1.2 Disease occurrence in populations

Populations and time

Disease occurs in people over time, and every measure in the course has a population and a period attached. A closed population (a cohort) gains no members after it is defined: the people enrolled in a trial, the children born in one hospital in 2010, the workers employed at a plant on a given date. It loses members only by death or by the event studied. An open population, such as the residents of a city, gains members by birth and immigration and loses them by death and emigration; individuals enter and leave throughout the period of observation.

A person is at risk of a disease while they are free of it and capable of getting it. Women who have had a hysterectomy are not at risk of uterine cancer; a child immune after measles is not at risk of measles. The population at risk is the right denominator for every measure of how often a disease begins.

The natural history of disease

For a chronic disease the sequence is: exposure begins; after an induction period the disease process starts; after a latent period it becomes detectable, then symptomatic, and is diagnosed; it ends in recovery, chronic illness or death. The epidemiologist usually sees only the date of diagnosis. Two consequences recur. Exposure measured shortly before diagnosis may be the wrong exposure, because the relevant one acted years earlier; and a disease that is present but not yet diagnosed makes a person look disease-free when they are not.

Three measures of occurrence

There are three basic ways of saying how often a disease occurs, studied fully in Section 3. Here they are introduced informally, because the study designs differ in which of them they can estimate.

1.

The risk (cumulative incidence) of a disease over a period is the probability that a person at risk at the start develops it during the period. It is a proportion, between \(0\) and \(1\), and means nothing without the length of the period: the five-year risk is larger than the one-year risk.

2.

The rate (incidence rate, incidence density) is the number of new cases divided by the total person-time at risk: cases per person-year. It has units of \(\text {time}^{-1}\) and can exceed one.

3.

The odds of disease is \(p/(1-p)\), where \(p\) is a risk. It carries the same information as the risk but behaves better mathematically, and it is what a case-control study can compare.

The prevalence of a disease is different from all three: it is the proportion of a population that has the disease at a given time, counting old cases as well as new ones. Prevalence mixes how often a disease begins with how long it lasts.

The fourfold table

When both exposure and disease are binary, the data of almost any study can be laid out as a \(2 \times 2\) table. The notation below is used throughout the course.

The columns are exposure groups and the rows are disease groups. Association is measured by:

• the risk ratio (relative risk) \(\RR = \dfrac {a/n_1}{b/n_0}\);
• the risk difference \(\RD = \dfrac {a}{n_1} - \dfrac {b}{n_0}\);
• the odds ratio \(\OR = \dfrac {a/c}{b/d} = \dfrac {ad}{bc}\).

Whether these sample quantities estimate anything depends on how the table was obtained, which is the subject of the next two subsections.