Signature
R = E / N
| Inputs | Definition | Unit |
|---|---|---|
E | Number of people in the cohort who have a new occurrence of the event during the period | count of people |
N | Number of people free of the event and able to have it at the start of the period, greater than zero | count of people |
R | Probability that a person at risk at the start of the period has the event by its end | probability from 0 to 1, over a stated period |
|---|
Function
Absolute risk estimation function
Maps the number of people who have a new event during a stated period, and the number at risk at the start of that period, to the probability of the event over the period. The result is a risk, tied to the length of the period, not a rate per unit of time. Moving a risk to a different period, such as a model cycle, goes through a rate and is covered on the Transition Probability page.
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Implementations
Excel
Absolute risk from named counts
Excel divides the event count by the number at risk and returns #N/A when the denominator is not positive.
=IF(AtRisk>0,Events/AtRisk,NA())
Assumptions
Closed cohort with complete follow-up
Every person counted in N is followed to the end of the period or to the event. When people are lost to follow-up or censored, dividing by N understates the risk, and a survival method such as the Kaplan-Meier estimator is used instead.
Risk stated with its period
R applies only to the period over which E was counted. A one-year risk and a five-year risk for the same cohort are different quantities, and the period is reported with every risk.
Numerator contained in the denominator
E counts only new events among the people in N, so R cannot exceed 1. N excludes people who already have the condition or cannot have it.
Worked examples
One-year risk of myocardial infarction
A cohort of 2,000 people is followed for one year with no loss to follow-up, and 120 have a myocardial infarction. The one-year absolute risk is 0.06, as in the article. The figures are illustrative.
E = 120; N = 2000; R = 0.06
Thirteen-year risk of death in a diabetic cohort
In the CDC teaching example, 100 of 189 diabetic men died during 13 years of follow-up, a 13-year risk of about 0.529. The risk describes the whole 13 years and is not an annual figure.
E = 100; N = 189; R = 0.529
Food-specific attack rate in an outbreak
In the CDC outbreak example, 30 of the 99 people who ate potato salad developed gastroenteritis, a risk of about 0.303 over the outbreak period.
E = 30; N = 99; R = 0.303
Common errors
Dividing by the starting number after losses to follow-up
In the CDC example of 16 cases among 2,100 people followed for four years, dividing by 2,100 gives about 7.6 per 1,000 but understates the risk, because it assumes that people lost to follow-up stayed free of disease for the whole period.
Using the complement of Kaplan-Meier survival under competing risks
Where another event, such as death from other causes, can prevent the event of interest, one minus the Kaplan-Meier survival estimate overstates the absolute risk. The cumulative incidence function gives the risk in that setting.
Dividing a risk by the number of cycles
Dividing a one-year risk of 0.06 by 12 gives a monthly probability of 0.00500, which over 12 cycles implies a one-year risk of about 0.0584 rather than 0.06. The rate conversion on the Transition Probability page gives about 0.00514.
Quoting a risk without its period
A risk of 6 per cent cannot enter a model until it is known whether it applies over one year or five, and risks from studies with different follow-up are not combined without conversion.
Sources
Incidence proportion as a measure of risk
Centers for Disease Control and Prevention. Principles of Epidemiology in Public Health Practice. 3rd ed. Atlanta: CDC; 2012. Lesson 3: Measures of Risk, section 2: Morbidity frequency measures. Definition of incidence proportion (risk), the method for calculating it, examples A and B, and the comparison with the incidence rate for a cohort with losses to follow-up.
Probabilities and rates differ in their denominators
Gidwani R, Russell LB. Estimating transition probabilities from published evidence: a tutorial for decision modelers. PharmacoEconomics. 2020;38(11):1153-1164. Section on changing the time frame of probabilities: a probability is the number of events in a period divided by the number of people followed for that period, and a rate divides by time at risk.
Cumulative incidence in the presence of competing risks
Austin PC, Lee DS, Fine JP. Introduction to the analysis of survival data in the presence of competing risks. Circulation. 2016;133(6):601-609. The complement of the Kaplan-Meier survival function overstates incidence when competing risks are present; the cumulative incidence function is used instead.
Canonical Identity
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