Quantifying Risk in Epidemiology: Key Measures

An easy-to-skim guide to core epidemiology risk measures, explaining what each term means, when to use it, and how to interpret results in studies and public health reports.

It clarifies odds versus probability with a simple everyday example and highlights where odds ratio and relative risk fit in different study designs.

The content defines risk, relative comparisons, and reductions in risk in plain language, focusing on practical understanding rather than computation.

It also introduces measures used to judge benefits and harms, such as number needed to treat and number needed to harm, and explains why they matter for decision-making.

Population metrics like case fatality rate, mortality rate, and attack rate are summarized to show how outbreaks and health impacts are assessed across groups.

A final table pulls the pieces together so learners can connect each measure to its meaning and common use case.

1. Quantifying risk formulas
Odds of event = P / (1-P)
Odds = 1 num / 1 num (Rest)
P: probability
Example: In Dice, P=1/6 , Odds= 1/5
Odds Ratio (OR) = Odds of exposure in cases / Odds
of exposure in control
Used in case-control studies
Risk: probability of developing a disease over a certain
period of time.
Risk = 1 num / 2 num (Sum)
Relative risk (RR) = Risk of disease in exposed / risk in
unexposed group
Used in cohort studies
Relative risk reduction (RRR) = Proportion by which the intervention reduces the risk of an outcome compared to the
control group.
Relative risk reduction (RRR) = Absolute risk reduction / Risk in control
Attributable risk (AR) aka Absolute risk increase =
Risk of disease in exposed - risk in unexposed group
Number Needed to Harm (NNH) = Number of people
who need to be exposed to a risk factor for one
additional person to be harmed.
Attributable risk Percentage (AR%)
Absolute risk reduction (ARR) = Risk of disease in
control - risk of disease in treatment group
Number Needed to Treat (NNT) = Number of people
who need to receive a treatment to prevent one
additional bad outcome.
Case Fatality Rate (CFR) = (Deaths from disease / Total cases of disease) × 100
Mortality Rate = (Total deaths / Total population) × 1000 ( or other unit)
Odds=​
1−P
P
OR=​=
(b/d)
(a/c)
​
bc
ad
Risk=​
Total individuals in exposure group
Number of affected individuals
RR=​
c/(c+d)( )
a/(a+b)( )
RRR=1−RR=​=
Risk in Control (ARC)
Absolute Risk Reduction (ARR)
​
ARC
ARC−ART
AR=​−(
a+b
a
)​ (
c+d
c
)
NNH=​
AR
1
ARP=​×(
RR
RR−1
)100 
ARR=ARC−ART=​−(
c+d
c
)​(
a+b
a
)
NNT=​
ARR
1
CFR=
​×(
Total cases of disease
Deaths from disease
)100 
Mortality Rate=​×(
Total population
Total deaths
)1000Quantifying risk formulas 1

2. Attack Rate = (Number of new cases / Total population at risk) × 100
Here is a table summarizing the formulas along with their meanings:
Measure Formula Meaning
Odds Ratio (OR) (a/c) / (b/d) = (a * d) / (b * c)
Ratio of the odds of exposure in
cases to the odds of exposure
in controls (used in case-control
studies).
Relative Risk (RR) (a / (a + b)) / (c / (c + d))
Ratio of the risk of an outcome
in the exposed group to the risk
in the unexposed group (used in
cohort studies).
Relative Risk Reduction (RRR) 1 - RR
Proportion by which the
intervention reduces the risk of
an outcome compared to the
control group.
Attributable Risk (AR) (a / (a + b)) - (c / (c + d))
Difference in incidence of an
outcome between exposed and
unexposed groups (excess risk
due to exposure).
Absolute Risk Reduction (ARR) (c / (c + d)) - (a / (a + b))
Reduction in absolute risk of an
outcome due to an intervention.
Number Needed to Treat (NNT) 1 / ARR
Number of people who need to
receive a treatment to prevent
one additional bad outcome.
Number Needed to Harm (NNH) 1 / AR
Number of people who need to
be exposed to a risk factor for
one additional person to be
harmed.
Case Fatality Rate (CFR)
(Deaths from disease / Total
cases of disease) × 100
Percentage of individuals with a
disease who die from it.
Mortality Rate
(Total deaths / Total
population) × 1000 ( or other
unit)
Number of deaths in a given
population over a specific
period.
Attack Rate
(Number of new cases / Total
population at risk) × 100
Proportion of a population that
develops a disease during an
outbreak.
Attack Rate=​×(
Total population at risk
Number of new cases
)100Quantifying risk formulas 2