Absolute Risk

Absolute Risk as the baseline behind a decision model

Absolute risk under the comparator is the starting point for estimating events in a decision model. Relative treatment effects from trials say how much a treatment changes risk, but a model needs to know how many events will occur in the population being treated, and that comes from absolute risk. Getting it wrong shifts every downstream estimate of events avoided, costs and QALYs.

Risk, rate and time

Absolute risk is a probability, so it only has meaning over a stated period. In epidemiology it is the incidence proportion, also called cumulative incidence, which is the number of new cases during a period divided by the number of people at risk at the start of that period. A one-year risk and a five-year risk for the same population are different numbers, and a risk quoted without its period cannot be used in a model.

An incidence rate is a different quantity. It puts person-time in the denominator, so it measures how quickly events occur rather than the chance that they occur by a given time. Gidwani and Russell describe the distinction for modellers. A rate accounts for the time each person spends at risk, while a probability is the number of events in a period divided by the number of people followed for that period.

Estimating absolute risk from data

Absolute risk is estimated from a cohort or trial arm followed over a defined period. With complete follow-up it is a simple proportion.

$$R = \frac{E}{N}$$

where $R$ is the absolute risk over the follow-up period, $E$ is the number of people who have the event during the period and $N$ is the number at risk at the start. Most data sets lose people to follow-up before the period ends, and dividing by the starting number then understates risk because censored people might still have had the event.

The Kaplan-Meier estimator handles censoring by using each person's information up to the time they are censored, on the assumption that censored people have the same prospects as those still followed. One minus the Kaplan-Meier survival estimate gives the cumulative incidence of the event over time. Where a competing risk such as death from another cause can prevent the event of interest, Austin, Lee and Fine show that this complement overstates incidence, and the cumulative incidence function should be used instead.

Converting risk for use in a model

A Markov or state-transition model applies a transition probability in each cycle, and published risks rarely match the model's cycle length. The standard route is to convert the risk to a rate, rescale the rate to the new period and convert back, which assumes the rate is constant over the period.

$$r = \frac{-\ln(1 - p)}{t}, \qquad p_{\text{cycle}} = 1 - e^{-r \, t_{\text{cycle}}}$$

where $p$ is the risk observed over period $t$, $r$ is the constant rate implied by that risk, $t_{\text{cycle}}$ is the model's cycle length in the same time units and $p_{\text{cycle}}$ is the probability of the event in one cycle. Gidwani and Russell give this rate-to-probability conversion together with the equivalent conversions between time frames.

Worked example converting a one-year risk to a monthly probability

The figures below are illustrative. A cohort study follows 2,000 people for one year with no loss to follow-up, and 120 have a myocardial infarction.

$$R = \frac{120}{2000} = 0.06$$

where 0.06 is the one-year absolute risk. A model with monthly cycles needs a one-month probability. Converting to a rate gives the following.

$$r = -\ln(1 - 0.06) = 0.061875$$

where $r$ is the annual rate, with $t$ equal to one year. Dividing the rate by 12 and converting back gives the monthly probability.

$$p_{\text{month}} = 1 - e^{-0.061875/12} = 0.00514$$

where $p_{\text{month}}$ is the monthly transition probability. Dividing the annual risk by 12 would give 0.00500 instead. Applied over twelve cycles, the converted value reproduces the one-year risk and the divided value does not.

$$1 - (1 - 0.00514)^{12} = 0.0600$$

where 0.0600 is the one-year risk implied by the converted monthly probability.

$$1 - (1 - 0.005)^{12} = 0.0584$$

where 0.0584 is the one-year risk implied by the divided value, which understates the observed risk. The gap is small at low risks and widens as risks rise, which is why the conversion matters most for common events.

Baseline risk and treatment effects

Absolute risk under the comparator, often called baseline risk, is usually modelled separately from the relative effect of treatment. Dias and colleagues, in the evidence synthesis series produced for the NICE Decision Support Unit, recommend separate modelling of baseline and relative effects whenever possible. They advise that baseline response should be as specific as possible to the population of interest, which may favour recent trials, relevant cohorts or registers over the full set of trials used for relative effects.

The NICE methods manual (PMG36) takes the same approach. It notes that baseline risk can be quantified, including from observational studies, and that relative treatment effects from randomised trials may then be applied to baseline risk for the populations or subgroups of interest. It asks that the choice of data sets be justified by their suitability to the population in the evaluation.

Why baseline risk drives results

Treatment benefit in absolute terms is the product of baseline risk and the relative risk reduction, and a constant relative effect is usually assumed across risk levels. The same treatment can be highly cost-effective in a high-risk group and poor value in a low-risk group. The absolute risk used for the comparator arm therefore often drives the result as strongly as the trial evidence, and it is a natural candidate for scenario and sensitivity analysis.

Absolute risk also supports communication. A decision-maker told that a treatment halves risk has no sense of scale until the baseline risk is known, and the absolute risk reduction and number needed to treat both require it.

Absolute risk, relative measures and hazards

Absolute risk is the probability of an event in one group. Relative risk compares the risks in two groups as a ratio, and the risk difference compares them by subtraction.

Absolute risk also differs from a hazard. A hazard is an instantaneous rate among people still at risk, whereas absolute risk accumulates over a period. Under a constant hazard $h$, the risk over a period of length $t$ is $R(t) = 1 - e^{-ht}$, which rises less than in proportion to time; this is why dividing an annual risk by 12 understates the monthly probability.

Errors with time periods and populations

The most common error is to quote or use a risk without its time period. A 6 per cent risk means nothing for a model until it is known whether it applies over one year or five, and combining risks from studies with different follow-up periods without conversion mixes incompatible quantities.

Another is to transfer a risk from one population to another without justification. Absolute risk varies with age, disease severity and care setting, so a baseline risk taken from a trial population may not describe the patients a decision applies to. The rate conversion also rests on an assumption of a constant rate over the period, which is unlikely to hold where risk changes sharply with time since diagnosis or treatment. Gidwani and Russell add that the conversion does not yield correct probabilities when three or more transitions can occur from a state within a cycle, a common situation in multi-state models.

Sources

• Centers for Disease Control and Prevention. Principles of Epidemiology in Public Health Practice, 3rd edition. Lesson 3: Measures of Risk. 2012.
• Gidwani R, Russell LB. Estimating transition probabilities from published evidence: a tutorial for decision modelers. PharmacoEconomics. 2020;38(11):1153-1164.
• Goel MK, Khanna P, Kishore J. Understanding survival analysis: Kaplan-Meier estimate. International Journal of Ayurveda Research. 2010;1(4):274-278.
• 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.
• Dias S, Welton NJ, Sutton AJ, Ades AE. Evidence synthesis for decision making 5: the baseline natural history model. Medical Decision Making. 2013;33(5):657-670.
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 2022; updated 2026.