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. Why a glance at advanced stats? Like in a live case, we want to expose you to the next level of statistical analysis It is not highly complex in itself, but only builds upon a solid knowledge of standard statistics, ie what we have seen today If you are interested in more, let us know…

4. What you will learn Advanced statistics at a glance: –Mulivariable analysis –Multiple linear regression –Logistic regression –Cox proportional hazards model –Generalized linear models –Propensity analysis –Resampling methods –Meta-analysis

5. A hierarchy of analysis levels Statistical analyses can be distinguished in –Univariate (eg describing a variable such as lesion length) –Bivariate (eg comparing two different variables such as CKMB release and subsequent LVEF) –Multivariable (eg appraising the impact of two or more independent/moderator variables on a single dependent variable) –Multivariate (eg appraising the impact of two or more independent/moderator variables on two or more dependent variables)

6. An example of multivariable analysis Vlaar et al, Lancet 2008

7. An example of multivariable analysis Vlaar et al, Lancet 2008

8. An example of multivariable analysis Vlaar et al, Lancet 2008

9. What you will learn Advanced statistics at a glance: –Mulivariable analysis –Multiple linear regression –Logistic regression –Cox proportional hazards model –Generalized linear models –Propensity analysis –Resampling methods –Meta-analysis

10. Multiple linear regression How can I predict the impact of balloon dilation pressure on angiographic late loss, taking concomitantly into account diabetes status and ACC/AHA lesion type?

11. Multiple linear regression How can I predict the impact of balloon dilation pressure on angiographic late loss, taking concomitantly into account diabetes status and ACC/AHA lesion type? In other words, how can I predict the impact of a given variable (aka independent) on another continuous variable (aka dependent), taking concomitantly into account other variables?

12. Multiple linear regression Multiple linear regression is just an extension of bivariate linear regression Thus we can move from bivariate regression to multivariable regression analysis A great deal of emphasis should be placed on model building and validation, eg checking residuals and avoiding overfitting

13. Identifying predictors of late loss Sangiorgi et al, AHJ 2008

14. Identifying predictors of late loss Sangiorgi et al, AHJ 2008

15. What you will learn Advanced statistics at a glance: –Mulivariable analysis –Multiple linear regression –Logistic regression –Cox proportional hazards model –Generalized linear models –Propensity analysis –Resampling methods –Meta-analysis

16. Logistic regression How can I predict the impact of left ventricular ejection fraction (LVEF) on the 12-month risk of ARC-defined stent thrombosis?

17. Logistic regression How can I predict the impact of left ventricular ejection fraction (LVEF) on the 12-month risk of ARC-defined stent thrombosis? In other words, how can I predict the impact of a given variable (aka independent) on another dichotomous variable (aka dependent)

18. Logistic regression Logistic regression is based on the logit which transforms a dichotomous dependent variable into a continuous one Thus a number of assumptions should be valid to trust its results Logistic regression can also be applied to multivariable and polichotomous analyses Emphasis should again be placed on model building and validation, eg checking residuals and avoiding overfitting

19. Logistic regression

20. Sangiorgi et al, AHJ 2008

21. What you will learn Advanced statistics at a glance: –Mulivariable analysis –Multiple linear regression –Logistic regression –Cox proportional hazards model –Generalized linear models –Propensity analysis –Resampling methods –Meta-analysis

22. Cox proportional hazard model How can I predict the impact of left ventricular ejection fraction (LVEF) on the risk of ARC- defined stent thrombosis over a variable period of follow-up? In other words, how can I predict the impact of a given variable (aka independent) on another dichotomous variable (aka dependent), but with variable follow-up and aiming to exploit as much as possible all event data

23. Cox proportional hazard model Cox proportional hazard analysis is a parametric analysis that can be used for dichotomous dependent variables occurring over time and to test its association with one or more independent variables A number of assumptions should hold true In particular, hazards should be constant over time → log−log survival function

24. Agostoni et al, Am J Cardiol 2005 Cox proportional hazard model

25. Agostoni et al, Am J Cardiol 2005 Cox proportional hazard model

26. Marroquin et al, New Engl J Med 2008 Cox proportional hazard model

27. What you will learn Advanced statistics at a glance: –Mulivariable analysis –Multiple linear regression –Logistic regression –Cox proportional hazards model –Generalized linear models –Propensity analysis –Resampling methods –Meta-analysis

28. First things first The generalized linear model (GLM) is a flexible generalization of ordinary least squares regression It relates the random distribution of the measured variable of the experiment (the distribution function) to the systematic (non- random) portion of the experiment (the linear predictor) through a function called the link function (g)

29. First things first EarthOxford

30. Generalized linear model (GLM) Through differing link functions, GLM corresponds to other well known models DistributionNameLink Function Mean Function NormalIdentity Exponential Inverse Gamma Inverse Gaussian Inverse squared PoissonLog BinomialLogit

31. What you will learn Advanced statistics at a glance: –Mulivariable analysis –Multiple linear regression –Logistic regression –Cox proportional hazards model –Generalized linear models –Propensity analysis –Resampling methods –Meta-analysis

32. Propensity analysis How can appraise the impact of a specific stent type on long-term risk of stent thrombosis outside the context of a randomized controlled trials? In other words, how assess the independent impact of a given independent/moderator variable when my dataset is not based on randomization and likelihood of underlying confounding is very high

33. Propensity analysis Propensity analysis is a peculiar type of multivariable analysis in which the propensity to choose one treatment versus the other(s) is explictly assessed and measured Building upon such propensity (usually by means of non-parsimonious scores), the dataset is matched and/or analysed Propensity are usually exploited in: a) matched pairs, b) quintiles/deciles, or c) in logistic/Cox regression models

34. Propensity score analysis Seung et al, New Engl J Med 2008

35. Propensity score analysis Seung et al, New Engl J Med 2008

36. Propensity score analysis Seung et al, New Engl J Med 2008

37. Propensity score analysis Seung et al, New Engl J Med 2008

38. What you will learn Advanced statistics at a glance: –Mulivariable analysis –Multiple linear regression –Logistic regression –Cox proportional hazards model –Generalized linear models –Propensity analysis –Resampling methods –Meta-analysis

39. Resampling methods A friendly question for our best pupil: how can I build 95% confidence intervals for medians? In other words, how can I make statistical inference when the variable I am focusing onto does not follow standard statistical distributions, is highly skewed or sparse?

40. Resampling methods Resampling methods are powerful validation and quantitation tools, as they can be much more distribution-independent than all other statistical methods The 2 most commonly used resampling methods are: - Jacknife - bootstrap

41. Bootstrap

42. What you will learn Advanced statistics at a glance: –Mulivariable analysis –Multiple linear regression –Logistic regression –Cox proportional hazards model –Generalized linear models –Propensity analysis –Resampling methods –Meta-analysis

43. Meta-analysis How can I decide whether first generation DES increase stent thrombosis given the plethora of several small, conflicting, and/or inconclusive pertinent clinical studies? In other words, how can I combine data from several small, conflicting, and/or inconclusive primary studies?

44. Meta-analysis Meta-analysis is a group of statistical methods used to combine quantitative estimates from several primary research studies Meta-analysis increase statistical power, boost external validity, and can test/explore secondary hypotheses (eg meta-regression) When conducted in the context of a systematic literature review and focusing only on randomized clinical trials, they are considered the top level of clinical evidence

45. Study-level meta-analysis De Luca et al, Eur Heart J 2008

46. Study-level meta-analysis De Luca et al, Eur Heart J 2008

47. Study-level meta-analysis De Luca et al, Eur Heart J 2008

48. Study-level meta-analysis De Luca et al, Eur Heart J 2008

49. Study-level meta-analysis De Luca et al, Eur Heart J 2008

50. Patient-level meta-analysis Mauri et al, New Engl J Med 2007

51. Patient-level meta-analysis Mauri et al, New Engl J Med 2007 Pooled patient-level analysis for protocol-defined stent thrombosis

52. 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