1.1 What epidemiology studies

Definition 1.1.1. Epidemiology is the study of the distribution and the determinants of health-related states and events in specified populations, and the application of that study to the control of health problems.

Three words in the definition carry the subject. Distribution asks who becomes ill, where and when; answering it is descriptive epidemiology. Determinants asks why: which exposures, behaviours, genes or circumstances change the chance of becoming ill. Answering it is analytic epidemiology, and almost all of this course is about it. Populations says the unit of interest is a group, not a patient. A clinician asks whether this patient has the disease; an epidemiologist asks how often the disease occurs in a group and whether it occurs more often in one group than another.

The word exposure is used for any characteristic whose effect on disease is being studied: a drug, an occupation, smoking, a gene, a water supply. The outcome is usually the occurrence of a disease or death, coded \(D\) (disease) and \(\bar D\) (no disease); exposure is coded \(E\) and \(\bar E\). Both may be more than two-valued, but the binary case carries every idea and is used throughout.

The statistical problems of the subject come from the fact that in most epidemiological work the investigator cannot assign the exposure. Nobody can be told to smoke for twenty years or to drink from a contaminated well. The data are observational: people chose, or were given by circumstance, their exposures, and whatever led them to it may also affect their disease. Separating the effect of the exposure from the effects of everything that travels with it is the central task, and the methods of the later sections (standardisation, stratification, the Mantel–Haenszel procedure, regression) are all tools for it.

Example 1.1.2 (Snow and the London water companies). In 1854 two companies supplied water to the same districts of south London, their pipes running down the same streets. The Southwark and Vauxhall Company drew its water from the Thames below the sewage outfalls; the Lambeth Company had moved its intake upstream. John Snow counted cholera deaths in the first seven weeks of the epidemic by the company supplying each house, and the deaths per \(10{,}000\) houses:

Supply Houses Deaths Per \(10{,}000\) houses
Southwark and Vauxhall \(40{,}046\) \(1{,}263\) \(315\)
Lambeth \(26{,}107\) \(98\) \(38\)

The death rate in houses supplied by Southwark and Vauxhall was \[ \frac {1263/40046}{98/26107} = \frac {0.03154}{0.00375} = 8.4 \] times that in houses supplied by Lambeth.

Snow’s argument for causation did not rest on the size of the ratio alone. He pointed out that the two supplies were intermixed house by house, so that the customers of the two companies were alike in wealth, occupation, crowding and every other respect he could think of, and differed only in their water. In modern language the comparison was exchangeable (Section 1.5): a natural experiment in which circumstance had assigned the exposure almost at random. The table also shows the first data problem of the subject. The denominator is houses, not people, because houses were what Snow could count; a rate per person, or per person-week at risk, would need the number of residents, which he did not have.

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