Risk: a statistician's viewpoint

Presented at the SCTS Annual Meeting 2018, Glasgow, UK

Transcript

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

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

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

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

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20. 1 https://understandinguncertainty.org/node/759
    

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21. 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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22. 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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23. 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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24. Questions?
    Slides available from
    www.glhickey.com
    

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