Measuring Disease Occurrence in Epidemiology

$$\text{Point prevalence} \approx \text{Incidence} \times \text{Duration}$$

Exam Tip: If a disease is highly infectious (high incidence) but people recover very quickly (short duration), the prevalence may remain low. Conversely, a disease that is not very "new" (low incidence) but is chronic and incurable (long duration) will result in high prevalence.

Incidence: Measuring New Events

Incidence measures the frequency of new events occurring in a population at risk over a specific period. It is a fundamental tool for analytical epidemiology because it allows researchers to estimate the actual risk of developing a condition, which is essential for assessing causal associations.

Incidence is divided into two main approaches based on how the denominator is constructed:

1. Incidence Based on Individuals at Risk

This approach treats incidence as a probability and is often referred to as cumulative incidence or incidence proportion. In a study with perfect follow-up, it is simply the number of new events divided by the initial population at risk.

However, real-world studies often face the challenge of censored observations. Censoring occurs when follow-up is incomplete—for example, when a participant dies from an unrelated cause, moves away (migration), or withdraws from the study. To handle these incomplete data points, epidemiologists use two specialized statistical methods:

• The Life Table (Actuarial) Approach: This method divides the follow-up period into specific time intervals. It calculates the probability of an event within each interval, correcting the denominator for individuals lost during that period. A common convention is to subtract half of the censored observations from the denominator, assuming they were at risk for only half of the interval.
• The Kaplan-Meier Method: Unlike the life table, the Kaplan-Meier approach calculates the probability of an event at the exact time it occurs. It is highly efficient because it uses all available information from every individual up to the moment they are censored or experience the event.

2. Incidence Based on Person-Time Units

Instead of using a simple count of people, this approach uses person-time (e.g., person-years) as the denominator. This represents the total amount of time all individuals in the study were "at risk" and under observation.

Incidence rates based on person-time are often called incidence density. This is analogous to "velocity"—it measures the instantaneous rate at which events occur. Because the time unit is arbitrary, a rate can range from 0 to infinity.

Odds and the Odds Ratio

While proportions (like incidence and prevalence) are intuitive, epidemiologists frequently use odds. Odds represent the ratio of the probability of an event occurring to the probability of it not occurring:

$$\text{Odds} = \frac{\text{Probability of event}}{\text{Probability of no event}}$$

For example, if the proportion of smokers in a population is 0.20, the odds are:

$$\begin{aligned} \text{Odds} &= \frac{0.20}{1 - 0.20} \\ &= \frac{0.20}{0.80} \\ &= 0.25 \text{ (or 1:4)} \end{aligned}$$

Note: While absolute odds are rarely used as a standalone descriptive measure, the odds ratio (the ratio of two odds) is one of the most powerful tools in epidemiology. It is widely used in case-control studies to estimate relative risk and is the standard output for logistic regression models.