Are You Thinking About Risk the Wrong Way?
It is important to understand the difference between relative and absolute risk to make effective risk assessments.
A recent episode of the BBC's Radio Four program More or Less featured an alarming statistic concerning deaths after surgery: Women undergoing surgical procedures are 32 percent more likely to die if their surgeon is a man. The fact that men outnumber women in most surgical specialties and that there were 6.6 million surgeries performed in 2019 makes a 32 percent increase in the risk of surgery-related death for women under the care of male surgeons all the more shocking.
A quick fact check is necessary to determine the validity of the claim made. The NIH report states that 52.9% of the 6.6 million surgeries were performed on women while 86% of surgeons are men according to the Statista chart. A simple calculation (6.6 million surgeries times 52.9 percent women patients times 86 percent men surgeons times a 32 percent mortality rate) reveals that 960,833 women would have died from surgery in 2019. According to the CDC, the leading cause of death in the United States in 2019 was heart disease. Why is that?
Different Risks
The headline figure reads "32 percent more likely to die." The words "more likely" imply that there is a quantifiable difference in the respective likelihoods of either of two situations occurring. The headline figure represents the 32% increase in the probability that a woman will die at the hands of a male surgeon as opposed to a female surgeon.
The 32 percent is a relative risk, while the underlying probabilities of male and female surgeons killing female patients are the respective absolute risks. The absolute risk of a situation not occurring is the probability that it will not occur. The increase in likelihood from the second scenario to the first represents the relative risk between these two scenarios.
The distinction between absolute and relative risk is often overlooked but it is very important to understand when to employ each type of risk. Misunderstanding relative and absolute risks can have major consequences for individuals, businesses, and policymakers.
The absolute risks of patient deaths under the care of male and female surgeons have not been determined. According to the medical statistician, the absolute risks in the cited study are 0.66 percent and 0.5 percent, respectively. This means that the absolute increase in women’s deaths due to having a male surgeon is 1.6 deaths per every 1,000 surgeries. For every 1,000 surgeries performed by a male surgeon, there are 6.6 more deaths among female patients than there are among male patients. This translates into a 32% higher chance of death for women who undergo surgery by a male surgeon.
ABSOLUTE VERSUS RELATIVE RISK
Relative risk measures the likelihood of an event occurring among a specific group within the data, while absolute risk measures the overall probability of the event happening.
Relatively Speaking
The results of the study were more eye-catching when reported in the media as a result of confusing a relative risk for an absolute risk. However, the way in which a researcher constructs the relation of one event to another can change the relative risks. For instance, what would happen if the question was not how many women die due to having a male surgeon, but how many women survive thanks to a woman as their surgeon?
The absolute risk that a female patient survives a female-surgeon operation is 995 survivals per 1,000 surgeries. For male surgeons, the female-patient survival risk is 993.4. The difference turns out to 1.6 more women die within 1000 surgeries when male surgeons operate. The relative risk would therefore be 0.16% more.
The study's lead researcher, Dr. Christopher Wallace, alludes to the "degree of sensationalism in how things are presented" in the More or Less episode, suggesting that journalists may have been engaging in a bit of selection bias about which of the study's findings to highlight.
Though popular-media journalists may be tasked with sifting through reams of recently published scientific articles and preprint archives, carefully scouring each work for headline-grabbing statistics, most journalists are not highly trained scientists and certainly don’t have the time to vet all new studies that come out for the most newsworthy findings.
According to Stuart Ritchie, a psychologist and science communicator, members of the press usually discover interesting numbers, such as the 32 percent figure, from press releases. He also states that the scientists conducting the research often play a big role in creating these releases. Because researchers want their work to be well-known and to receive future funding, they tend to include findings in their press releases that will grab journalists' attention. For example, they may choose to present large relative risks without providing information about the absolute risks on which the relative risks are based.
A Theory of Relativity
However, there are situations where relative risks are important. Absolute risks depend on their base groups and don't generalize well.
The absolute risk of death from heart disease is, for instance, higher for elderly smokers than for elderly non-smokers. Similarly, the absolute risk of death from heart disease is greater for smokers 40 and younger than for non-smokers who are also 40 and younger. Nevertheless, the absolute risk of heart disease among all members of the elderly group surpasses that of all members of the group consisting of those who are 40 and younger by a large margin. Does this mean that smokers who are 40 and younger are in a good position to keep smoking until they reach their elderly years?
How does relative risk account for the absolute risks of heart disease for smokers and nonsmokers across age cohorts, and what does this tell us about the general risk profile of death from heart disease due to smoking for all ages society-wide?
The relation between Covid vaccinations and Covid related deaths is another recent and good example of relative risk. Data collected in the UK revealed that within about a month, covid related deaths for vaccinated people aged 50 to 79 was 55.3 deaths per 100.000 people. For unvaccinated people of the same age, the deaths were 213.4 deaths per 100.000 people. Covid related deaths are defined as deaths that followed within 60 days of a positive covid test result.
For people aged 40 or younger, vaccinated deaths were 0.3 per 100.000 and unvaccinated deaths were 1.7 per 100.000 people. The absolute risk here is far lower for both vaccinated and unvaccinated people of younger age. The relative risk however results in a growth of 470% for ages 40 and lower and 510% for ages 50 to 79.
The relative risk ranges from 217% to 808% for people above 18 years of age. Absolute risk however ranges from 0.4 per 100.000 to 129 per 100.000 deaths for unvaccinated people and from 0.1 per 100.000 to 40.8 per 100.000 deaths for vaccinated people.
The risk must be generalizable though. Taking the average across all ages produces a fatality-rate for people over 18 years of age of 32.9 per 100.000 people for unvaccinated people and 8.2 per 100.000 people for vaccinated people. In a scenario in which vaccines are not available, this corresponds to about 4 times more deaths than in a scenario in which people can get the vaccine freely.
The absolute risks however bring forward a high standard deviation of 47 per 100.000 deaths and 14.8 per 100.000 deaths. In that case, the standard deviation is larger than the average of the same data points, meaning that the data is either driven by an unconsidered factor or is very volatile and therefore it can be argued that the averages of all age-ranges is not a very good approximation for Covid-related fatalities. Therefore, splitting the age-ranges is the way to go for these datasets. The average relative risk increase from vaccinated to unvaccinated is 4.9 times. or 491%.
The high standard deviation in the UK data sets would also mean that for every death a vaccinated person suffers, 3 to 7 unvaccinated people would die across all age-ranges. This is a better estimate and can be used for general context and statistics.
Assess risks properly.
When risks are undertaken at the individual or group level, it is best to use absolute risk differences to guide decision-making.
Relative risk is a more accurate measure than absolute risk in cases where the outcomes of decisions affect different groups to different degrees, the risks between specific groups are highly disparate, or information on absolute risks for certain groups is limited.
For instance, if a business purchases product liability insurance, it implies that the manufacturer understands the underlying absolute risk of the insured product’s failing.
By understanding the relative risk of newly designed products' failure rates versus older products' failure rates, we can gain insight into the likely increase in the absolute failure rate of a newly designed electric saw versus these rates in older models.
Risk communication should provide absolute and relative risk estimates in a way that contextualizes risks in terms of relevant outcomes at the decision level in order to build trust.
