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Introduction to Thinking About Data I:

The Importance of Being Earnest–Why Numbers Matter in Public Health

MMED

African Institute for the Mathematical Sciences

Muizenberg, South Africa

May, 2017

Brian G Williams, PhD

Stellenbosch University

Slide Set Citation: DOI: 10.6084/m9.figshare.5043136

The ICI3D Figshare Collection

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Goals

Learn to

1. See patterns in data

2.Formulate hypothesis

3.Test theories

2The purpose of models is not to fit the data but to sharpen the questions. S. Karlin

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The supreme goal of all theory is to make the

irreducible basic elements as simple and as

few as possible without having to surrender

the adequate representation of a single

datum of experience.

Albert Einstein:1933

On the Method of Theoretical Physics The Herbert Spencer Lecture, Oxford (10 June 1933)

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Three rules of good modelling

• Stay as close to the data as you can

• Put in as much biology as you can

• Keep it simple

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Semelweiss

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Ignaz Semmelweiss: 1818–1865

Or why washing your hands matters

Junior doctor in

Vienna General Hospital

Puerperal fever and

maternal mortality

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Ignaz Semmelweiss

About one in fifteen mothers were dying of puerperal fever during childbirth

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In 1840 maternal mortality in the red wards fell below that in the blue

wards. Medical students, who were doing autopsies before delivering

babies, were still working in the blue wards but had stopped delivering

in the red wards. In 1847 his colleague Jakob Kolletschka was cut with

a student's scalpel while performing a post-mortem and died with a

pathology similar to that of the mothers.

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Only midwives

in red wards

Ignaz SemmelweissKolletschka dies

of septicaemia

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In 1848, aged 30 years, he made the medical students wash their hands in

chlorinated lime before they went into the maternity wards.

Mortality in the blue wards dropped to the same level as in the red wards.

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Semmelweiss makes the

medical students wash

their hands

Ignaz Semmelweiss

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Problem Pattern in the data Think of an explanation

Do an intervention See if it works

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In 1849 he was fired for criticizing his superiors. In 1865 he died of septicaemia in an insane asylum but it seems that the medical students must have gone on washing their hands

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Ignaz Semmelweiss

Semmelweiss fired

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We can now work out odds-ratios and put confidence limits on the estimates.

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blu

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Ignaz SemmelweissSemmelweiss makes the

medical students wash

their hands

Only midwives

in red wards

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Snow

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Cholera and its mode of

transmission

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William Farr: 1851

Miasma theory: Cholera was the result of

breathing polluted air

‘The amount of organic matter…[and] its

distribution will bear … resemblance to the

law regulating the mortality from cholera at

the various elevations’

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Cholera mortality in London: 1849

( )a

m hh b

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John Snow: 1854

Cholera is a water borne disease

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Oxford Street

Regen

t Stre

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Snow 1854 cases of cholera

Oxford Street

Regen

t Stre

et

Oxford Street

Regen

t Stre

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Snow 1854 cases of cholera

Work

house

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Oxford Street

Regen

t Stre

et

Snow 1854 cases of cholera

Oxford Street

Regen

t Stre

et

Oxford Street

Regen

t Stre

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Snow 1854 cases of cholera

Work

house

Water pumps

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Lancet 1858 Obituary columnDR JOHN SNOW—This well-known physician died at noon on the 16th instant, at his house in Sackville-street, from an attack of apoplexy. His researches on chloroform and other anaesthetics were appreciated by the profession.

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In 1854 Filippo Paccini ‘Microscopical observations and pathological deductions on cholera’ in which he discovered a bacillus which he called Vibrio, and described the organism and its relation to cholera. Recognized in 1965

In 1884 Robert Koch became famous for his identification of the cholera bacillus [among other things] and is the acknowledged discoverer of the cholera organism.

Vibrio cholerae

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Lancet 2014 Retraction

The Lancet wishes to correct, after an unduly

prolonged period of reflection, an impression that

it failed to recognise Dr Snow’s remarkable

achievements in the field of epidemiology and [in]

deducing the mode of transmission of cholera. …Comments in 1855 such as In riding his hobby

very hard, he has fallen down through a gully-

hole and has never since been able to get out

again and Has he any facts to show in proof? No!

were perhaps … overly negative in tone.

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Historical data

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Infectious diseases in England and Wales

1900 to 1990

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Deaths at Baragwanath by age, sex and HIV-status 2006-2009

Men Positive Negative UndecidedWomen Positive Negative Undecided

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Mendel

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Mendel’s Peas

1822 to 1884

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Question• Peas have tall or short stems but never in between.

• We can breed true; so that tall plants only produce

tall plants and short plants only produce short

plants

• What happens when we cross them to get the first

filial or F1 generation?

• What happens when we cross the F1 plants to get

the F2 generation?

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Experimental design

Observation: Only two kinds of peas: Tall or short.

Experiment:

Tall Short

Tall Short

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•••

Tall Short

Tall Short

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•••

F1 Tall

F2 Tall:Short

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Character Dominants Recessives Ratio

Round v. wrinkled seeds 5474 1850 2.96

Yellow v. green seeds 6022 2001 3.01

Purple v. white flowers 705 224 3.15

Smooth v. constricted pods 882 299 2.95

Axial v. terminal flowers 651 207 3.14

Green v. yellow unripe pods 428 152 2.82

Tall v. dwarf stems 787 277 2.84

Total 14949 5010 2.98

F2 Data

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Theory!

• Gene has two alleles: T or t

• Breed TT and tt.

• TT x tt Tt

• F1: are tall. T is dominant

• Tt x Tt TT, Tt, tT or tt

• F2: 3 tall plants for each short plant.

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Mendel did not understand that he had just discovered genetics.

Darwin must have read Mendel’s paper but even he did not understand that Mendel had just given him the mechanism underlying his theory of evolution.

Statistics helps us to define the question; the answer is always in the biology!

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Advice to young epidemiologists

Never make a calculation until you know the answer.

Make an estimate before every calculation, try a

simple biological argument (R0, generation time,

selection, survival, control). Guess the answer to

every puzzle. Courage: no one else needs to know

what the guess is. Therefore, make it quickly, by

instinct. A right guess reinforces this instinct. A wrong

guess brings the refreshment of surprise. In either

case, life as an epidemiologist, however long, is more

fun.

Plagiarised from E.F. Taylor and J.A. Wheeler Space-time

Physics (1963)

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Thank you for listening

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Summary

1. Stay as close to the data as you can

2. Look for interesting patterns

3. Put in as much biology as you can

4. Keep it simple

5. Always remember that the purpose of models is not to fit the data but to sharpen the question

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This presentation is made available through a Creative Commons Attribution license. Details of the license and permitted uses are available at

http://creativecommons.org/licenses/by/3.0/

© 2010 International Clinics on Infectious Disease Dynamics and DataWilliams BG. “Introduction to Thinking About Data” Clinic on the Meaningful Modeling of

Epidemiological Data. DOI:10.6084/m9.figshare.5043136.

For further information or modifiable slides please contact figshare@ici3d.org.

See the entire ICI3D Figshare Collection. DOI: 10.6084/m9.figshare.c.3788224.

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