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Interpreting randomized trial data: different ways of reporting differences

Graeme Hickey
October 05, 2016

Interpreting randomized trial data: different ways of reporting differences

Presented at the 30th Annual EACTS Meeting, Barcelona, Spain (1-5 October 2016)

Graeme Hickey

October 05, 2016
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  1. Interpreting randomized trial data Graeme L. Hickey Department of Biostatistics,

    University of Liverpool
  2. None
  3. Relative differences sells newspapers!

  4. 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

  5. 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
  6. 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
  7. 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
  8. 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
  9. 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 0.4 − 0.3 = 10%
  10. 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
  11. 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
  12. 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
  13. None
  14. Measure Formula Example Relative risk (RR) = ( + )

    ( + ) = 0.75 Odds ratio (OR) = odds9:;<9 odds=>?9:>@ = 18 28 = 0.64
  15. low baseline risk RR = OR 1 − AR=>?9:>@ +

    1 − AR=>?9:>@ 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. 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
  18. 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.
  19. None