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What you will learn

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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What you will learn

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  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. Let's start the serious things!!

  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 QUANTITY discrete continuous measuring counting BMI Blood pressure QCA data (MLD, late loss) Stent diameter Stent length

  7. Types of variables Variables PAIRED OR REPEATED MEASURES UNPAIRED OR INDEPENDENT MEASURES eg blood pressure measured twice in the same patients at different times eg blood pressure measured in several different groups of patients only once

  8. Parametric and non-parametric tests Whenever normal or Gaussian assumptions are valid, we can use PARAMETRIC tests, which are usually more sensitive and powerful However, if an underlying normal cannot be safely assumed (ie there is non-gaussian distribution), NON-PARAMETRIC alternatives should be employed, as they are more robust and efficient

  9. Alternatives to non-parametric tests In some cases, albeit uncommonly in clinical cardiovascular research, there are alternatives to non-parametric tests in the presence of violations to normality assumptions Such alternatives are mathematical transformations, such as the logarithmic (Ln), the power (^x), or the square root (√) trasformation

  10. Alternatives to non-parametric tests

  11. Statistical tests Are data categorical or continuous? Categorical data: compare proportions in groups Continuous data: compare means or medians in groups How many groups? More than two groups; normal data? Two groups; normal data? Non-normal data; use Mann Whitney U test Non-normal data; use Kruskal Wallis Normal data; use ANOVA Normal data; use t test

  12. Statistical tests Variables CATEGORY QUANTITY nominal ordinal discrete continuous ordered categories measuring counting ranks Student’s t test Mann-Whitney U test Wilcoxon test Analysis of Variance Kruskal-Wallis test Kolmogodorov-Smirnov test Linear correlation Linear regression Spearman rho test Chi-square test Sign test K-S test Kruskal-Wallis test Mann-Whitney U test Spearman rho test Wilcoxon test Binomial Chi-square test Fisher test

  13. Softwares Freewares Epi-info www.cdc.gov RevMan www.cochrane.org …or just go to www.google.com and search for the test you need… Proprietary softwares BMDP Minitab Primer SAS SPSS Stata Statistica

  14. SPSS

  15. SPSS

  16. SPSS

  17. SPSS

  18. Questions • How can we compare EF in men vs. females after MI? • How does blood pressure change before and after therapy in a group of patients treated with B-blockers? • How can we test if there is difference in in-hospital death in patients treated with trombolysis vs. PCI?

  19. Questions • How can we compare the occurrence of stroke • in AF patients treated with oral anticoagulant therapy vs. • oral aspirin during a long term follow-up? • 5) Can we predict discharge EF using peak CK values after MI?

  20. 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

  21. What you will learn • Finding differences in mean between two groups • independent groups (two-sample t-test) • dependent groups (paired t-test) • non-parametric alternatives: Mann-Whitney U test (rank sum) and Wilcoxon test (signed rank)

  22. Compare variables Agostoni et al. AJC 2007

  23. Compare variables Late loss in 2 different stents Continuous or categorical variable?

  24. Compare continuous variables Late loss in 2 different stents Paired or unpaired data?

  25. Compare continuous unpaired variables Late loss in 2 different stents Parametric or non-parametric test?

  26. Compare variables Mean: 0.55 SD: 0.76 Mean: 0.45 SD: 0.76

  27. Compare variables Median: 0.41 IQR: -0.02–0.85 Median: 0.29 IQR: -0.09–0.66

  28. Compare variables Mean: 0.55 SD: 0.76 Mean: 0.45 SD: 0.76 Median: 0.41 IQR: -0.02–0.85 Median: 0.29 IQR: -0.09–0.66

  29. If parametric… SD SD Frequency Mean Mean Value Student t test for unpaired data: p=0.14 Unpaired: same variable in different patients at same time

  30. If non-parametric… IQR Frequency IQR Median Median Value Mann Whitney U test for unpaired data: p=0.03

  31. Unpaired Student t test

  32. A B Unpaired Student t test

  33. Student t test • A t-test is any statistical hypothesis test in which the test statistic has a Student's t distribution if the null hypothesis is true • It is applied when the population is assumed to be normally distributed but the sample sizes are small enough that the statistic on which inference is based is not normally distributed because it relies on an uncertainestimate of standard deviation rather than on a precisely known value (if we knew it, we could use the Z-test)

  34. Student t test • It is used to test the null hypothesis that the means of two normally distributed populations are equal • Given two data sets (each with its mean, SD and number of data points) the t test determines whether the means are distinct, provided that the underlying distributions can be assumed to be normal • the Student t test should be used if the variances (not known) of the two populations are also assumed to be equal; the form of the test used when this assumption is dropped is sometimes called Welch's t test

  35. Student t test

  36. Mann Whitney rank sum U test

  37. A B Mann Whitney rank sum U test

  38. Ranking • The basic concept of non-parametric tests is ranking • The single values of the variable to analyze are not evaluated according to their absolute value but to the “rank” (or position) they assume in the merged distributon of the values from lower to higher. Driver Endeavor 6-17-17-18-19-19-21-21-21-21 12 3 4 5 6 7 8 9 10 17 21 19 21 19 21 17 21 18 6

  39. Comparisonparametric/non-parametric tests Robustness: non-parametric tests are much less likely than the t tests to give a spuriously significant result because of outliers – they are more robust Efficiency: when normality holds, non-parametric tests have an efficiency of about 95% when compared to parametric tests. For distributions sufficiently far from normal and for sufficiently large sample sizes, non-parametric tests can be considerably more efficient

  40. Compare variables Mean: 0.55 SD: 0.76 Mean: 0.45 SD: 0.76 Median: 0.41 IQR: -0.02–0.85 Median: 0.29 IQR: -0.09–0.66 Student t test for unpaired data: p=0.14 Mann Whitney U test for unpaired data: p=0.03

  41. Unpaired Student t test Late loss in restenotic lesions in two different stents Mean: 1.82 SD: 0.62 Mean: 1.75 SD: 0.51 Unpaired Student t test: p=0.48

  42. Unpaired Student t test Late loss in non restenotic lesions in two different stents Mean: 0.27 SD: 0.44 Mean: 0.14 SD: 0.39 Unpaired Student t test: p=0.002

  43. Paired Student t test Frequency Value Paired: same variable in same group at different time

  44. Paired Student t test 55.1% (7.4) 48.7% (8.3) Only 11 patients !!! EF at baseline and FU in patients treated with BMC for MI Significant increase in EF by paired t test P=0.005 MAGIC, Lancet 2004

  45. Paired Student t test Does MLD change from post-procedure to follow-up in a group of patients receiving a stent?

  46. Paired Student t test Difference MLD fu MLD post

  47. Paired Student t test

  48. Wilcoxon signed rank test Wilcoxon test: non-parametric comparison of 2paired variables

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