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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

  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 Dead at 30-days n = 30 Alive at 30-days n = 70 Dead at 30-days 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 prevent one additional event
  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. None
  13. None
  14. Measure Formula Example Relative risk (RR) = !(# + %)

    #(! + ') = 0.75 Odds ratio (OR) = odds01230 odds4560157 = 8 ! ' # % 18 28 = 0.64
  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.
  16. RRsurvival = 0.7 0.6 = 1.17 ≠ 1 RRdeath ORsurvival

    = 28 18 = 1.56 = 1 ORdeath
  17. • Logistic regression ‘risk factors’ absolute risk • Case-control studies

    can’t estimate RR
  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
  19. instantaneous rate ! " ≤ $ < " + '"

    $ ≥ "] proportional hazards reference
  20. 1 https://understandinguncertainty.org/node/759

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