Module 06 of 15

Absolute vs. Relative Risk

Why “risk doubles” can describe a tiny change or a large one.

AMathematical Foundation

If the risk of an outcome is p₀ without an exposure and p₁ with it, the absolute risk difference is p₁ − p₀ (in percentage points) and the relative risk is p₁ / p₀. Relative change is (p₁ − p₀) / p₀. The number needed to treat (or harm) is 1 / |p₁ − p₀|: how many people must be exposed for one additional outcome. The same relative change can correspond to very different absolute changes depending on the baseline.

\text{ARD}=p_1-p_0,\qquad \text{RR}=\frac{p_1}{p_0},\qquad \text{NNT}=\frac{1}{|p_1-p_0|}

In words: The absolute risk difference is p one minus p zero; the relative risk is p one over p zero; the number needed to treat is one over the absolute difference.

$p_0$: baseline risk
$p_1$: risk with the exposure or policy

Assumptions

Both risks refer to the same outcome, population and time period.
Relative risk is undefined when the baseline risk is zero, and the number needed to treat is undefined (infinite) when the two risks are equal.

BIntuitive Explanation

“This doubles your risk” sounds alarming. If the risk goes from 1 in 100,000 to 2 in 100,000, the extra risk is one person in 100,000. If it goes from 20% to 40%, one in five people is affected. Headlines prefer relative numbers because they are larger; decisions usually need absolute numbers because they describe how many people are affected.

CConnection to Debate

Impact weighing depends on scale. When a speaker says a policy “halves” a harm, ask for the baseline. When an opponent dismisses a harm as rare, ask how many people that is at population scale: a small absolute risk across millions of people may still be a large number of cases. Using both numbers honestly is a sign of a strong speaker.

DReal-World Application

Reporting the mortality risk of social isolation
Competing interpretation
Holt-Lunstad et al.'s meta-analysis reports that social isolation was associated with a 29% increased likelihood of mortality. That is a relative figure: how many extra deaths it implies depends on the baseline risk of the group over the follow-up period, which is very different for 20-year-olds and 80-year-olds. Before weighing it in the Voluntary Solitude debate, convert it to an absolute difference for the relevant population, and remember that the studies are observational and do not separate chosen solitude from unwanted isolation.
Sources
- Loneliness and Social Isolation as Risk Factors for Mortality: A Meta-Analytic ReviewJulianne Holt-Lunstad, Timothy B. Smith, Mark Baker, Tyler Harris, David Stephenson (Perspectives on Psychological Science 10(2), 227–237), 2015-03-11(abstract only)

These examples describe real policies and research. The numbers in the interactive below and in the practice questions are hypothetical teaching data unless a question says otherwise.

EInteractive Visualization

Set baseline and comparison risks and see absolute difference, relative change, risk ratio and number needed to treat.

Illustrative example — hypothetical data.Hypothetical risks for two groups; adjust both to compare the framings.

Baseline risk0.20%

Probability of the outcome without the exposure or policy.

Comparison risk0.40%

Probability of the outcome with the exposure or policy.

\text{relative change} = \frac{p_1 - p_0}{p_0} \qquad \text{absolute change} = p_1 - p_0

In words: relative change is the difference divided by the baseline; absolute change is just the difference.

Relative change

+100%

Absolute change

+0.20 pts

Risk ratio

2.00

Number needed to harm

500

Relative framing: “Risk rises by 100%.”

Absolute framing: “From 20 to 40 in every 10,000 people.”

Both sentences describe the same numbers. Which one would each side of a debate prefer to quote?

FDebate Practice

GLimitations

Absolute numbers describe how many people are affected, but not how severely, how reversibly, or whether the affected people are especially vulnerable. Those are separate weighing questions. Risk numbers also depend on the study population and may not transfer to another country or age group.

AMathematical Foundation

\text{ARD}=p_1-p_0,\qquad \text{RR}=\frac{p_1}{p_0},\qquad \text{NNT}=\frac{1}{|p_1-p_0|}

In words: The absolute risk difference is p one minus p zero; the relative risk is p one over p zero; the number needed to treat is one over the absolute difference.

$p_0$: baseline risk
$p_1$: risk with the exposure or policy

Assumptions

Both risks refer to the same outcome, population and time period.
Relative risk is undefined when the baseline risk is zero, and the number needed to treat is undefined (infinite) when the two risks are equal.

BIntuitive Explanation

CConnection to Debate

DReal-World Application

Reporting the mortality risk of social isolation
Competing interpretation
Holt-Lunstad et al.'s meta-analysis reports that social isolation was associated with a 29% increased likelihood of mortality. That is a relative figure: how many extra deaths it implies depends on the baseline risk of the group over the follow-up period, which is very different for 20-year-olds and 80-year-olds. Before weighing it in the Voluntary Solitude debate, convert it to an absolute difference for the relevant population, and remember that the studies are observational and do not separate chosen solitude from unwanted isolation.
Sources
- Loneliness and Social Isolation as Risk Factors for Mortality: A Meta-Analytic ReviewJulianne Holt-Lunstad, Timothy B. Smith, Mark Baker, Tyler Harris, David Stephenson (Perspectives on Psychological Science 10(2), 227–237), 2015-03-11(abstract only)

These examples describe real policies and research. The numbers in the interactive below and in the practice questions are hypothetical teaching data unless a question says otherwise.

EInteractive Visualization

Set baseline and comparison risks and see absolute difference, relative change, risk ratio and number needed to treat.

Illustrative example — hypothetical data.Hypothetical risks for two groups; adjust both to compare the framings.

Baseline risk0.20%

Probability of the outcome without the exposure or policy.

Comparison risk0.40%

Probability of the outcome with the exposure or policy.

\text{relative change} = \frac{p_1 - p_0}{p_0} \qquad \text{absolute change} = p_1 - p_0

In words: relative change is the difference divided by the baseline; absolute change is just the difference.

Relative change

+100%

Absolute change

+0.20 pts

Risk ratio

2.00

Number needed to harm

500

Relative framing: “Risk rises by 100%.”

Absolute framing: “From 20 to 40 in every 10,000 people.”

Both sentences describe the same numbers. Which one would each side of a debate prefer to quote?