 percentage points lower (PMID 41461087).

Converting 0.78 into a relative risk reduction gives "22% lower." Converting 0.83 percentage points into a number of people gives "about 8 per 1,000 people over 10 years." These two translations are the arithmetic performed by this article, and the same result becomes two sentences. The authors conclude that starting statins was associated with a reduction in all-cause mortality and major cardiovascular events across all brackets, from people with low predicted risk to those with high risk. This study used medical records, and who received the drug was not decided by a draw. The authors therefore also note the limitation that unmeasured factors may have mixed into the results.

Relative numbers and absolute numbers come from the same two numbers, but one number cannot recover the other.

How Many Were There Originally — Baseline Risk

Let's apply the same sentence, "50% lower risk," to three different groups. The three groups have different rates of getting the disease when they do not take the medication. Baseline risk is the rate at which that event happens in the untreated group. In the previous example, the absolute risk of the group that did not take the medicine is the baseline risk itself. All three rows are examples created for this article, and the time period for all is 1 year.

In all three rows, the relative risk reduction is 50%. However, the number of people who avoid the condition ranges from 10 per 100 to 1 per 1,000, which is a 100-fold difference. The only place where the three rows differ is the leftmost column—in other words, the baseline risk.

The baseline risks in the table above are 20%, 2%, and 0.2%. To cross over from relative numbers to "how many people," you must pass through this value. Half of 20% is 10%, and half of 0.2% is 0.1%. Even with the same 50%, the number of people who fall ill less often varies greatly depending on how many people the event originally happened to.

This property—that even with different baseline risks, the number remains the same—is also what makes relative numbers useful. When comparing benefits among groups with different risks, relative metrics are advantageous (PMID 16174840). That exact property is why the three rows in the table can be bundled together and referred to with a single word: "50%." However, the fact that 50% comes out identically in all three groups is an assumption set by this example, with no guarantee that it will always be so in actual treatment.

The heading for the side where risk increases is the same. Phrases like "dozens of times the risk" sound large, but you must hear how many people there were originally to get the actual head count. Sudden cardiac death in people who suffered a myocardial infarction at a young age is one such example. A myocardial infarction is a disease where a blood vessel supplying blood to the heart muscle gets blocked and part of the muscle dies, and sudden cardiac death is dying suddenly due to heart problems. The evidence is a study that tracked all of Denmark aged 18 to 35 for several years (PMID 22753866).

Scaled to 100,000 people tracked for 1 year each, sudden cardiac death was 4.1 people among those with no history of myocardial infarction. It was 305.0 people among those with a history of it.

The latter number comes from 10 deaths among people with a history of myocardial infarction, so its wobble is large. Simply dividing the two numbers gives about 74 times. The authors also measured the multiple using a model comparing the rate of occurrence over time. That multiple was 55.5 for sudden cardiac death and 8.3 for total mortality combining all-cause deaths. Because the calculation method differs, the values differ as well.

Either way, as a multiple, it is a very large number. Yet in terms of the number of people, it is just over 300 out of 100,000 people tracked for 1 year each. The authors placed both side by side in the paper's title. A history of myocardial infarction at a young age comes with both a high relative risk and a low absolute risk of sudden cardiac death.

When you hear "how many times" or "% lower risk," to know the number of people, you must first know how many people there were originally.

When Only Relative Numbers Remain — Paper Summaries and Press Releases

At the very beginning of a paper is an abstract, which briefly summarizes the results. Among the general medical journals with the highest impact, slightly less than half of the papers on drug trials that reported a positive result put the results in the abstract using only relative expressions. When all randomized drug trials published between 2008 and 2010 were counted, it was 69 out of 157 trials that reported positive results (PMID 21842324). A randomized trial is a study that compares treatments by assigning people to receive them through a random draw like flipping a coin. The authors conclude that papers should state the limitations of the items measured as results and report the results in absolute expressions.

Absolute effects are frequently omitted in review papers that gather and synthesize multiple studies. Out of 202 review papers, 73 stated absolute effects for the outcomes most important to patients (PMID 26560992). This investigation starts from the point that expressing things relatively makes the numbers look larger, which influences the judgments of doctors and patients. The authors write that even the papers that do include them often report them insufficiently, requiring readers to calculate the absolute effects themselves, and recommend reporting both relative and absolute effects.

A press release is an article introducing a paper that journals send to reporters, and it serves as the material for news articles. Here, the original number of people is frequently omitted. In a survey examining recent press releases from prominent medical journals in early 2001, out of 58 cases that described the difference between two groups, only about half included the original number of people. Because the number of cases and the percentages given in the abstract do not match, the exact value is not written.

The authors consider the format of including the original number of people together to be the least vulnerable to exaggeration. They also conclude that press releases frequently report numbers in formats that can make the importance of the results look inflated (PMID 12038933).

Relative numbers also move decisions. Pharmacists, doctors, and patients are easily inclined to start treatment when they see relative indicators, whereas using absolute indicators leads to more conservative decisions (PMID 16174840).

They are also easy to confuse. When baseline risk was provided together as a frequency such as "so many out of 100 people," the number of people who understood it correctly increased, while providing it as a percentage frequently hindered understanding. Many people misread relative risk reduction as absolute risk reduction. These are the results of an experiment that presented hypothetical treatments that lower or raise the risk of heart disease to 1,234 members of the general public (PMID 24803429). Still, the authors conclude that problems remain even when baseline risk is clearly provided if the information is conveyed as a relative change. They also note limitations such as hypothetical situations and a non-representative sample.

Experts are no exception. There is a study that randomly divided 101 Brazilian dentists and showed them hypothetical treatment benefits using absolute numbers or relative risk reduction (PMID 39109767). The dentists were asked two questions: out of 100 people, how many would avoid losing multiple teeth when treated without antibiotics versus when treated with them.

For the question regarding the use of antibiotics, 50% of those who received it in absolute numbers answered correctly, while 29% of those who received it as relative risk reduction answered correctly. The proportion of people who got both questions right was 31% and 25%. Most people failed to accurately understand the benefit regardless of which format they received it in, and only slightly more people understood it when absolute numbers were used.

There are also results in the opposite direction. In a study examining 91 elderly American Indians and Alaska Natives, the likelihood of interpreting things correctly was higher when expressed as relative risk (PMID 22188207). The comparison formats were absolute risk and "how many people need to be treated for one to benefit," which we will look at later. The authors recommend carefully checking whether the presentation format was considered and understood.

An association with judgment has also been reported. At a state-wide academic gathering of physicians, 88 out of 139 physicians responded to a questionnaire. The lower the data interpretation score, the higher the enthusiasm for cancer screening, and that association appeared to be driven by confusing relative risk and absolute risk (PMID 24732049). What this study measured is the association between interpretation ability and enthusiasm, not how beneficial screening actually is.

It is common for only relative numbers to remain in abstracts, and it is common for the original number of people to be omitted in press releases. Hearing only those numbers makes it easy to overestimate the effect. This is not always true for everyone, and providing the baseline risk alongside them does not make all confusion disappear.

How Many People Must Be Treated for One to Benefit — NNT

Let us return to our initial 100 people. If they do not take the preventive medicine, 2 people get sick over 1 year; if they take it, 1 person gets sick. Out of 100 people, 1 person got sick less, so 100 people must take it for one person to benefit. The name attached to this number is NNT (Number Needed to Treat). NNT is the inverse of absolute risk reduction, representing the number of people who must be treated for one person to benefit.

An inverse is 1 divided by that value. 1 percentage point is 0.01, so 1 ÷ 0.01 = 100. 100 people must take the preventive medicine for 1 year for one person to benefit. Translating this to the three rows of the previous table, the NNTs are 10, 100, and 1,000. Even with the same 50%, the NNT stretches out 100-fold.

Assuming no one gets a new disease because of the medicine, if we divide the 100 people who took the preventive medicine on average, it looks like this. 98 people are those who would not have gotten sick even if they had not taken it. 1 person is someone who got sick even though they took it. The remaining 1 person is the one who did not get sick thanks to the medicine, and it is impossible to know who that one person is.

NNT embeds the baseline risk. This is because what would have happened without treatment enters into the calculation (PMID 15827840). Therefore, NNT tells us not only whether a treatment is effective, but also how effective it is.

A period of time must necessarily be attached to NNT. "1 person out of 100" and "1 person out of 100 over 1 year" are different sentences. This is because the NNT differs when observed for 1 year versus when observed for 10 years. Let us look at treatments targeting diseases that progress over a long time, such as diseases where arteries harden or bones become weak.

In such treatments, neither the NNT nor the relative risk reduction and absolute risk reduction capture how long the observation lasted. NNT changes over time, and the disease may not have been avoided but merely delayed (PMID 16867164). This means that solely from this number, we cannot tell whether a person who did not experience the disease while taking the medicine ultimately avoided the disease or just experienced it later.

Like relative risk, NNT is inherently a metric that changes over time, so placing studies with different follow-up periods side by side makes them easy to misread (PMID 29769296).

There are five things that should be written alongside NNT. They are what was compared to what, how long the observation lasted, what the baseline risk of the study subjects was, what was counted as an outcome, and how uncertain the estimation is (PMID 15827840).

Among these, three—namely, baseline risk, duration, and uncertainty—have not always been written in actual papers. This is the result of an investigation examining 51 studies reporting NNT in high-impact medical journals (PMID 28571585). The authors concluded that incompletely reported NNTs cannot be interpreted, and added that further research is needed to confirm these findings. NNT can finally be read when duration, baseline risk, and how uncertain it is are written together.

The NNT of "100 people must take it for one person" is a phrasing that counts people, so it has received praise for being easy to understand and intuitive (PMID 16867164). However, appearing intuitive and being better understood are different. Among absolute metrics, absolute risk reductions like "1 person out of 100" can be easier to understand than NNT, and patients may find it difficult to understand what NNT means (PMID 16174840). There are also studies showing that both the general public and doctors misunderstand NNT (PMID 16867164).

Even in a study that presented hypothetical treatment results in various formats to multiple sclerosis patients in the UK, understanding was best with absolute expressions, while relative expressions and NNT were lower than that. In any format, adding background information improved understanding (PMID 30005747).

The extent to which NNT should be used is under debate. One proposal paper acknowledges that NNT is an absolute metric that is easy to understand. Even so, it proposes that we stop using NNT in settings that determine clinical guidelines and policies (PMID 40782977). There are two reasons. First, for results where effectiveness is uncertain, the range reporting the uncertainty of NNT encompasses nonsensical values. Second, comparing benefits and harms using NNT makes the math complicated.

A paper pointing out that NNT fails to capture how long the observation lasted concludes with the thought that there is probably no single metric that conveys all necessary information (PMID 16867164).

When You Read a News Headline

Suppose you encounter a headline like this: "New Preventive Drug Lowers Heart Disease Risk by 50%." Based on what we have seen so far, two things can be asked.

The first question is, "Out of how many people?" This asks how many people actually fell ill in the first place among those who did not take the drug, which is the baseline risk. If the answer is 20 out of 100 people, then 50% is 10 people per 100, and the NNT is 10. If the answer is 2 out of 1,000 people, the same 50% is 1 person per 1,000, and the NNT is 1,000. The 50% in the headline is identical in both cases.

The second question is, "Over how long?" Depending on whether the result is over 1 year or 10 years, the exact same number of people will mean something different. The NNT changes over time, and the disease may not have been avoided, but merely postponed (PMID 16867164). Whether dealing with relative or absolute numbers, the condition to consider the baseline risk and the observation period together remains the same (PMID 16174840).

The statin study we looked at earlier provides answers to almost both questions. It specifies a duration of "over 10 years." How many people there were originally is not in the abstract. Instead, the difference in absolute risk, which can be translated as "roughly 8 people out of 1,000," is written alongside a relative risk of 0.78 (PMID 41461087). When the difference is written as a number of people, you can immediately know the magnitude that the first question aims to reveal.

In press releases, only around half out of 58 cases reporting the difference between two groups also stated how many people there were originally (PMID 12038933). If you cannot find the answers to either question or the difference written in terms of number of people inside an article, that headline has not yet told you the magnitude.

If the article mentions side effects, we look at one more thing. Literature reviews note that it is common to present benefits in relative numbers and harms in absolute numbers, which makes benefits look exaggerated compared to harms (PMID 24732049). If "50% lower risk" and "side effects in 1 out of 100 people" appear side by side in the same article, the two numbers are written using different arithmetic methods. Both must be translated into "how many out of 100 people over the same period" to be comparable.

The two questions only reveal the magnitude; they do not decide whether or not to take the drug. Even with a better understanding of the numbers, your choice might remain the same. There is a hypothetical experiment where 600 American adults were shown materials explaining whether to remove or monitor an irregularly shaped mole on the skin. One group received materials written in numbers, and the other in words. Numerical data improved understanding, but did not change the choice of whether to have it removed. The proportion of people who chose to have it removed was nearly identical at 52% and 53% across the two materials.

What primarily swayed the choice was how severe the diagnosis was described to be. Even with high comprehension, about one-third chose the option contrary to expert recommendations. The authors write that personal values guide choices (PMID 41893389).

No matter what the headline is, if you ask the two questions—"Out of how many people?" and "Over how long?"—it reveals how many people 50% actually stands for.

Where to Look Further

This article discussed things while assuming one thing. It is the assumption that the relative risk reduction is the same even in groups with different baseline risks. Where that assumption wobbles in actual research and how to read the range of uncertainty attached to NNT are covered next in "What Does "50% Lower Risk" Mean in People? — Reading Relative Risk, Absolute Risk, and NNT".

How much writing the same number as a percentage versus as "how many out of 100 people" changes judgment is covered by "Same Result, Different Sentence — Where Format Changes Judgment, and Where It Doesn't". Other "times more likely" appearing in the abstract are looked at by "An Odds Ratio Is Not a Risk Ratio — What the 'Times More Likely' Is a Multiple Of" and "What Is a Hazard Ratio of 0.7 the 0.7 Of? — How to Read a Survival Curve".

Other articles in "Numbers from Scratch" are "What Does "Statistically Significant" Actually Say?", which asks whether these numbers are not by chance, "How Much Does a Number Counted Once Wobble?", which notes how much numbers can wobble, and "If People Who Take It Live Longer, How Were They Different to Begin With?", which deals with confounding where moving together does not mean causation.

Source Papers

• "Common pitfalls in statistical analysis: Absolute risk reduction, relative risk reduction, and number needed to treat." (2016) — PMID 26952180 — Risk is the probability of an event occurring and can be defined both absolutely and relatively; knowing what both measures represent is necessary to accurately interpret research results.
• "Relative risk versus absolute risk: one cannot be interpreted without the other." (2017) — PMID 28339913 — The appeal of relative risk—its nature of summarizing two numbers into one—is also its greatest weakness, as the underlying absolute risk is obscured and readers easily overestimate the effect. It recommends reporting both measures together with 95% confidence intervals (commentary).
• "Odds ratio, relative risk, absolute risk reduction, and the number needed to treat--which of these should we use?" (2002) — PMID 12201860 — Different metrics create different impressions. It recommends reporting both relative and absolute metrics together with appropriate confidence intervals.
• "Effectiveness and Safety of Statins in Type 2 Diabetes According to Baseline Cardiovascular Risk : A Target Trial Emulation Study." (2026) — PMID 41461087 — UK primary care patients with type 2 diabetes aged 25–84, 10-year follow-up. Hazard ratio for major cardiovascular events in the baseline predicted risk <10% subgroup was 0.78, with a risk difference of −0.83%. The conclusion is an association with reduction across all predicted risk ranges, with the limitation of unmeasured confounding (target trial emulation using observational data).
• "Number needed to treat: a descriptor for weighing therapeutic options." (2005) — PMID 16174840 — Looking at relative metrics makes it easier to start an intervention, while absolute metrics lead to more conservative decisions. Relative metrics are advantageous for comparisons between populations with differing risks. Absolute risk reduction may be easier to understand than NNT, and patients may find NNT difficult to understand.
• "Prior myocardial infarction in the young: predisposes to a high relative risk but low absolute risk of a sudden cardiac death." (2013) — PMID 22753866 — Denmark 2000–2006, 1,862,431 individuals aged 18–35: A history of myocardial infarction raised the incidence rate of sudden cardiac death from 4.1 to 305.0 per 100,000 person-years (10 sudden cardiac deaths among 1,234 individuals with a history), with hazard ratios of 55.5 for sudden cardiac death and 8.3 for all-cause mortality.
• "Endpoint selection and relative (versus absolute) risk reporting in published medication trials." (2011) — PMID 21842324 — Among 316 randomized medication trials in top 6 general medical journals from 2008 to 2010, 69 (44%) of 157 positive trials used only relative expressions in their abstracts. The conclusion is that limitations such as surrogate endpoints must be disclosed and results reported in absolute terms.
• "Systematic reviews experience major limitations in reporting absolute effects." (2016) — PMID 26560992 — Out of 202 systematic reviews, only 73 (36.1%) reported absolute effects for the most important outcomes, and those that did were often insufficient, requiring users to calculate them themselves. It recommends reporting both absolute and relative measures.
• "Press releases: translating research into news." (2002) — PMID 12038933 — 127 press releases from 9 prominent medical journals across 6 issues immediately preceding interviews in January 2001: Of 58 mentioning differences between groups, baseline rates were noted in 58 as written in the abstract as "26 (55%)" (where counts and percentages do not match). The conclusion is that press releases frequently present data in a format that omits limitations and industry funding, and can make importance appear inflated.
• "Communicating Relative Risk Changes with Baseline Risk: Presentation Format and Numeracy Matter." (2014) — PMID 24803429 — Virtual scenario experiment with 1,234 general participants: Providing baseline risk as frequencies improved understanding, while percentages frequently hindered it. Many participants mistook relative risk reduction for absolute risk reduction. It concludes that presenting changes relatively, even when baseline risk is provided, remains problematic (hypothetical situation, non-representative sample).
• "Randomized trial of dentists' understanding: treatment benefit in absolute numbers vs relative risk reduction." (2024) — PMID 39109767 — Randomized trial of 101 Brazilian dentists: Correct answers to questions on antibiotic co-prescription were 26 participants (50%) for absolute numbers and 14 (29%) for relative risk reduction. Most failed to accurately understand the benefit regardless of format, with slightly higher understanding when absolute numbers were used.
• "Health numeracy and understanding of risk among older American Indians and Alaska Natives." (2012) — PMID 22188207 — 91 older American Indians and Alaska Natives: The probability of correct interpretation was higher with relative risk formats than with absolute risk or NNT formats. It recommends considering presentation methods and thoroughly checking understanding.
• "Confusing Relative Risk With Absolute Risk Is Associated with More Enthusiastic Beliefs about the Value of Cancer Screening." (2014) — PMID 24732049 — 88 responses out of 139 physicians: Lower data interpretation scores were associated with higher enthusiasm for cancer screening, and confusion between relative and absolute risk appeared to drive this association. The background notes that the discrepancy of presenting benefits relatively and harms absolutely is common.
• "Number needed to treat (or harm)." (2005) — PMID 15827840 — NNT reflects baseline risk and tells us not only whether a treatment works, but how well it works. Comparators, observation periods, baseline risk, outcome definitions, and 95% confidence intervals should be reported together.
• "Number-needed-to-treat (NNT)--needs treatment with care." (2006) — PMID 16867164 — In interventions targeting chronic disease processes, NNT cannot capture a time component, so it varies over time, and events may be postponed rather than avoided. General the public and physicians misunderstand NNT. There is probably no single metric that conveys all information.
• "Interpreting risk reduction in clinical trials for pulmonary arterial hypertension." (2018) — PMID 29769296 — Like relative risk, NNT is inherently a time-dependent metric, so it can be misleading in studies with different follow-up durations.
• "Number needed to treat (NNT) in clinical literature: an appraisal." (2017) — PMID 28571585 — 51 papers reporting NNT from top 25 general and internal medicine journals: Baseline risk, duration, and confidence intervals were not always reported. It concludes that incompletely reported NNT cannot be interpreted and notes that confirmation through further research is needed.
• "Best Methods of Communicating Clinical Trial Data to Improve Understanding of Treatments for Patients with Multiple Sclerosis." (2018) — PMID 30005747 — UK patients with multiple sclerosis: Understanding was better with absolute expressions than with relative expressions or NNT, and adding baseline information significantly improved understanding across all formats.
• "The number needed to treat: it is time to bow out gracefully." (2025) — PMID 40782977 — Citing limitations such as confidence intervals breaking when risk differences are not significant, and the complexity of weighing benefits against harms, it proposes retiring the use of NNT in decision-making contexts (proposal paper).
• "Quantitative versus qualitative risk framing in patient decision aids for dysplastic nevi: A randomized A/B testing study." (2026) — PMID 41893389 — 600 US adults: Quantitative (numerical) decision aid materials increased understanding and certainty compared to qualitative (verbal) materials, but did not change the willingness to excise (52% vs. 53%). Indications of diagnosis severity primarily drove the intention to treat, and even with high comprehension, about one-third chose contrary to expert recommendations. It concludes that individual values drive choices.