Mapping an outbreak's source

How can scattered dots on a street map point to a cause nobody has yet seen?

The story is told as though the map did the work. John Snow marks each cholera death in Soho as a small bar against its address in the late summer of 1854, the marks pile up around the pump in Broad Street, the handle comes off, and the outbreak stops. A picture reveals a cause.

But hold the picture up and ask what it actually rules out. Deaths cluster around the pump — and also around a crowded, low-lying, filthy quarter, around a particular set of trades, around the poorest housing, around the densest population. Every one of those clusters in the same place. The reigning theory of the day held that cholera came from foul air rising off waste, and foul air would concentrate in exactly that district too. So the miasmatists looked at the same dots and saw their own theory confirmed. If two rival explanations both predict the picture, what has the picture told you?

Start with the most ordinary trap. Dots on a map are cases, and cases pile up wherever people pile up. Draw any illness at all on a city map and it will look clustered, because the population is clustered. So the first thing a cluster must be tested against is its denominator: how many people were at risk in that block, not how many fell ill. A cluster that merely reproduces the population map contains no information.

Suppose the cluster survives that test — there really is excess risk here. What have you learned? Only that something local is doing it. Everything that shares the same geography remains a candidate, and in a dense quarter that is almost everything: the air, the water, the drains, the poverty, the trade, the crowding. The dots cannot separate them, because the dots are the thing all the hypotheses agree about.

So where does discrimination come from? Ask a sharper question: where do the rival explanations disagree? Air and water are both local, but not identically local. Air is a property of a place; water is a property of a habit. That gap is where the evidence lives, and it shows up as two kinds of outlier.

First, the holes inside the cluster. On Broad Street itself stood a brewery whose workmen were allowed beer and which drew on its own deep well; its men were in the middle of the worst of it and were essentially untouched. A nearby workhouse held hundreds of people inside the affected area, had its own well and piped supply, and lost very few. Bad air cannot explain a dry island in the middle of its own pool. Drinking water can.

Second, the cases far outside it. A widow who had moved out to Hampstead liked the taste of Broad Street water and had a bottle carted to her regularly. She died of cholera, as did a niece visiting from Islington. Neither had breathed a molecule of Soho air. Do you see the shape of the argument? It is not the cluster that decides. It is the exceptions to the cluster — the people who shared the place but not the water, and the people who shared the water but not the place.

Snow also did something to the map itself that is easy to overlook. On a later version he drew a boundary enclosing all the points from which the Broad Street pump was the nearest pump by walking time through the actual streets, not by straight-line distance. That is a small but serious move: it says exposure follows behaviour along a network, and a person's true catchment is where their feet take them.

And the argument he thought strongest was not the Soho map at all. In south London two water companies had laid pipes along the same streets, so neighbouring houses — same air, same drains, same class, same rents — were supplied from different points on the Thames, one of them downstream of the city's sewage. Snow reported cholera mortality of about 315 deaths per 10,000 houses in the contaminated company's houses against about 37 per 10,000 in the other's. Every local explanation is held constant by the street; only the water varies.

Three corrections are worth making to the famous version of the story.

The map did not generate the hypothesis. Snow had argued for waterborne transmission years earlier; the Soho map was drawn to test and display an idea he already held. That distinction matters, because a picture built after the fact around a suspected cause will always look persuasive. The discipline is in specifying beforehand what pattern would have embarrassed you.

Removing the pump handle, on 8 September 1854, did not end the outbreak. Deaths were already falling steeply, partly because much of the neighbourhood had fled. It is remembered as the proof, but as evidence it is a single before-and-after with no comparison; the natural experiment across the two water companies carries the weight.

And the loop was closed by someone else. A local curate, Henry Whitehead, who initially set out to refute Snow, worked back through the parish records to a case at the start: an infant at 40 Broad Street whose soiled napkins were washed into a cesspool a few feet from the well, which was found to be leaking. Only with that does the map stop being a correlation and become a mechanism.

The general lesson survives all three. A cluster is a question, and the honest procedure is to ask what else clusters there, what the denominator is, whether chance alone would throw up a group this tight somewhere in a big city, and finally which observations would separate the surviving explanations.

• How modern scan statistics decide whether a cluster is tighter than chance would produce somewhere in a large map.
• Why case-mapping by residence can mislead for illnesses acquired at work, at school, or in transit.
• The ecological fallacy: reading a relationship measured over areas as one about people.

Every term the collection defines is gathered in the glossary.