Graeme Hickey
March 19, 2018
630

# Risk: a statistician's viewpoint

Presented at the SCTS Annual Meeting 2018, Glasgow, UK

March 19, 2018

## Transcript

1. Graeme L. Hickey
Department of Biostatistics

2. * http://www.dictionary.com/browse/risk

3. http://www.independent.co.uk/news/science/vitamin-d-asthma-
attacks-prevent-study-cochrane-a7226756.html
https://www.theguardian.com/society/2016/sep/05/vitamin-d-
supplements-could-halve-risk-of-serious-asthma-attacks
Absolute difference
Relative difference

4. Randomization
N = 200
Treatment
n = 100
Control
n = 100
n = 30
Alive at 30-days
n = 70
n = 40
Alive at 30-days
n = 60

5. Treatment Control Total
Died within 30-days 30 40 70
Alive at 30-days 70 60 130
Total 100 100 N = 200
A 2x2 contingency table + marginal totals

6. Treatment Control Total
Died within 30-days a b a + b
Alive at 30-days c d c + d
Total a + c b + d N = a + b + c + d
A 2x2 contingency table + marginal totals

7. Measure Formula Example
Absolute risk in treatment group (ARtreat
) =
"
" + \$
30
100
= 0.3
Absolute risk in control group (ARcontrol
) =
)
) + *
40
100
= 0.4
Absolute risk reduction (ARR) = ARcontrol
− ARtreat
0.4 − 0.3 = 0.1

8. Measure Formula Example
Absolute risk in treatment group (ARtreat
) =
"
" + \$
30
100
= 30%
Absolute risk in control group (ARcontrol
) =
)
) + *
40
100
= 40%
Absolute risk reduction (ARR) = ARcontrol
− ARtreat
40% − 30% = 10%

9. Measure Formula Example
Number needed to treat (NNT) =
1
ARR
1
0.1
= 10
Equivalent to the average number of patients who need to be treated to

10. Measure Formula Example
Relative risk (RR) =
ARtreat
ARcontrol
0.3
0.4
= 0.75
Relative risk reduction (RRR) = 1 − RR 1 − 0.75 = 0.25

11. 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
High risk Intermediate risk Low risk
Results from 3 hypothetical RCTs of the same treatment
Control Treatment
30-day mortality proportion
ARR = 0.1 (or 10%) ARR = 0.05 (or 5%) ARR = 0.01 (or 1%)
0.1
0.05
0.01
NNT = 10 ARR = 20 ARR = 100
RRR = 0.25 (or 25%) RRR = 0.25 (or 25%) RRR = 0.25 (or 25%)
High risk Intermediate risk Low risk

12. Measure Formula Example
Relative risk (RR) =
!(# + %)
#(! + ')
= 0.75
Odds ratio (OR) =
odds01230
odds4560157
= 8
!
'
#
%
18
28
= 0.64

13. low baseline risk
RR =
OR
1 − AR'()*+(,
+ 1 − AR'()*+(,
OR
Source: Grant, R. L. (2014). Converting an odds ratio to a range of plausible relative risks for better communication of research findings. BMJ, 348(4), f7450.

14. RRsurvival
=
0.7
0.6
= 1.17 ≠
1
RRdeath
ORsurvival
=
28
18
= 1.56 =
1
ORdeath

15. • Logistic regression
‘risk factors’
absolute risk
• Case-control studies
can’t estimate RR

16. Relative effect:
HR = 0.55 Absolute effect:
ARR(12-months) = 20.0%
30.7% in the TAVI group
50.7% in the standard
therapy group
NNT(12-months) = 5
• HR uses all data at each
time point
• Not robust to
departures from
proportionality

17. instantaneous rate
! " ≤ \$ < " + '" \$ ≥ "]
proportional hazards
reference

18. 1 https://understandinguncertainty.org/node/759

19. Survival
Survival
HR = 3
HR = 1.5
1
2
Treatment
A
B
Treatment
A
B
Treatment
arm
Panel 1
(HR = 3)
Panel 2
(HR = 1.5)
A 1 1
B 0.9 0.5
Median survival times (years)
Spruance SL et al. Hazard ratio in clinical trials. AntimicrobAgents Chemother 2004;48:2787–92.

20. Grant SW et al. Health Technol Assess 2015;19(32)
Holistic view of risk is required
Concato J et al. Ann Intern Med. 1993;118(3):201-210.

21. both
* Naylor et al. Measured enthusiasm: does the method of reporting trial results alter perceptions of therapeutic effectiveness? Ann Intern Med. 1992; 117(11):916-21.

22. Questions?
Slides available from
www.glhickey.com