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Chris and Abbie’s
Vital Statistics
Arghhh Statistics...
• It’s actually quite dull!!!
• But......It is quite easy if you think it
through.
Arghhh Statistics...
• Some Definitions…
Arghhh Statistics...
• Risk:
The probability that something
will occur…In a particular group
Arghhh Statistics...
• Risk Ratio:
The probability that something
will occur in one group
compared to another group.
Arghhh Statistics...
• Odds:
The chance of something
occurring compared to it
not occurring…
Arghhh Statistics...
• Odds Ratio…
The ratio of the odds of
something occurring in one
group compared to odds of it
occurring in a different group
Arghhh Statistics...
• Number needed to Treat…
Number of people needed to
treat to have one given
outcome....
= 1 ÷ Absolute Risk Reduction
Arghhh Statistics...
• An example…. Sausage Addicts!
• A study over one year.
Eats Sausage
Does not eat Sausage
Totals
Heart Attack
25
12
37
No Heart Attack
1675
1788
3463
Total
1700
1800
3500
Risk
• What is the risk of having a heart attack
in the sausage eating group?
Sausage Fans
Eats Sausage
Does not eat Sausage
Totals
25
12
37
No Heart Attack
1675
1788
3463
Total
1700
1800
3500
Heart Attack
Risk in sausage group
• Risk = Number of heart attack/total
population
= 25/1700 = 0.0147 (1.47%)
Sausage Fans
Heart Attack
Eats Sausage
Does not eat Sausage
Totals
25
12
37
No Heart Attack
1675
1788
3463
Total
1700
1800
3500
Risk in non sausage group
• Risk = Number of heart attack/total
population
= 12/1800 = 0.00667 (0.67%)
Sausage Fans
Heart Attack
Eats Sausage
Does not eat Sausage
Totals
25
12
37
No Heart Attack
1675
1788
3463
Total
1700
1800
3500
Relative Risk
• Relative Risk in one group/risk in
the other group.
= 0.147/0.0067 = 2.19
Sausage Fans
Heart Attack
Eats Sausage
Does not eat Sausage
Totals
25
12
37
No Heart Attack
1675
1788
3463
Total
1700
1800
3500
Absolute Risk
Absolute risk =
(Risk in sausage eaters) – (Risk in non
sausage eaters)
= (25/1700) - (12/1800) = 0.0080 (0.8%)
Sausage Fans
Heart Attack
Eats Sausage
Does not eat Sausage
Totals
25
12
37
No Heart Attack
1675
1788
3463
Total
1700
1800
3500
Number needed to harm
• Number needed to harm =
1 ÷ Absolute risk reduction
= 1/0.008 = 125
i.e. if 100 people ate sausages for 1 year an
additional 0.8 would have a heart attack. If 1000
people ate sausages for 1 year an additional 8
would have a heart attack. 1000/8 = 125....So 125
people are needed to eat sausages for 1 year to
get one additional heart attack.
Odds of heart attack in sausage group
Heart attack ÷ no heart attack
= 25/1675 = 0.0149.
i.e. For every person who does not have a heart
attack 0.0149 of a person does have a heart
attack.
Sausage Fans
Heart Attack
Eats Sausage
Does not eat Sausage
Totals
25
12
37
No Heart Attack
1675
1788
3463
Total
1700
1800
3500
Odds of heart attack in non sausage
group
Heart attack ÷ no heart attack
12/1788 = 0.00671.
i.e. For every person who does not have a heart attack
0.00671 of a person does have a heart attack. (its less)
Sausage Fans
Heart Attack
Eats Sausage
Does not eat Sausage
Totals
25
12
37
No Heart Attack
1675
1788
3463
Total
1700
1800
3500
Odd Ratio
• Odds of Heart attack in sausage
eaters: 0.0149
• Odds of Heart attack in none
sausage eaters: 0.00671
Odds ratio 0.00671/0.0149 = 2.22
So eating sausages doubles your odds of
having a heart attack in one year...
Arghhh more stats….!
• And Now Abbie…..!
Sensitivity and Specificity
• Why Bother?
• If disease is present a truly accurate,
test will always give a positive result
• If disease is not present, the test will
always give a negative result.
Sensitivity…
• …
• the proportion of people with disease
who have a positive test result
= true positive
(true positive + false negative)
Specificity
• …
• the proportion of people without
disease who have a negative test result
= true negative
(true negative + false positive)
An example
Allergy
test
Chocolate No
allergy
chocolate
allergy
Positive
35
5
True positive
Negative
1
40
False negative
Total
False positive
36
True negative
45
Work it out…
• Sensitivity =
35/36 = 0.97 (97%)
• Specificity =
40/45 = 0.89 (89%)
Clinically…
PSA for prostate cancer
Sensitivity is 46%
Specificity is 91%
Ca125 for ovarian cancer
Sensitivity is 72%
Specificity is 78%
Predictions…
PPV : proportion of positive test results that
are true positives
= number of true positives
No. of true positives + no. of false positives
Continued…
NPV : proportion of negative test results
that are true negatives
= number of true negatives
No. of true negatives + no. of false
negatives
An example
Allergy
test
Chocolate No
allergy
chocolate
allergy
Positive
35
5
True positive
Negative
1
40
False negative
Total
False positive
36
True negative
45
Worked example…
• PPV = 35/40 = 0.875 (88%)
• NPV = 40/41 = 0.975 (98%)
Papers…
• Meta analysis
• Systematic review
• Can anyone tell me the difference?
“Science is cumulative, with new ideas being based
on previous knowledge and observation, and new
advances in science should help us make sense
of what we already know and have observed. But
if we don't collect previous knowledge and
observation in a systematic way, we are unlikely
to make progress as quickly as we could.”
The Cochrane Collaboration open learning material
http://www.cochrane-net.org/openlearning/html/mod1-2.htm
Meta-analysis
• Calculating the results of each study
identified by the reviewer, and then to
calculate an average of those results in
a meta-analysis.
• Systematic reviews do not have to have
a meta-analysis - there are times when
it is not appropriate or possible and
vice-versa
• We tend to use forest plots to present
the results of a meta-analysis…
Forest Plots
• Forest plots show the information at a
glance from the individual studies
that went into the meta-analysis.
• It provides a simple visual
representation of the amount of
variation between the results of the
studies, as well as an estimate of the
overall result of all the studies
together.
Can someone talk me through it?
Give papers out…
Paper to work on…
• Can you decipher the forest plot?
And again…
And now for some fun…
• CRITICAL APPRAISAL!
Critical Appraisal
Critical Appraisal
Critical Appraisal
Critical Appraisal
Critical Appraisal
Critical Appraisal Skills Programme (CASP)
The Answers…
The Answers…
The Answers…
Rosuvastatin
Placebo
Total
Primary End point
44
91
135
No Primary Endpoint
3021
2939
5960
Total
3065
3030
6095
Results
Risk Rx
Risk Placebo
Relative Risk
Absolute risk
NNT
0.01436
0.03003
0.478
0.01568
63.7862
Percent
1.435563
3.0033
47.79951
1.567738