Goldsmith’s teachers lecture
2010
Medical statistics
Joan Morris
Professor of Medical Statistics
Aims
• To describe medical statistics
• To give examples of where medical
statistics has contributed to society
• Use of statistics in screening
• To mention some novel statistical
methods
Statistics - definition
Statistics is a mathematical science
pertaining to the collection, analysis,
interpretation or explanation, and
presentation of data.
Data Collection
Data Collection
• Florence Nightingale
– She realised that soldiers were dying from
malnutrition, poor sanitation, and lack of
activity.
– She kept meticulous records of the death toll
in the hospitals as evidence of the importance
of patient welfare.
National Data Collection
• National Mortality Statistics
• Health survey for England and Wales
• Population statistics …..
• Large amounts of data are available on
the web
Standardised mortality ratios:
Mortality from skin cancer
All births in England and Wales according to
maternal age :1989-91 compared with 2005-2007
200
150
2005-07 : 1991,000 births
1989-91 : 2090,000 births
100
50
0
15
20
25
30
35
Maternal age at birth (years)
40
45
50
Epidemiology
Epidemiology
Comparisons of individuals
Comparisons of populations
Observational
cross-sectional
case-control studies
cohort studies
Time trends
Interventional
Randomised controlled
trials
Ecological studies:
Geographical variations
Age/sex patterns
Social variations
Comparison of Individuals
• Study Design
– Ensure “valid” data is collected
– Ensure enough data is collected
• Main designs
– Case control studies
– Cohort studies
– Clinical trials
Richard Doll (doctor) and Austin
Bradford Hill (statistician)
Is there a relationship between
smoking and lung cancer?
British Doctors Cohort Study
(BMJ 1994;309:901-911)
34,000 British male doctors who replied to a postal
questionnaire in 1951 and further questionnaires in
1957, 66, 72, 78, 90, …
Flagged the doctors at NHSCR and obtained their death
certificates as they died. Compared death rates in
smokers and non-smokers..
Is there a relationship between
smoking and lung cancer?
Number of cigarettes
smoked per day
None
Risk of dying from lung
cancer compared to
non smokers
1.0
1 to 9
4.1
10 to 19
10.5
20 to 30
23.6
More than 30
41.9
What causes Sudden Infant Death
Syndrome ?
• Sudden Infant Death Syndrome Case Control
Study
• Methods
– Collected information about infants that were potential
“SIDS”
– Identified “similar” children who had not died
– Compared the differences
• Results
– Children who died were much more likely to have
been put on their fronts to sleep than children who did
not die
Randomised Controlled Trial
• A clinical trial is an experiment in which a
treatment is administered to humans in order to
evaluate its efficacy and safety
• Randomised = allocated to groups on basis of
chance e.g. tossing a coin (ensures fair
comparison)
• Controlled = a comparison group
Can folic acid reduce neural tube
defects (e.g. spina bifida)?
• MRC Vitamin trial - randomised controlled
trial
• Large: 1817 women who had had a
previous NTD, 33 centres, 7 countries
Can folic acid reduce neural tube
defects (e.g. spina bifida)?
• Results : Women who did not receive folic
acid were 3 times more likely to have a
second NTD pregnancy
• Impact : Women are advised to take folic
acid prior to becoming pregnant
• Majority of countries around the world
fortify flour with folic acid
Collection of Data
• Study Design
– Cohort
– Case Control
– Clinical Trial
Analysis
• Could the observed results have arisen by
chance ?
• Given that we have a sample what can we
say about the population from which the
sample comes
Folic Acid vs Placebo for
Neural Tube Defects
Neural Tube Defects
Folic
Acid
Yes
No
Total
Yes
6
587
593
No
21
581
602
Risk of NTD in treated group
Risk of NTD in control group
=
=
Relative Risk of NTD in treated
group compared to control group =
1%
3.5%
1%/3.5% = 0.29
P values
• P is the probability of the observed event
or one more extreme occurring if the null
hypothesis is true
• Null hypothesis : No difference in
treatments
• P = probability out of 27 babies with an
NTD what is the chance that 6 or less are
in the FA group and 21 in placebo group IF
FA has no effect
P values
• These are just probability calculations with
prob NTD in group A = prob NTD in group
B
• And comparing numbers of combinations
of obtaining a total of 21 NTDs
Interpreting the results of a trial
No. treated No. died
A
20
4
B
20
2
A
100
20
B
100
10
A
200
40
B
200
20
RR death in A vs B = 2.0
Is it due to chance or not ?
Mainly Yes
P = 0.37
Split Yes / No
P = 0.07
Mainly No
P = 0.008
P values
• P < 0.05 is taken to mean statistical
significance
• This means if there is no difference
between treatments, and you do 20 trials
one will be statistically significant
Folic Acid vs Placebo for
Neural Tube Defects
RR = 0.29
P = 0.008
Therefore we assume there is a real difference between the
folic acid group and the placebo group
But how big is the reduction ?
Folic Acid vs Placebo for
Neural Tube Defects
RR = 0.29
P = 0.008
95% Confidence Interval : 0.10 to 0.76
95% confidence intervals means that 95% of the time this
interval contains the true reduction
Therefore it gives an indication of the likely size of the
reduction
0
1
2
3
4
5
6
7
8
Folic Acid and NTD Dose Response
0
2
4
6
Plasma folate (ng/ml)
8
10
0
1
2
3
4
5
6 7 8
Folic Acid and NTD Dose Response
2
4
Plasma folate (ng/ml)
6
8
10
Interpretation
• The same proportional increase in serum
folate has the same proportional reduction
in NTD
• All women benefit from taking folic acid.
There is not a threshold effect
So far….
• Collection
– Nightingale
– National statistics
– Study design
• Presentation
– Estimates and confidence intervals
• Analysis
– Vital to interpretation
Use of Statistics in Screening
Screening is the identification, among apparently
healthy individuals, of those who are sufficiently at
risk from a specific disorder to benefit from a
subsequent diagnostic test, procedure or direct
preventive action.
Screening for Heart Disease
Relative odds of major IHD event by fifths of the distribution of haemostatic and lipid markers
for all men (•——•) and for men free of IHD at baseline examination (∘–––∘).
Yarnell J et al. Eur Heart J 2004;25:1049-1056
The European Society of Cardiology
Unaffected
Affected
Biomarker : ZZ
Unaffected
Affected
Biomarker : ZZ
Screen negative
Screen positive
False
negatives
False
positives
FPR=5%
Unaffected
Affected
Biomarker : ZZ
Screen negative
Screen positive
Screening for a medical disorder
Good test
Affected
Unaffected
Risk Factor
Screening for a medical disorder
Poor test
Affected
Unaffected
Risk Factor
Is Cholesterol any good for
screening ?
8
6
4
2
Risk screen
converter
.2
.4
fol
.6
.8
http://www.wolfson.qmul.
ac.uk/rsc/
Unaffected
Affected
Detection Rate
False Positive Rate
4.2mm Hg
7.5mm Hg
• Are there any good screening tests ?
Antenatal screening for Down’s syndrome
Quadruple test markers
AFP
Down’s
syndrome
0.25
uE3
Unaffected
0.5
1
2
Unaffected
Down’s
syndrome
4
8
16
0.25
0.5
Maternal serum AFP (MoM)
1
0.25
0.5
2
8
16
8
16
Inhibin-A
Unaffected
Down’s
syndrome
1
4
Maternal serum uE3 (MoM)
Total hCG
Unaffected
2
4
Maternal serum total hCG (MoM)
8
16
0.25
0.5
Down’s
syndrome
1
2
4
Maternal serum inhibin-A (MoM)
Distribution of risk in Down’s syndrome and unaffected
pregnancies using AFP, uE3, total hCG and inhibin-A measured
at 14-20 weeks (+ maternal age)
Unaffected
Down’s
syndrome
1:108
1:106
1:104
1:102
1:10
102:1
Risk of a Down’s syndrome pregnancy at term
104:1
Analysis based on….
• Understanding probability
• Properties of combinations of random
variables
• Properties of normal distribution
• Understanding hypothesis testing
Recent Developments
•
•
•
•
Collection
Analysis
Interpretation or explanation
Presentation
Collection
• Danish mother and child study
– Recruiting people on the internet
• Linking data sets
– Probability linking eg
• Date of mother’s birth fairly accurate
• Gestational age of baby often wrong
• Weight of baby –REALLY ACCURATE !!!
Analysis
•
•
•
•
Meta-analysis
Monte-carlo simulations
Bayesian analysis
Analysis of micro-arrays
Several studies looking at the same
thing
• Each study may be relatively inconclusive
because of too much uncertainty (too small)
• Statistical (mathematical) method of combining
and presenting results from several studies
• Can indicate more robust results
Pooled odds ratio for thiazolidinediones compared with other treatments for all cause
mortality
Eurich, D. T et al. BMJ 2007;335:497
Forest plot
Proportions dying
in each group
Copyright ©2007 BMJ Publishing Group Ltd.
Odds ratio
Relies on the
logarithm of the
odds ratio being
approximately
normally
distributed
Comparing institutions, individual
doctors and identifying outliers
• What’s the problem?
– Lots of variables important
– Random variation
– Random variation greater for smaller
units or institutions
• Way of presenting the values for units
so that this is taken into account
Funnel plot
Conclusion
• As much about collection, interpretation
and presentation as calculation
• Concepts of random variables, probability
feed into analyses
• Making sense out of uncertainty
• Changing techniques as times change