PM 515 Behavioral Epidemiology Meta Analysis and Advanced Programming in SAS and Excel

1. PM 515Behavioral EpidemiologyMeta Analysis and Advanced Programming in SAS and Excel Ping Sun, Ph.D. Jennifer Unger, Ph.D.

2. Review of Basic Statisticspopulation, sample, and sample mean Normal Distribution of x in a sample

3. Excel Demonstration • Population Description • 2 Guassian Distribution • Mean and Std for a population • Samples (estimates and confidence Intervals) • se for means from multiple samples (std vs. se)

4. Excel DemonstrationSimple Meta Analysis • Estimation of mean and standard error of mean when raw data is available • Both study level and subject level covariates can be controlled in meta analysis • Estimation of mean and standard error of mean when raw data is not available, rather only the mean and se(mean) for individual studies are available. Notes: See measures from 10 studies, and meta analysis worksheets in the excel file

5. Key Concept • Gaussian distribution is assumed for model parameters (mean, beta, etc.) • Variance of the estimates from an individual study is inversely proportional to sample size, and proportional to the variance of the disturbance • Meta analysis (the addition of more samples) should reduce the Variance of estimates accordingly --- but not always. • Samples from individual studies must be independent.

6. What if the parameter is not Gaussian? • Transform it before conducting meta analysis! • Correlation: • Transform to Fisher’s Zr Score: • Backward transform: • Odds Ratio: • Transform to beta: beta = log(OR) • Backward transform: OR = exp(beta)

7. Beta and se(beta) for 2 x 2 table x y OR (x=1 vs x=0) = (20/50) / (30/100) = 0.4/0.3 = 1.33 Ln (OR) = 0.285 se(Ln(OR)) = sqrt(1/50+1/100+1/20+1/30) = 0.337 T = ln(OR) / se(ln(OR) = 0.285 / 0.337 = 0.85

8. Estimation • Beta ± se is what we are focusing on for meta analysis. • What if we can only find beta (p value) from the published results? • What if we can only find OR (95% CI) from the published results?

9. Statistical Methods in Meta Analysis • The Problem of Heterogeneity • Choice of Effect Measure • Fixed Effects Model • Random Effects Model

10. The Problem of Heterogeneity • What are the main goal of meta analysis? • To estimate a summary effect, or • To study what caused the specific clinical differences between studies? • It is equally important to study both

11. Fixed Effects Model • To answer the question whether the treatment has caused an effect in the included studies • Methods: • Mantel Haenszel Method • Peto’s Method • General Variance Based Methods • Tests of Homogeneity • Calculation of Q Statistic

12. General Variance Based Methods Weight 1 / Variance Mean ES SE of the Mean ES Z-test for the Mean ES 95% Confidence Interval

13. Test of Homogeneity • Null Hypothesis: Effect Sizes Are Equal in All of the Studies • Q statistic: • The Q statistic comply with Chi-square distribution with N-1 degree of freedom, N=number of studies

14. Random Effects Model • Not just summarize the findings and get an average finding, but assume that the findings from the sub-studies are all instances of a general finding (which is random). The purpose is to estimate the statistics of the general finding. Or, to answer the question whether the treatment will generate an effect • Dersimonian and Laird Method

15. Example • Organize the studies • Generate the work dataset and conduct statistic analysis • Paper Writing

16. Statistics in ExcelAn Example • Step by Step Multiple Regression in Excel • Reference\Session 11\Multiple Regression in Excel.xls

17. Advanced SAS Data Management and Analysis • SAS Data Management • With Conventional Data Step • With SAS Proc SQL • SAS Data Analysis • Analysis + Graph in SAS • Analysis in SAS and Graph in EXCEL