Why is it important?
Why is it important?
Why is it important?
Why is it important?
Statistics – a hard nut to crack
Example 1
• 1996 – Mammography screening reports 21%
reduction in breast cancer mortality
• Represented a reduction from five to four in every thousand
women i.e. 0.1%
• In a representative sample, 92% of about 5000 women
overestimated the benefit 10-fold, 100-fold, and more.
!!DOCTORS ALSO STRUGGLE WITH STATISTICS!!
• 31% of 150 gynaecologists answered that for every 1000 women
who were screened, 25 or 250 fewer would die
Statistics – a hard nut to crack
Example 2
• 1995 - UK Committee on Safety of Medicines issues
a warning that third generation oral contraceptive pills
increase the risk of potentially life threatening thrombosis
twofold.
• 13 000 additional abortions in the next year in England and Wales
• For every 7000 women who took the earlier, second generation
pills, one had a thrombosis, and this number increased to two in
women who took third generation pills.
• This study was only reporting on the relative risk
Good News – common threadsRelative Risk Reduction (%)
Annualized Relapse Rate for Placebo
Absolute Risk Reduction
No. needed to treat
IFN – β1b ScPivotal Trial
34 1.27 0.43 2.3
IFN – β1a ScPRISMS Trial
33 1.28 0.42 2.4
IFN – β1a IMMSCRG
32 0.90 0.29 3.4
GA Pivotal Trial 29 0.84 0.24 4.2
Natalizumab AFFIRM Trial 68 0.78 0.50 2.0
FingolimodFREEDOMS
54 0.40 0.22 4.5
BG – 12 DEFINE 53 0.36 0.19 5.3
CladribineCLARITY
58 0.33 0.19 5.3
TEMSO 31.5 0.54 0.17 5.9
Relative risk reduction = difference
original
2 – 1 1= = 50%
2 2
Relative risk reduction = difference
original
Relative risk reduction = difference
original
2 – 1 1= = 50%
2 2
Absolute risk reduction = simply the difference
between the two
2 – 1 = 1 = 10% 10 10 10
Relative risk reduction = difference
original
Relative risk reduction = difference
original
8 – 6 2= = 25%
8 8
8 – 6 = 2 = 20% 10 10 10
Absolute risk reduction = simply the difference
between the two
Learning points!
• The relative risk reduction does not take
into account the baseline risk making an
insignificant finding appear significant
• Always check the baseline risk
• Always check the absolute risk reduction
Number Needed to Treat
“The average number of patients who need
to be treated to prevent one additional bad
outcome”
NNT = 100
ARR
NNT = 100 = 5 20
Number needed to Treat = 100
Absolute risk reduction
Trial Example 1A double blind Placebo controlled study with a new M.S.
drug (x) included 100 Placebo cases and 100 treated cases
(x). The primary end point was the occurrence of a relapse.
4 relapses in the placebo group versus 2 relapses in the
treated group at the end of the trial.
Event Rate (Relapse)
Control Drug ARR RRR NNT
4 = 4%100
2 = 2%100
4 – 2 = 2 2 = 50%4
100 = 502
Trial Example 2A double blind Placebo controlled study with a new M.S.
drug (y) included 100 Placebo cases and 100 treated cases
(y). The primary end point was the occurrence of a relapse.
40 relapses in the Placebo group versus 20 relapses in the
treated group (y) at the end of the trial.
Event Rate (Relapse)
Control Drug ARR RRR NNT
40 = 40%100
20 = 20%100
40 – 20 = 20
20 = 50%40
100 = 520
Trial Example 3
A double blind Placebo controlled study with a new M.S.
drug (z) included 100 Placebo cases and 100 treated cases
(z). The primary end point was the occurrence of a relapse.
90 relapses in the placebo group versus 60 relapses in the
treated group at the end of the trial.
Event Rate (Relapse)
Control Drug ARR RRR NNT
90 = 90%100
60 = 60%100
90 – 60 = 30 30 = 33.3%90
100 = 3.3 30
Comparison
Trial (1) Trial (2) Trial (3)
Risk (Relapse) in Placebo Group 4% 40% 90%
Relative Risk Reduction (RRR) 50% 50% 33.3%
NNT 50 5 3.3
• Treatments with very large RRR may have a small effect
in conditions where the control group has a very low
event rate.
• On the other hand, modest RRR can assume major
clinical importance if the control event rate is large.
Two-year Relapse Reduction: Relative Risk
Reduction Vs. Absolute Risk Reduction
Relative Risk Reduction (%)
Annualized Relapse Rate for Placebo
Absolute Risk Reduction
No. needed to treat
IFN – β1b ScPivotal Trial
34 1.27 0.43 2.3
IFN – β1a ScPRISMS Trial
33 1.28 0.42 2.4
IFN – β1a IMMSCRG
32 0.90 0.29 3.4
GA Pivotal Trial 29 0.84 0.24 4.2
Natalizumab AFFIRM Trial 68 0.78 0.50 2.0
FingolimodFREEDOMS
54 0.40 0.22 4.5
BG – 12 DEFINE 53 0.36 0.19 5.3
CladribineCLARITY
58 0.33 0.19 5.3
TEMSO 31.5 0.54 0.17 5.9
Conclusions
• The value of the relative risk reduction of the Relapse
Rate as a clinical outcome, depends on the risk of an
event in the control group.
• Low relapse rates in the control group may yield high
relative risk reductions yet they are clinically less
significant, as reflected by a high NNT.
• Modest relative risk reductions may be clinically more
significant if the relapse rate of the control group is high.
Food for thought• An analysis of the articles published in the Annals of Internal
Medicine, BMJ, JAMA, Journal of the National Cancer
Institute, Lancet, and the New England Journal of Medicine,
2003-4, showed that 68% (150/222) failed to report the
underlying absolute risks in the abstract.
• An analysis of 119 systematic reviews in BMJ, JAMA, and
Lancet from 2004 to 2006 showed that every second article
discussed only relative risks or odds ratios.
Misleading communication of
risk
BMJ 2010;