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Published byImogene Bridges Modified over 9 years ago

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**Correlation, Regression Covariate-Adjusted Group Comparisons**

and Covariate-Adjusted Group Comparisons 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 Dept. of Epidemiology, GSPH

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**Flow chart for group comparisons**

Measurements to be compared continuous discrete ( binary, nominal, ordinal with few values) Distribution approx normal or N ≥ 20? Chi-square Fisher’s Exact No Yes Non-parametrics T-tests

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**Flow chart for regression models (includes adjusted group comparisons)**

Outcome variable continuous or dichotomous? continuous dichotomous Predictor variable categorical? Time-to-event available? No Yes (e.g. groups) No Yes Multiple linear regression ANCOVA (Multiple linear regression - using dummy variable(s) for categorical var(s) Multiple logistic regression Cox proportional hazards regression

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**Health, Aging and Body Composition Study (HABC)**

Observational study of 3075 men and women (now in year 13 followup) age 70-79 45% African-American Pittsburgh, PA and Memphis, TN Able to walk 1/4 mile and climb 10 steps (study eligibility criteria) Designed to assess the relationship of weight and body composition to incident weight related diseases and disability Funded by National Institute on Aging 1997-continuing University of Pittsburgh University of Tennessee, Memphis Coordinating Center: University of California, San Francisco Laboratory for Epidemiology, Demography and Biometry, NIA

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HABC: Knee OA Substudy Year 2: Knee x-rays and MRIs were done on participants with “qualifying knee pain” “knee OA” Cases (N=862): Sx (Knee-Pain) SxRxKOA (KL ≥ 2) African-American female African-American male White female White male

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Today’s Objective In HABC: Examine Association between SxRxKOA (knee OA) and CRP adjusted for BMI. Sowers M, Hochberg M et. al. C-reactive protein as a biomarker of emergent osteoarthritis. Osteoarthritis and Cartilage Volume 10, Issue 8, August 2002, Pages N=1025 women aged 27-53; 18% had Knee OA of those Higher CRP associated with prevalent KOA (also incident KOA) Bilateral KOA had higher CRP than unilateral Conclusion: “CRP is highly associated with Knee OA; however, its high correlation with obesity limits its utility as an exclusive marker for knee OA”

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**All White Females in HABC (N=844)**

[includes SxRxKOA (n=93); also rest of parent study cohort] N=5 had CRP > 30 (max=63.2) N=5

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log CRP

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**White Females Knee OA P-value No (n=752) Yes (n=92) Mean (SD)**

Equal vars Unequal logCRP 0.43 (0.83) 0.76 (0.58) 0.0002 < BMI 25.4 (4.3) 28.8 (5.2) logCRP SD’s were signif diff (p<0.0001) => Use Satterthwaite unequal variance test Difference in average logCRP: – 0.43 = 0.33

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**Two-Group Unadjusted Comparison Of Means Using Regression with Dummy-coded Groups**

proc reg data=kneeOA_vs_noOA; model logCRP= KneeOA; where female=1 and white=1; run; * No OA is “referent” group (i.e. kneeOA=0) HABCID logCRP kneeOA BMI

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**proc reg data=kneeOA_vs_noOA; model logCRP= KneeOA; where female=1 and white=1; run;**

(intercept) KneeOA=0 logCRP= *0 = KneeOA=1 logCRP= *1 =

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**White Females: 2-Group Comparison Using Dummy-coded Groups**

* No OA is “referent” group (KneeOA=0); proc reg data=kneeOA_vs_noOA; model logCRP= KneeOA; where female=1 and white=1; run; “No OA” mean “kneeOA” mean difference from referent Note: Regression using Dummy (0, 1) for group variable (e.g. KneeOA=0,1) In regression, equal (pooled) variance is assumed

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**White Females: 2-Group Comparison Using Dummy-coded Groups**

* No OA is “referent” group (KneeOA=0); proc reg data=kneeOA_vs_noOA; model logCRP= KneeOA; where female=1 and white=1; run; “No OA” mean “kneeOA” mean difference from referent Same p-value as equal variance t-test Note: Regression using Dummy (0, 1) for group variable (e.g. KneeOA=0,1) In regression, equal (pooled) variance is assumed

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Pearson Correlation Pearson Correlation = a measure of linear association

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**Pearson vs Spearman Correlation**

A measure of rank order correlation Works for any general trend that is increasing or decreasing and not necessarily linear

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**Pearson vs Spearman Correlation**

A measure of rank order correlation Works for any general trend that is increasing or decreasing and not necessarily linear Equals Pearson Correlation using the ranks of the observations instead of actual values Heuristically: Spearman measures degree that low goes with low, middle with middle, high with high

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**Regression on a continuous independent variable (BMI)**

proc reg data=kneeOA_vs_noOA; model logCRP=bmi; where female=1 and white=1 and kneeOA=1; run; logCRP= *BMI Exact same p-value as test of H0: Correlation=0

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**Effect of Centering BMI at 25**

proc reg data=kneeOA_vs_noOA; model logCRP=bmi_minus25; where female=1 and white=1 and kneeOA=1; run; logCRP= *(BMI-25) = at BMI=25 (see graphic)

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**Effect of Centering BMI at 25**

Model 2: logCRP= *(BMI-25) = * *BMI = *BMI

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Unadjusted Mean Difference {

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**Notice: At any BMI level,**

the mean logCRP difference between KneeOA vs Not is smaller than the unadjusted difference Unadjusted Mean Difference {

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**ANCOVA (Analysis of Covariance) Compare logCRP adjusted for BMI**

proc reg data=kneeOA_vs_noOA; model logCRP=KneeOA bmi; where female=1 and white=1; run; Unadjusted diff Was 0.33 BMI partially “explains” this difference Note: Equal BMI slopes in each group is being modeled

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**ANCOVA (Analysis of Covariance) Centering BMI at 25**

proc 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

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**ANCOVA (Analysis of Covariance) Compare logCRP adjusted for BMI**

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**Check of ANCOVA Assumption: Equality of BMI slopes: KneeOA vs Not**

proc reg data=knee_vs_noOA; model logCRP=KneeOA bmi BMI_x_KneeOA; where female=1 and white=1; run; (“interaction term”) HABCID logCRP kneeOA BMI BMI_x_KneeOA

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**Check of ANCOVA Assumption: Equality of BMI slopes: KneeOA vs Not**

proc reg data=knee_vs_noOA; model logCRP=KneeOA bmi BMI_x_KneeOA; where female=1 and white=1; run; The “BMI” slopes are not signif different (p=0.8019) => they are parallel

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**logCRP between KneeOA vs Not Adjusted for BMI, Age and Anti-inflammatory Meds**

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**Thank you Questions, comments, suggestions or insights?**

Remaining time: Open consultation …

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