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 Analysis of time-to-event data (survival analysis) –Kaplan-Meier estimate of the survival function –Comparing distributions of time until occurrence of an event with the log-rank and Tarone-Ware tests

4. How can I decide which of 2 stents is safer in terms of freedom from long-term stent thrombosis? In other words, how can I quantitate and compare the risk of a given dichotomous event taking into account variable lengths of follow-up? Survival analysis

5. Patients experiencing one or more events are called responders Patients who, at the end of the observational period or before such time, get out of the study without having experienced any event, are called censored Survival analysis

6. Patients experiencing one or more events are called responders Patients who, at the end of the observational period or before such time, get out of the study without having experienced any event, are called censored Survival analysis Survival analysis expoits all units of information, giving adequate weight to each case, depending on the corresponding duration of follow-up in case of event occurrence or censoring

7. There are 2 methods available for survival analysis: –Actuarial survival analysis (life tables): the probability of survival is computed at fixed time points (eg every 30 days) → uncommonly used in clinical research (but your car insurance is based on this!), unless you have very extensive datasets –Product limit survival analysis (Kaplan-Meier): the probability of survival is computed every time an event occurs → most commonly used in clinical research, given the small datasets Survival analysis

8. Actuarial analysis (life tables)

9. Product limit (Kaplan-Meier) analysis

10. Survival conditional probability at time t j is: where q j = d j /n j is the conditional probability of failure at time t j The cumulative survival probability at t is: Product limit (Kaplan-Meier) analysis

11. Any survival curve has a ladder trend, with many steps Each step occurs when an event occurs, and the height of the step depends on the number of events and of censored data at each specific time Impact of a few changes in events

12. Any survival curve has a ladder trend, with many steps Each step occurs when an event occurs, and the height of the step depends on the number of events and of censored data at each specific time Impact of a few changes in events

13. Any survival curve has a ladder trend, with many steps Each step occurs when an event occurs, and the height of the step depends on the number of events and of censored data at each specific time Impact of a few changes in events

14. Kaplan-Meier curve: hazard Vlaar et al, Lancet 2008

15. Kaplan-Meier curve: hazard Lee et al, EuroInterv 2007

16. Kaplan-Meier curve: hazard Lee et al, EuroInterv 2007

17. Agostoni et al, Am J Cardiol 2005 Kaplan-Meier curve: survival

18. Agostoni et al, Am J Cardiol 2005 Kaplan-Meier curve: survival

19. Kaplan-Meier curves and SE Lotan et al, for the E-Five Registry Investigators, TCT 2008 12-month MACE after ZES implantation for AMI Time after Initial Procedure (days) 15% 12% 9% 6% 3% 0% 03090180270 360390 Cumulative Incidence AMI <72 hr 6 – 24 hr <6 hr MACE030180270360 AMI <72hr11531144108510611027 6-24hr205204190181174 <6hr184183174172169

20. Kaplan-Meier curves and CI Time since PCI in years Cumulative Incidence of ARC definite/probable ST 5 4 3 2 1 0 01234 2.1% (17) — CYPHER Stent 2.1% (26) —TAXUS Stent Cypher & Taxus Pooled Analyses 1 1 Mauri et al, N Engl J Med 2007 5.7% [95% CI] CYPHER & TAXUS (n=8,146) Bern-Rotterdam 2 2 Wenaweser et al, J Am Coll Cardiol 2008

21. What you will learn Analysis of time-to-event data (survival analysis) –Kaplan-Meier estimate of the survival function –Comparing distributions of time until occurrence of an event with the log-rank and Tarone-Ware tests

22. Comparison between survival curves is usually performed with the non-parametric Mantel-Haenzel- Cox test (aka, log-rank test) or its derivates: Gehan- Breslow and Tarone-Ware tests It may also be possible to stratify/adjust for other relevant factors which may be heterogeneously distributed across groups We thus create subgroups (strata) of cases with similar prevalence of such relevant factors Analysis maintains its alpha as the population is not truly dividided in subgroups, but rather analyzed as a whole Hypothesis testing for survival

23. The log-rank test is the most commonly used test The log-rank, Gehan-Breslow, and Tarone-Ware tests are quite similar, but differ in the weight they assign each survival value The Gehan-Breslow test weighs more earlier failures, while the log-rank test weighs equally all failures. The Tarone-Ware test falls in between Our suggestion is to use both log-rank and Tarone-Ware tests, hoping they agree on direction and magnitude of statistical significance Did you know…that If there is no censoring, the Mann- Whitney U rank sum test can be used? Which test should you use?

24. Kaplan-Meier and log-rank Marroquin et al, New Engl J Med 2008

25. Survival analysis with SPSS

28. 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