Biostat Didactic Seminar Series Biostat Didactic Seminar Series Correlation and Regression Correlation and Regression Part 2 Part 2 Robert Boudreau, PhD Robert Boudreau, PhD Co-Director of Methodology Core Co-Director of Methodology Core PITT-Multidisciplinary Clinical Research Center PITT-Multidisciplinary Clinical Research Center for Rheumatic and Musculoskeletal Diseases for Rheumatic and Musculoskeletal Diseases Core Director for Biostatistics Core Director for Biostatistics Center for Aging and Population Health Center for Aging and Population Health Dept. of Epidemiology, GSPH Dept. of Epidemiology, GSPH
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Biostat Didactic Seminar Series Correlation and Regression Part 2 Robert Boudreau, PhD
Biostat Didactic Seminar Series Correlation and Regression Part 2 Robert Boudreau, PhD Co-Director of Methodology Core PITT-Multidisciplinary Clinical Research Center for Rheumatic and Musculoskeletal Diseases Core Director for Biostatistics Center for Aging and Population Health - PowerPoint PPT Presentation
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Biostat Didactic Seminar SeriesBiostat Didactic Seminar Series
Correlation and Regression Correlation and Regression
Part 2Part 2
Robert Boudreau, PhDRobert Boudreau, PhD
Co-Director of Methodology CoreCo-Director of Methodology Core
PITT-Multidisciplinary Clinical Research Center PITT-Multidisciplinary Clinical Research Center
for Rheumatic and Musculoskeletal Diseasesfor Rheumatic and Musculoskeletal Diseases
Core Director for BiostatisticsCore Director for Biostatistics
Center for Aging and Population Health Center for Aging and Population Health
Dept. of Epidemiology, GSPHDept. of Epidemiology, GSPH
Fall 2009 – Spring 2010 Fall 2009 – Spring 2010 1.1. Descriptive Statistics: Examining Your Data Descriptive Statistics: Examining Your Data Data types: Qualitative (Categorical), Ordinal, QuantitativeData types: Qualitative (Categorical), Ordinal, Quantitative Mean, SD, medians, quartiles, IQR, skewness, histograms, Mean, SD, medians, quartiles, IQR, skewness, histograms,
boxplotsboxplots
2.2. Group Comparisons: Part 1Group Comparisons: Part 1 Normal dist (mean, SD: 68%, 95%, 99% Normal dist (mean, SD: 68%, 95%, 99%
interpretation)interpretation) t-dist, degrees of freedom (n-1)t-dist, degrees of freedom (n-1) Confidence interval for the meanConfidence interval for the mean
3.3. Group Comparisons: Part 2Group Comparisons: Part 2 Comparing means: Two-sample independent t-testComparing means: Two-sample independent t-test
pooled and unequal variance (Satterthwaite) versionspooled and unequal variance (Satterthwaite) versions interpretation of p-values, type I (false positive) and type II interpretation of p-values, type I (false positive) and type II
Fall 2009 – Spring 2010 Fall 2009 – Spring 2010 5.5. Correlation, Regression and Covariate-Correlation, Regression and Covariate-Adjusted Group Comparisons Adjusted Group Comparisons
Pearson vs Spearman correlation Pearson vs Spearman correlation
=> linear vs monotone association => linear vs monotone association Regression: Regression: interpretation of beta coefficients interpretation of beta coefficients
Standard errors, p-valuesStandard errors, p-values Continuous predictor => beta coeff is a slopeContinuous predictor => beta coeff is a slope Dichotomous (e.g. group “dummy” 0,1 valued variable)Dichotomous (e.g. group “dummy” 0,1 valued variable)
=> beta coeff is difference in response vs “referent” => beta coeff is difference in response vs “referent”
ANCOVA (Analysis of ANCOVA (Analysis of Covariance)Covariance)
Centering BMI at 25Centering BMI at 25proc reg data=kneeOA_vs_noOA; model logCRP=KneeOA bmi_minus25; where female=1 and white=1;run;
Note: Equal BMI slopes in each group is being modeled
Check of ANCOVA Assumption: Check of ANCOVA Assumption:
Equality of BMI slopes: KneeOA vs Equality of BMI slopes: KneeOA vs NotNotproc reg data=knee_vs_noOA;proc reg data=knee_vs_noOA;
model logCRP=KneeOA bmi BMI_x_KneeOA;model logCRP=KneeOA bmi BMI_x_KneeOA; where female=1 and white=1;where female=1 and white=1;run;run; (“interaction term”)(“interaction term”)