Event Probability

Event Probability: Concept Architecture

Put a defined event inside a defined interval

An event probability is the chance that a specified event occurs for a specified person or group during a stated period, conditional on the information used to define the risk set. This page shows how to interpret the number, derive it from evidence, and place it in a health economic model without confusing it with a rate or hazard.

State exactly what can happen and to whom

Define the event, population, starting condition, interval, and whether the number refers to a first occurrence or any occurrence. For example, a one-year probability of first stroke among people who have not had a stroke is different from a one-year probability of at least one admission among all people with established disease. Treatment, age, history, and calendar time may change that probability.

A probability lies between 0 and 1 and has no per-time unit, although its interval must be reported. The value 0.10 over one year does not mean a 0.10 probability in each month. A transition probability in a state-transition model is an event probability conditional on starting a cycle in a particular state and may also identify the destination state.

Estimate a risk from complete follow-up

If 12 of 200 initially event-free patients have a first qualifying event over a fully observed year, the observed one-year event probability is $12/200=0.06$, or 6%. This simple proportion assumes a common interval, complete ascertainment, and a denominator consisting of people at risk at the start.

With incomplete follow-up, a time-to-event method may be needed; when death or another event prevents the event of interest, the relevant real-world risk may be a competing-risk cumulative incidence rather than one minus a Kaplan–Meier estimate that censors the competing event. A probability estimated in one group or period should not automatically be transferred to another. The tutorial on estimating transition probabilities for decision models examines how evidence measures are translated into model probabilities.

Convert a rate only under its assumptions

A constant event hazard $r$ over an interval of length $\Delta t$ implies a first-event probability of at least one event during that interval:

$$p(\Delta t)=1-\exp(-r\Delta t).$$

For an illustrative constant hazard of 0.12 per person-year over one month, the probability is $1-\exp(-0.12/12)\approx0.00995$, or about 1.0%. Multiplying $0.12$ by one-twelfth gives a close small-interval approximation, but the exact exponential conversion follows the specified constant-hazard model. The hazard is a rate conditional on remaining event-free; the probability is the chance of experiencing the event over the whole interval.

This simple expression does not by itself solve a model with multiple competing destinations, time-varying hazards, or recurrent events. Separate conversion of each destination's probability can produce incoherent rows or fail to preserve the original multistate process. Research on time in economic evaluation and the transition-probability tutorial describe these conversion problems.

Use probabilities consistently in a model

Assign probabilities to mutually exclusive outcomes within the model's interval and ensure all destinations, including remaining in the current state, sum to one for each starting state. If a patient can experience several events within one interval, decide whether the model represents their sequence, a combined outcome, or only the state at the next boundary. A longer cycle can conceal clinically consequential intermediate events.

Document the evidence source, outcome definition, denominator, follow-up, treatment arm, conversion method, and uncertainty. A relative risk or hazard ratio is not itself an event probability; combining it with a compatible baseline requires an explicit method and assumptions. Test alternative plausible inputs and cycle lengths when the estimated event chance materially affects costs, quality-adjusted life years, or the decision.