Primer on Statistics for Interventional Cardiologists Giuseppe Sangiorgi, MD Pierfrancesco Agostoni, MD Giuseppe Biondi-Zoccai, MD. What you will learn. Introduction Basics Descriptive statistics Probability distributions Inferential statistics

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

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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

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

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

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

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

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

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?

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

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

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 )

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

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 )

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

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/

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

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)

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

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!

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

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

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