1 / 34

Comparing Three or More Groups: Multiple Comparisons vs Planned Comparisons Robert Boudreau, PhD

Comparing Three or More Groups: Multiple Comparisons vs Planned Comparisons Robert Boudreau, PhD Co-Director of Methodology Core PITT-Multidisciplinary Clinical Research Center for Rheumatic and Musculoskeletal Diseases. First a simple thought experiment.

josephine-stephens
Télécharger la présentation

Comparing Three or More Groups: Multiple Comparisons vs Planned Comparisons Robert Boudreau, PhD

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Comparing Three or More Groups: Multiple Comparisons vs Planned Comparisons Robert Boudreau, PhD Co-Director of Methodology Core PITT-Multidisciplinary Clinical Research Center for Rheumatic and Musculoskeletal Diseases

  2. First a simple thought experiment Flip a fair coin 100 times: Let H=# heads H = 0,1,2, …, 100 are the possible outcomes H has a binomial distribution with known probs Prob[ 40 < H < 60 ] very close to 0.95  Prob [ H ≤ 40 ] + P[ H ≥ 60] = 0.05 -------------------------------------------------------------------------------------------------------

  3. First a simple thought experiment Flip a fair coin 100 times: Let H=# heads H = 0,1,2, …, 100 are the possible outcomes H has a binomial distribution with known probs Prob[ 40 < H < 60 ] very close to 0.95  Prob [ H ≤ 40 ] + P[ H ≥ 60] = 0.05 ------------------------------------------------------------------------------------------------------- Experiment: 20 people flip their own coin 100 times Q: Approx how many will get 40 or fewer heads or 60+ heads?

  4. First a simple thought experiment Flip a fair coin 100 times: Let H=# heads H = 0,1,2, …, 100 are the possible outcomes H has a binomial distribution with known probs Prob[ 40 < H < 60 ] very close to 0.95  Prob [ H ≤ 40 ] + P[ H ≥ 60] = 0.05 ------------------------------------------------------------------------------------------------------- Experiment: 20 people flip their own coin 100 times Q: Approx how many will get less than 40 heads or 60+ heads? Answer: One

  5. First a simple thought experiment Flip a fair coin 100 times: Let H=# heads H = 0,1,2, …, 100 are the possible outcomes H has a binomial distribution with known probs Prob[ 40 < H < 60 ] very close to 0.95  Prob [ H ≤ 40 ] + P[ H ≥ 60] = 0.05 ------------------------------------------------------------------------------------------------------- Experiment: 20 people flip their own coin 100 times Q: Approx how many will get less than 40 heads or 60+ heads? Answer: One (1/20 = 5%)

  6. First a simple thought experiment Experiment: 20 people flip their own coin 100 times One (1/20=0.05) will flip an unusually small or unusually large # heads (on average) Q: Can we conclude that this person “X” flips an “unfair” coin, or was this explainable by “chance”?

  7. Controlling Experiment-wise Error Experiment: 20 people flip their own coin 100 times • Person X’s confidence interval didn’t cover 0.5 Q: What alpha level should be used so that 95% of the time all 20 confidence intervalseach cover 0.5? (i.e. so that the correct conclusion is drawn about every single coin)

  8. Controlling Experiment-wise Error Experiment: 20 people flip their own coin 100 times • Person X’s confidence interval didn’t cover 0.5 Q: What alpha level should be used so that 95% of the time all 20 confidence intervalseach cover 0.5? (i.e. so that the correct conclusion is drawn about every single coin)  Equivalent to drawing a “wrong” conclusion about at least one of the coins only 5% of the time (Experiment-wise Type I error)

  9. Controlling Experiment-wise Error Q: What alpha level should be used so that there’s a 95% probability that all 20 confidence intervals each cover 0.5? (aka Experiment-wise correct conclusion) Experiment-wise α=0.05, solve for comparison-wise α*: α = Prob[ At least one C.I. misses 0 ] = 1 – Prob[ All C.I.’s cover 0 ] = 1 – (1 – α* )20 Sidak: Comparison-wise α* = 1 – (1 – α)1/n n=20 “comparisons”: α* = 1 – (1-.05)1/20 = 0.00256

  10. Controlling Experiment-wise Error Q: What alpha level should be used so that there’s a 95% probability that all 20 confidence intervals each cover 0.5? Sidak: Comparison-wise α* = 1 – (1 – α)1/n n=20 “comparisons”: α* = 1 – (1-.05)1/20 = 0.00256 Bonferroni:α* = α/n ( 0.05/20=0.0025)

  11. Controlling Experiment-wise Error Mathematically: α/n < 1 – (1 – α)1/n Bonferroni < Sidak(i.e. higher α-level) But usually very close  Sidak slightly more powerful Bonferroni works in all situations to guarantee control of experimentwise error (but may be conservative) Sidak (derived assuming independence) can under-control in presence of high correlations

  12. Comparison of Adverse Effect of 4 Drugs on Systolic BP

  13. Comparison of Adverse Effect of 4 Drugs on Systolic BP

  14. Comparison of Adverse Effect of 4 Drugs on Systolic BP

  15. Unadjusted pairwise t-tests (α = 0.05 each comparison)critical value of t=2.13145

  16. Pairwise t-tests (Bonferroni) critical value of t=3.03628

  17. Pairwise t-tests (Sidak) critical value of t=3.02585

  18. Comparison of critical values Scheffe: * Designed for arbitrary post-hoc testing * Controls experimentwise error for all possible simultaneous comparisons and contrasts

  19. Comparison of Adverse Effect of 4 Drugs on Systolic BP (v2) s s Note: For Drug 4, I’ve subtracted 6 from the previous values

  20. Comparison of Adverse Effect of 4 Drugs on Systolic BP (v2) ANOVA F-test

  21. Unadjusted pairwise t-tests (v2) (α = 0.05 each comparison)critical value of t=2.13145

  22. Pairwise t-tests (Bonferroni) (v2)critical value of t=3.03628

  23. Pairwise t-tests (Sidak) (v2)critical value of t=3.02585

  24. Tukey’sStudentized Range Test Related in concept to Scheffe’s Method Designed for all pairwise comparisons exclusively (recall: Scheffe applies to all possible simultaneous pairwise comparisons and contrasts) Exact experimentwise error coverage if sample sizes equal Critical values smaller than Bonferroni or Sidak  More powerful in finding differences

  25. Pairwise t-tests (Tukey) (v2) critical value of t=2.88215

  26. Comparison of Adverse Effect of 4 Drugs on Systolic BP

  27. Dunnett’s Method(Comparison vs a Control) Related in concept to Scheffe and Tukey Methods Designed for pairwise comparisons vs a single control exclusively Exact experimentwise error coverage of those comparisons if sample sizes equal Critical values smaller than Bonferroni, Sidak or Tukey  More powerful in finding differences vs control

  28. Comparison vs Control (Dunnett) (v2) critical value of t=2.61702

  29. Controlling for Multiple Comparisons in Exploratory Analyses Caterina Rosano, Howard J. Aizenstein, Stephanie Studenski, Anne B. Newman. A Regions-of-Interest Volumetric Analysis of Mobility Limitations in Community-Dwelling Older Adults. Journal of Gerontology: Medical Sciences 2007

  30. Controlling for Multiple Comparisons in Exploratory Analyses A Regions-of-Interest Volumetric Analysis of Mobility Limitations in Community-Dwelling Older Adults. Journal of Gerontology: Medical Sciences 2007

  31. Controlling for Multiple Comparisons in Exploratory Analyses

  32. Controlling for Multiple Comparisons in Exploratory Analyses c

  33. Thank you ! Any Questions? Robert Boudreau, PhD Co-Director of Methodology Core PITT-Multidisciplinary Clinical Research Center for Rheumatic and Musculoskeletal Diseases

More Related