Correlation, Regression Correlation, Regression and and Covariate-Adjusted Group Covariate-Adjusted Group Comparisons Comparisons 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
Transcript
Correlation, Regression Correlation, Regression
and and
Covariate-Adjusted Group Covariate-Adjusted Group Comparisons Comparisons
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
Flow chart for group Flow chart for group comparisonscomparisons
Measurements to be compared
continuous
Distribution approx normal or N ≥ 20?
No Yes
Non-parametrics T-tests
discrete
( binary, nominal, ordinal with few values)
Chi-squareFisher’s Exact
Flow chart for regression Flow chart for regression modelsmodels
(includes adjusted group comparisons)(includes adjusted group comparisons)Outcome variable continuous or dichotomous?
dichotomouscontinuous
Time-to-event available?
No Yes
Multiple logistic regression
Cox proportionalhazards regression
Predictor variable categorical?
No Yes(e.g. groups)
Multiple linear regression
ANCOVA(Multiple linear regression -using dummyvariable(s) forcategorical var(s)
Health, Aging and Body Health, Aging and Body Composition Study (HABC)Composition Study (HABC)
Observational study of 3075 men and women (now in year 13 followup)Observational study of 3075 men and women (now in year 13 followup) age 70-79age 70-79 45% African-American45% African-American Pittsburgh, PA and Memphis, TNPittsburgh, PA and Memphis, TN Able to walk 1/4 mile and climb 10 steps Able to walk 1/4 mile and climb 10 steps (study eligibility criteria)(study eligibility criteria)
Designed to assess the relationship of weight and body composition toDesigned to assess the relationship of weight and body composition to incident weight related diseases andincident weight related diseases and disabilitydisability
Funded by National Institute on Aging 1997-continuingFunded by National Institute on Aging 1997-continuing University of PittsburghUniversity of Pittsburgh University of Tennessee, MemphisUniversity of Tennessee, Memphis Coordinating Center: University of California, San Francisco Coordinating Center: University of California, San Francisco Laboratory for Epidemiology, Demography and Biometry, NIALaboratory for Epidemiology, Demography and Biometry, NIA
HABC: Knee OA HABC: Knee OA SubstudySubstudy
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 263 147African-American male 124 56White female 252 93White male 223 87
Today’s ObjectiveToday’s Objective In HABC: Examine Association between SxRxKOA (knee OA) In HABC: Examine Association between SxRxKOA (knee OA)
and CRP adjusted for BMI.and CRP adjusted for BMI.
Sowers M, Hochberg M et. al. C-reactive protein as a biomarker of emergent osteoarthritis. Osteoarthritis and CartilageVolume 10, Issue 8, August 2002, Pages 595-601
N=1025 women aged 27-53; 18% had Knee OA of those 40-53. 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”
All White Females in HABC (N=844)[includes SxRxKOA (n=93); also rest of parent study cohort]
N=5N=5 had CRP > 30 (max=63.2)
log CRP
White FemalesWhite Females
Difference in average logCRP: 0.76 – 0.43 = 0.33
Knee OA
P-value
No (n=752) Yes (n=92)
Mean (SD) Mean (SD)
Equal vars Unequal
logCRP 0.43 (0.83) 0.76 (0.58) 0.0002 < 0.0001
BMI 25.4 (4.3) 28.8 (5.2) < 0.0001 < 0.0001
logCRP SD’s were signif diff (p<0.0001) => Use Satterthwaite unequal variance test
model logCRP=KneeOA bmi; where female=1 and white=1;run;
Note: Equal BMI slopes in each group is being modeled
Unadjusted diffWas 0.33
BMI partially“explains” thisdifference
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
ANCOVA (Analysis of ANCOVA (Analysis of Covariance)Covariance)
Compare logCRP adjusted Compare logCRP adjusted for BMIfor BMI
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”)
