1. Primer on Statistics for Interventional Cardiologists Giuseppe Sangiorgi, MD Pierfrancesco Agostoni, MD Giuseppe Biondi-Zoccai, MD

2. What you will learn Introduction Basics Descriptive statistics Probability distributions Inferential statistics Finding differences in mean between two groups Finding differences in mean between more than 2 groups Linear regression and correlation for bivariate analysis Analysis of categorical data (contingency tables) Analysis of time-to-event data (survival analysis) Advanced statistics at a glance Conclusions and take home messages

3. What you will learn Introduction Basics Descriptive statistics Probability distributions Inferential statistics Finding differences in mean between two groups Finding differences in mean between more than 2 groups Linear regression and correlation for bivariate analysis Analysis of categorical data (contingency tables) Analysis of time-to-event data (survival analysis) Advanced statistics at a glance Conclusions and take home messages

4. What you will learn Analysis of categorical data (contingency tables) –Estimating a proportion with the binomial test –Comparing proportions in two-way contingency tables –Relative risk and odds ratio –Fisher exact test for small samples –McNemar test for proportions using paired samples –Comparing proportions in three-way contingency tables with the Cochran-Mantel- Haenszel test

5. Variables nominalordinaldiscretecontinuous ordered categories ranks counting measuring Death: yes/no TLR: yes/no TIMI flow BMI Blood pressure QCA data (MLD, late loss) Stent diameter Stent length Types of variables Radial/brachial/femoral QUANTITYCATEGORY

6. Variables nominalordinal ordered categories ranks Death: yes/no TLR: yes/no TIMI flow Types of variables Radial/brachial/femoral CATEGORY

7. What you will learn Analysis of categorical data (contingency tables) –Estimating a proportion with the binomial test –Comparing proportions in two-way contingency tables –Relative risk and odds ratio –Fisher exact test for small samples –McNemar test for proportions using paired samples –Comparing proportions in three-way contingency tables with the Cochran-Mantel- Haenszel test

8. Binomial test Diabetesn=13 Yes538.5% No861.5% Variable type NominalOrdinalContinuous Patient IDDiabetesAHA/ACC Type Lesion Length 1YA18 2NB124 3NA17 4NC25 5YB223 6NA15 7NA16 8YB218 9NB121 10YB219 11NB114 12YC22 13NC27

9. Binomial test Is the percentage of diabetics in this sample comparable with the known CAD population? We fix the population rate at 15%

10. Binomial test Is the percentage of diabetics in this sample comparable with the CAD population? We fix the population rate at 15%

11. Binomial test Agostoni et al. AJC 2007

12. Binomial test

13. What you will learn Analysis of categorical data (contingency tables) –Estimating a proportion with the binomial test –Comparing proportions in two-way contingency tables –Relative risk and odds ratio –Fisher exact test for small samples –McNemar test for proportions using paired samples –Comparing proportions in three-way contingency tables with the Cochran-Mantel- Haenszel test

14. The first basis for the chi-square test is the contingency table χ 2 test or chi-square test Compare discrete variables ENDEAVOR II. Circulation 2006

15. χ 2 test or chi-square test Compare discrete variables

16. χ 2 test or chi-square test Compare discrete variables

17. ab cd TVF No TVF Endeavor Driver s1s1s1s1 s2s2s2s2 r2r2r2r2 r1r1r1r1 N Compare discrete variables

18. The second basis is the “observed”-“expected” relation

19. TVF Stent

20. χ 2 test or chi-square test Compare discrete variables

21. χ 2 test or chi-square test Compare discrete variables

22. More than 2x2 contingency tables Post-hoc comparisons Compare discrete variables Is there a difference between diabetics and non- dabetics in the rate of AHA/ACC type lesions?

23. the chi-square test was used to determine differences between groups with respect to the primary and secondary end points. Odds ratios and their 95 percent confidence intervals were calculated. Comparisons of patient characteristics and survival outcomes were tested with the chi-square test, the chi-square test for trend, Fisher's exact test, or Student's t-test, as appropriate. This is a sub-group ! Bonferroni ! The level of significant p-value should be divided by the number of tests performed… Or the computed p-value, multiplied for the number of tests… P=0.12 and not P=0.04 !! Post-hoc groups Wenzel et al, NEJM 2004

24. What you will learn Analysis of categorical data (contingency tables) –Estimating a proportion with the binomial test –Comparing proportions in two-way contingency tables –Relative risk and odds ratio –Fisher exact test for small samples –McNemar test for proportions using paired samples –Comparing proportions in three-way contingency tables with the Cochran-Mantel- Haenszel test

25. a b cd TVFNo TVF Endeavor Driver Absolute Risk = [ d / ( c + d ) ] Absolute Risk Reduction = [ d / ( c + d ) ] - [ b / ( a + b ) ] Relative Risk = [ d / ( c + d ) ] / [ a / ( a + b ) ] Relative Risk Reduction = 1 - RR Odds Ratio = (d/c)/(b/a) = ( a * d ) / ( b * c ) Compare event rates

26. Absolute Risk (AR) 7.9% (47/592) & 15.1% (89/591) Absolute Risk Reduction (ARR) 7.9% (47/592) – 15.1% (89/591) = -7.2% Relative Risk (RR) 7.9% (47/592) / 15.1% (89/591) = 0.52 (given an equivalence value of 1) Relative Risk Reduction (RRR) 1 – 0.52 = 0.48 or 48% Odds Ratio (OR) 8.6% (47/545) / 17.7% (89/502) = 0.49 (given an equivalence value of 1) Odds Ratio Reduction (ORR) 1 – 0.49 = 0.51 or 51% Compare event rates

27. Relative Risk (RR) 7.9% (47/592) / 15.1% (89/591) = 0.52 or 52% (given an equivalence value of 1) Odds Ratio (OR) 8.6% (47/545) / 17.7% (89/502) = 0.49 or 49% (given an equivalence value of 1) For small event rates (b and d) OR ~ RR Compare event rates RR = [ d / ( c + d ) ] / [ a / ( a + b ) ] OR = (d/c)/(b/a) = ( a * d ) / ( b * c ) a b cd TVFNo TVF Endeavor Driver

28. ARc: 56% ARt: 46.7% ARR: 9.3% RR: 0.83 RRR: 17% OR: 0.69 ROR: 31% *152 pts in the invasive vs 150 in the medical group SHOCK, NEJM 1999

29. NNT=1/ARR Compare event rates Testa, Biondi Zoccai et al. EHJ 2005

30. Compare event rates ENDEAVOR II. Circulation 2006 Absolute Risk Reduction (ARR) 7.9% (47/592) – 15.1% (89/591) = -7.2% Number Needed to Treat (NNT) 1 / 0.072 = 13.8 ~ 14 I need to treat 14 patients with Endeavor instead of Driver to avoid 1 TVF The larger the ARR, the smaller the NNT Low NNT => Large benefit

31. Compare event rates

32. https://www.som.soton.ac.uk/cia/ To compute Confidence Intervals for ARR, RR, OR, NNT SPSS is not so good… Confidence Interval Analysis (CIA) downloadable software [with the book “Statistics with Confidence”, Editor: DG Altman, BMJ Books London (2000)]

33. Compare event rates

35. “Incidence study” (RCTs) for Relative Risk

36. Compare event rates

37. “Unmatched case control study” for Odds Ratio

38. Compare event rates

39. http://www.quantitativeskills.com/sisa/statistics/twoby2.htm Free in internet, always available!

40. Compare event rates http://www.quantitativeskills.com/sisa/statistics/twoby2.htm

41. Compare event rates http://www.quantitativeskills.com/sisa/statistics/twoby2.htm

42. What you will learn Analysis of categorical data (contingency tables) –Estimating a proportion with the binomial test –Comparing proportions in two-way contingency tables –Relative risk and odds ratio –Fisher exact test for small samples –McNemar test for proportions using paired samples –Comparing proportions in three-way contingency tables with the Cochran-Mantel- Haenszel test

43. Every time we use conventional tests or formulas, we ASSUME that the sample we have is a random sample drawn from a specific distribution (usually normal, chi- square, or binomial…) It is well known that as N increases, an established and specific distribution may be ASYMPTOTICALLY assumed (usually N≥30 is ok) Exact tests

44. Whenever asymptotic assumptions cannot be met (small, non-random, skewed samples, with sparse data, major imbalances or few events), EXACT TESTS should be employed Exact tests are computationally burdensome (they involve PERMUTATIONS)*, but they do not rely on any underlying assumption If in a 2x2 table a cell has an expected event rate ≤5, Pearson chi-square test is biased (ie ↑alpha error), and Fisher exact test is warranted *6! is a permutation, and equals 6x5x4x3x2x1=720 Exact tests

45. ab cd Event No event ExpCtrl s1s1s1s1 s2s2s2s2 r2r2r2r2 r1r1r1r1 N P = s 1 ! * s 2 ! * r 1 ! * r 2 ! N! * a ! * b! * c! * d! Fisher Exact test

46. Exact tests

48. What you will learn Analysis of categorical data (contingency tables) –Estimating a proportion with the binomial test –Comparing proportions in two-way contingency tables –Relative risk and odds ratio –Fisher exact test for small samples –McNemar test for proportions using paired samples –Comparing proportions in three-way contingency tables with the Cochran-Mantel- Haenszel test

49. McNemar test The McNemar test is a non parametric test applicable to 2x2 contingency tables It is used to show differences in dichotomous data (presence/absence; +/-; Y/N) before and after a certain event / therapy / intervention (thus to evaulate the efficacy of these), if data are available as frequencies

50. McNemar test Migraine after No migraine after TOT Migraine before aba+b No migraine before cd c+d TOTa+cb+dn The test determines whether the row and column marginal frequencies are equal a+b = a+c c+d =b+d b = c Migraine and PFO closure

51. What you will learn Analysis of categorical data (contingency tables) –Estimating a proportion with the binomial test –Comparing proportions in two-way contingency tables –Relative risk and odds ratio –Fisher exact test for small samples –McNemar test for proportions using paired samples –Comparing proportions in three-way contingency tables with the Cochran-Mantel- Haenszel test

52. 3-way contingency tables This is a 2-way 2x4 contingency table… And if we know the ratio of smokers? 3-way 2x4x2 contingency table! That means 2 different 2-ways 2x4 contingency tables

53. 3-way contingency tables The Cochran-Mantel-Haenszel chi-square tests the null hypothesis that two nominal variables are conditionally independent in each stratum, assuming that there is no three-way interaction. It works in a 3-way (3-dimensional) contingency table, where the last dimension refers to the strata

54. 3-way contingency tables

55. SAINT I, NEJM 2006

56. Thank you for your attention For any correspondence: gbiondizoccai@gmail.com For further slides on these topics feel free to visit the metcardio.org website: http://www.metcardio.org/slides.html gbiondizoccai@gmail.com http://www.metcardio.org/slides.html