What’s the risk? People discuss risk frequently, but it’s not always clearly understood. It is your exposure to danger or adverse outcomes. Statistically, we define risk as the probability of a negative outcome occurring, and there are several ways to calculate it.

Imagine deciding whether to take a medication to reduce the chances of an illness. Ideally, this decision involves understanding different types of risk. These include knowing your absolute risk for the medical condition and the relative risk reduction if you take the medication. How many people need to take the drug to prevent one case?

Understanding and calculating these statistics can help you make informed decisions in your daily life. Risk assessment and management play a crucial role in countless fields, including the following:

**Healthcare**: Evaluating treatment efficacy and patient outcomes.**Finance**: Managing portfolios to balance potential gains against the likelihood of losses.**Public Safety**: Planning and implementing safety protocols by analyzing the probabilities of events such as criminal activities or public health crises.**Engineering**: Ensuring structural safety and reliability by evaluating the chances of failure or accidents in designs and materials.

This guide explores key concepts like relative vs absolute risk, risk reduction, and the number needed to treat. These measures quantify the probability of adverse outcomes in different ways. Some of these statistics show how treatments or exposure to various conditions help you avoid negative events. In the conclusion, I provide tips for when and why you should use each type of risk statistic.

## Absolute Risk (AR)

Absolute risk (AR) is a straightforward measure that reflects the likelihood of an event occurring within a specific population over a defined period. It’s expressed as a simple probability, focusing on a single group without comparing it to others. For instance, if you’re looking at the risk of developing a medical condition within a group, AR gives us the direct probability.

The absolute risk formula is the following:

For example, suppose we have a group of 100 people who don’t take the medication, and 12 of them get sick. The absolute risk for this group is the following:

The calculated absolute risk is 12%. This result indicates that individuals in the untreated group have a 12% probability of developing the condition over a year.

Throughout the rest of this post, I’ll build up this hypothetical medical condition, showing you various ways to assess risk and the reduction associated with a medication. We’ll consider this AR of 0.12 for unmedicated people to be the control group.

Next, let’s add a treatment group!

## Relative Risk (RR)

Relative risk (RR) is a ratio of the absolute risks for two groups. It tells us how the chances in one group relates to those in another. This statistic helps you understand how a particular factor, like a treatment or lifestyle change, affects the outcome probability.

The relative risk formula includes the exposure or treatment group in the numerator and the unexposed or control group in the denominator, as shown below. This comparison shows how much a factor alters the probability of the outcome.

To calculate RR, you first need to calculate the absolute risks (ARs) for both groups. Then, divide one by the other.

Imagine a study where 4 out of 100 people in a treatment group develop a condition, compared to 12 out of 100 in a control group. The calculated RR is the following:

This RR indicates that the chances of developing the illness in the treatment group is one-third that of the control group, suggesting that the treatment might effectively reduce the likelihood of the medical condition. Lower RRs indicate greater effectiveness or protection.

Learn more in-depth about Relative Risk: Definition, Formula & Interpretation.

## Absolute Risk Reduction (ARR)

Absolute risk reduction (ARR) is the difference between the ARs for the control and treatment groups. It’s another method for understanding the effect of a treatment or condition. For this calculation, you’re again working with ARs for two groups, but instead of dividing them, you use subtraction.

The absolute risk reduction formula is the following:

Using the values from the previous medical condition example, the ARR calculation is:

This calculated risk shows that treatment reduces the chance of getting the condition by 8%. In other words, if 100 people took the medication for a year, it would prevent eight cases.

## Relative Risk Reduction (RRR)

Relative risk reduction (RRR) compares the probability of an event occurring in two groups by showing the proportionate reduction in probability.

The relative risk reduction formula is the following:

Alternatively, use the following formula with RR to obtain the same results:

Let’s return to the medical condition example, where 12/100 of the controls got the disease compared to 4/100 in the treatment group. The calculated relative risk reduction is the following:

Or, using the RR we found previously:

This result indicates the medication reduced the disease’s relative probability in the treatment group by 67% compared to the untreated group.

RRR measures can range from 0 – 100%, where higher values indicate greater reduction. 100% represents the complete elimination of risk. RRR is particularly useful when you want to compare the impact of a treatment or intervention across populations.

## Calculating the Number Needed to Treat (NNT)

Number needed to treat (NNT) is the number of people who need to undergo a specific treatment to prevent one additional bad outcome.

The formula for the number needed to treat is the inverse of the absolute risk reduction:

For example, our previously calculated ARR of 8% for the treatment group corresponds to the following number needed to treat calculation:

This NNT result means you need to treat about 12 people with the medication to prevent the disease in one person.

A lower number needed to treat is generally preferable because fewer people need the treatment to prevent an adverse outcome. As NNT increases, weighing the treatment benefits against side effects grows in importance.

## Tips for Using the Types of Risk

Given this choice of statistics, which ones should you use? That depends on the risks themselves and what you want to show. For the following sections, we’ll consider the probabilities associated with a treatment that researchers give to high and low-risk populations.

Odds Ratios and Hazard Ratios are two other risk statistics that I don’t discuss in this post. Click the links to learn more about them.

### Using Relative Measures (RR &RRR)

Because RR and relative risk reduction use a ratio, they tend to remain constant across different populations having differing chances.

For example, suppose a treatment reduces the chances of an illness from 20% to 10% in a higher-risk population and from 4% to 2% in a lower-risk population. The RRR is 50% in both cases. The treatment halves the probability, irrespective of the starting level.

This property facilitates comparisons between different populations.

However, relative measures can be less effective for communicating the absolute magnitude of the effects because they mask the baseline risk level.

Consider that a low baseline AR can inflate both RR and RRR, making them sound more dramatic than warranted.

For instance, if the treatment has an RRR of 50%, that sounds impressive. But if the absolute risk reduction is only 2% (from 4% to 2%), you might reconsider its effectiveness.

In this scenario, AAR and NNT give a clearer picture of actual benefits. More on that in the next section!

### Using Absolute Measures (AR, ARR, & NNT)

Absolute risk measures tend to provide more concrete information about the impact of a treatment in a specific population. Consider that the real-world effect of a treatment varies depending on the baseline AR. The ARR and NNT formulas incorporate the baseline AR to convey the practical importance for populations with differing risk levels.

Specifically, treating a population with a higher baseline AR produces a greater ARR than in a lower-risk population.

Continuing with the example in the previous section, the ARR in the higher-risk population is 20% – 10% = 10%. Conversely, the lower group has an ARR of only 4% – 2% = 2%. Their RRs are the same (50%), but the absolute risk reductions are strikingly different (10% vs 2%).

Similarly, the number needed to treat (NNT), the inverse of ARR, will be lower in populations with higher baseline risks. In the higher level group, the NNT is 1 / 0.10 = 10, meaning you need to treat 10 people to prevent one illness. In the lower group, the NNT is 1 / 0.02 = 50, indicating you need to treat 50 people to prevent one illness.

These differences in the absolute measures *might* indicate that using the treatment is warranted in the higher-risk population but not the low level population. But you wouldn’t know that from the RRs!

You gain deeper insight into managing adverse outcomes by understanding and applying these formulas to calculate the relative and absolute risks, their reductions, and the number needed to treat. Understanding these statistics can help you make decisions.

## Reference

Monaghan, T.F.; Rahman, S.N.; Agudelo, C.W.; Wein, A.J.; Lazar, J.M.; Everaert, K.; Dmochowski, R.R. Foundational Statistical Principles in Medical Research: A Tutorial on Odds Ratios, Relative, Absolute Risk, and Number Needed to Treat. *Int. J. Environ. Res. Public Health* **2021**, *18*, 5669.

MEGUENNI Kaouel says

Merci pour cet exposÃ© clair et pÃ©dagogique. Puis-je l’utiliser pour mes Ã©tudiants ?

Jim Frost says

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