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Risk: a statistician's viewpoint

Risk: a statistician's viewpoint

Presented at the SCTS Annual Meeting 2018, Glasgow, UK

Graeme Hickey

March 19, 2018
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  1. Graeme L. Hickey
    Department of Biostatistics

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

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  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

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

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  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

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  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

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  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

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  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%

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  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
    prevent one additional event

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  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

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  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

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

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  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.

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

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

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  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

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

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

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  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.

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  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.

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  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.

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

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