EP 521, Spring 2007, Vol I, Part 1 Center for Clinical Epidemiology and Biostatistics School of Medicine, University of Pennsylvania Copyright © 2006 Trustees of the University of Pennsylvania 1CStatistical Methods in Epidemiologic Research (FOR CLASS USE ONLY – DO NOT CITE OR REPRODUCE) EP 521 Spring 2007 Course Notes – Vol I (Part 1 of 5) A. Russell Localio*, and Jesse A Berlin (“The Great Master”)† *Department of Biostatistics and Epidemiology Center for Clinical Epidemiology and Biostatistics School of Medicine University of Pennsylvania Philadelphia PA 19104-6021 †Statistical Science, Biometrics and Clinical Informatics (BCI). J&J Pharmaceutical Research and Development, LLC 1125 Trenton-Harbourton Road PO Box 200 Titusville, NJ 08560 Overview – Some basic principles EP 521, Spring 2007, Vol I, Part 1 Center for Clinical Epidemiology and Biostatistics School of Medicine, University of Pennsylvania Copyright © 2006 Trustees of the University of Pennsylvania 2C Principle #1 --Perspective This course is about analyzing data -- the issues and methods. It is not about learning “rules” and applying them to data. Changing Perspectives – From Religion to Science After 17 years of interacting with physicians, I have come to realize that many of them are adherents of a religion they call Statistics. ... To the physician who practices this religion, Statistics refers to the seeking out and interpreting of p-values. Like any good religion, it involves vague mysteries capable of contradictory and irrational interpretation. It has a priesthood and a class of mendicant friars. And it provides Salvation: Proper invocation of the religious dogmas of Statistics will result in publication in prestigious journals. Salsburg DS. The religion of statistics as practiced in medical journals. Am Statistician 1985;39:220-223.EP 521, Spring 2007, Vol I, Part 1 Center for Clinical Epidemiology and Biostatistics School of Medicine, University of Pennsylvania Copyright © 2006 Trustees of the University of Pennsylvania 3CBut this course is also about learning where to find answers rather than just learning what the teacher thinks is best: “We should not elevate our autonomy as individual faculty members above every other value. … [Professors have a responsibility] to resist the allure of certitude, the temptation to use the podium as an ideological platform, to indoctrinate a captive audience, to play favorites with the like-minded and silence the others.” Arenson KW. Columbia chief takes disputes over professors. The New York Times. (March 24, 2005) (Quoting Columbia President Lee C. Bollinger) . EP 521, Spring 2007, Vol I, Part 1 Center for Clinical Epidemiology and Biostatistics School of Medicine, University of Pennsylvania Copyright © 2006 Trustees of the University of Pennsylvania 4CPrinciple #2. --Common themes: We relate concepts of epidemiology (and we must be careful about taxonomy) to elements of probability to see some simple methods of analyzing data. We distinguish terms carefully: odds ratio, relative risk, rate ratio, hazard ratio. Each has a mathematical interpretation. They are not generally interchangeable. We try to look at data first and only then implement the statistical tools Interpretation of computer output is not only important, it is essential.EP 521, Spring 2007, Vol I, Part 1 Center for Clinical Epidemiology and Biostatistics School of Medicine, University of Pennsylvania Copyright © 2006 Trustees of the University of Pennsylvania 5CPrinciple #3. Applying principles of statistics (from EP 520) to epidemiologic research Principle #4. Common statistical methods include: a) descriptive data (Means, medians, plots, tables of counts and percentages) – “Looking at the data” b) Statistical test, e.g., t-test comparing cholesterol levels in CHD patients and controls (de-emphasized) c) comparisons of groups, in general. [treated vs. control, exposed vs. unexposed] d) Estimating “effect size” -- A measure of the effect of treatment or exposure on outcome expressed in any number of different metrics (odds ratios, relative risks, risk differences, differences in means, area under the ROC curve – all of which are related. EP 521, Spring 2007, Vol I, Part 1 Center for Clinical Epidemiology and Biostatistics School of Medicine, University of Pennsylvania Copyright © 2006 Trustees of the University of Pennsylvania 6CPrinciple #5. Critically important issues - Sampling Variability and power What does the figure suggest? The differences in the two sets of samples are about the same (the difference between the sets of peaks). But peaks in right set have less overlap because they are higher and steeper. Why? Because the variance is smaller. 0 .05 .1 .15 .2y0 12 24 36 48 60 Sampling Variability and PowerDifferences between each set of distributions = 12SD = 4 on left pairs; 2 on right pairsEP 521, Spring 2007, Vol I, Part 1 Center for Clinical Epidemiology and Biostatistics School of Medicine, University of Pennsylvania Copyright © 2006 Trustees of the University of Pennsylvania 7C- Probability distributions (~N(mean, var), or ~B(n,p) ) - Null hypothesis (hypothesis testing) - Confidence interval (meaning and construction) Definition of 95% CI (from frequentist perspective)? (See Woodward, Second Edition p 34) In 1000 repeated samples taken from a population that has a true but unobserved parameter (such as an odds ratio), the estimated “95% confidence interval” from each sample should cover the true parameter in 950 of the samples. - Regression ( and the idea of modeling) - All these share underlying goals: Distinguish Signal from noise Systematic differences from random variation EP 521, Spring 2007, Vol I, Part 1 Center for Clinical Epidemiology and Biostatistics School of Medicine, University of Pennsylvania Copyright © 2006 Trustees of the University of Pennsylvania 8CPrinciple #6. Biases in generating data -- Observed sources of bias we can handle by: Exclusion criteria Separate analyses for each group Stratified analyses (Mantel Haenszel methods represent an example) Regression (a statistical model) Unobserved sources: Must undertake sensitivity analysis Ask what would be effect of an omitted confounder that has a stipulated Association with