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

1. Primer on Statistics for Interventional CardiologistsGiuseppe Sangiorgi, MDPierfrancesco Agostoni, MDGiuseppe 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. Types of variables Variables CATEGORY QUANTITY nominal ordinal discrete continuous Death: yes/no TLR: yes/no measuring counting ordered categories ranks BMI Blood pressure QCA data (MLD, late loss) Stent diameter Stent length TIMI flow Radial/brachial/femoral

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

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

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. Compare discrete variables χ2 test or chi-square test The first basis for the chi-square test is the contingency table ENDEAVOR II. Circulation 2006

15. Compare discrete variables χ2 test or chi-square test

16. Compare discrete variables χ2 test or chi-square test

17. Compare discrete variables No TVF TVF r1 a b Driver c d r2 Endeavor s2 N s1

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

19. Stent TVF

20. Compare discrete variables χ2 test or chi-square test

21. Compare discrete variables χ2 test or chi-square test

22. AHA/ACC type A B1 B2 C Total no Count 3 3 0 2 8 % within DIABETES 37,5% 37,5% ,0% 25,0% 100,0% DIABETES yes Count 1 0 3 1 5 % within DIABETES 20,0% ,0% 60,0% 20,0% 100,0% Total Count 4 3 3 3 13 % within DIABETES 30,8% 23,1% 23,1% 23,1% 100,0% Compare discrete variables More than 2x2 contingency tables Post-hoc comparisons Is there a difference between diabetics and non-dabetics in the rate of AHA/ACC type lesions?

23. Post-hoc groups 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 !! 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. Compare event rates No TVF TVF a b Driver Endeavor c d 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 )

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 No TVF TVF a b Driver c d Endeavor RR = [ d / ( c + d ) ] / [ a / ( a + b ) ] OR = (d/c)/(b/a) = ( a * d ) / ( b * c )

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

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

30. Compare event rates • 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 NNTLow NNT => Large benefit ENDEAVOR II. Circulation 2006

31. Compare event rates

32. Compare event rates 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)] https://www.som.soton.ac.uk/cia/

33. Compare event rates

34. Compare event rates

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

36. Compare event rates

37. Compare event rates “Unmatched case control study” for Odds Ratio

38. Compare event rates

39. Compare event rates 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. Exact tests • 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)

44. Exact tests • 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

45. Fisher Exact test Exp Ctrl r1 Event a b No event c d r2 s2 N s1 s1! * s2! * r1! * r2! P = N! * a! * b! * c! * d!

46. Exact tests

47. 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 and PFO closure a+b = a+c c+d =b+d b = c The test determines whether the row and columnmarginal frequencies are equal