Methods and Statistical analysis. A brief presentation. Markos Kashiouris, M.D.

Points of discussion: Jupiter trial endpoints. What is censored data and how they are analyzed. Kaplan-Meier product-limit method. Comparison of two curves (logrank test and Mantel–Haenszel test ). Power analysis, type I and type II errors. Hazard ratios. The Cox’s proportional hazard model. Number-Needed to treat. The Intention-to-treat principle.

Primary End-Points Non-fatal Myocardial Infarction Any Myocardial infarction Non-Fatal stroke Any Stroke Arterial Revascularization Hospitalization for unstable angina Confirmed death from CV causes

Secondary End-Points Secondary end points included the components of the primary end point considered individually. Death from any cause

Data of the study When research involves time-related variables, such as survival and recurrence, we generally do not know the outcome for all patients at the time the study is published, so these outcomes are called censored. Censored Multivariate Numerical Death Censored

Kaplan-Meier Product Limit Method The Kaplan–Meier procedure is the most commonly used method to illustrate survival curves. The Kaplan–Meier method of estimating survival is similar to actuarial analysis except that time since entry in the study is not divided into intervals for analysis.

Power Analysis JUPITER was an event-driven trial designed to continue until 520 confirmed primary end points. Designed to provide a statistical power of 90% to detect a 25% reduction in the rate of the primary end point, with a two-sided significance level of 0.05.

Power Analysis If the study finds a difference in treatments, when in actuality there is no difference (cell B), a type I error is present. If the study fails to find a difference in treatments when in actuality there is a difference (cell C), a type II error is said to have occurred.

Power Analysis n is the number of subjects for each treatment group, c and t are the proportion of patients who will reach the end point in the placebo group and in the treatment group (rosuvastatin therapy). Respectively, and z a and z b are the values that include alpha in the two tails and beta in the lower tail of the standard normal distribution. These values can be determined from tables available in most statistical texts.

Comparing two-survival curves The logrank statistic is one of the most commonly used methods to learn if two curves are significantly different. The logrank test compares the number of observed deaths in each group with the number of deaths that would be expected. The Mantel–Haenszel test combines a series of 2 x 2 tables formed at different survival times into an overall test of significance of the survival curves. The Mantel–Haenszel statistic is very useful because it can be used to compare any distributions, not simply survival curves.

The Hazard ratio Hazard Ratio = O 1 /E 1 divided by O 2 /E 2 (O= Observed events, E = Expected events) HAZARD RATIO ≠ RELATIVE RISK

Comparing two-survival curves The logrank statistic assumes that the ratio of hazard rates in the two groups stays the same throughout the period of interest. When a constant hazard ratio cannot be assumed, the generalized Wilcoxon procedure is preferred.

Predicting a censored outcome Cox’s proportional Hazard Model

Predicting a censored outcome Cox’s proportional Hazard Model Formulation of Model: Group (rosuvastatin) hazard = Baseline hazard x (Group Factor)

Number Needed to treat So how NNT is calculated from Kaplan- Meier curves? NTT=1 / [ (S c (t)) haz - S c (t) ] e.g 1/(0.95^0.56 – 0.95) NNT = 1/ARR

Control 2 years NTT=1/{[S c (t)] h - S c (t)} 1/(0.975^(0.56) – 0.975) = 1/0.011 = Calculated Hazard ratio = 0.56 Treatment

The intention-to-treat principle In the method section, the researchers state: "All analyses were based on the intention-to-treat principle...."

Thoughts about statistics used Appropriate methods? NNT appropriate? Confidence intervals? Hazard ratios are NOT equivalent to relative risk.

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