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33151-33161 - GEE and Mixed Models for longitudinal data...

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1 GEE and Mixed Models for  longitudinal data   Kristin Sainani Ph.D. http://www.stanford.edu/~kcobb Stanford University Department of Health Research and Policy
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2 Limitations of rANOVA/rMANOVA They assume categorical predictors. They do not handle time-dependent covariates  (predictors measured over time). They assume everyone is measured at the same time  (time is categorical) and at equally spaced time  intervals.  You don’t get parameter estimates (just p-values) Missing data must be imputed. They require restrictive assumptions about the  correlation structure.
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3 Example with time-dependent,  continuous predictor… id time1 time2 time3 time4 chem1 chem2 chem3 chem4 1 20 18 15 20 1000 1100 1200 1300 2 22 24 18 22 1000 1000 1005 950 3 14 10 24 10 1000 1999 800 1700 4 38 34 32 34 1000 1100 1150 1100 5 25 29 25 29 1000 1000 1050 1010 6 30 28 26 14 1000 1100 1109 1500 6 patients with depression are given a drug that increases levels of a “happy  chemical” in the brain.  At baseline, all 6 patients have similar levels of this happy  chemical and scores >=14 on a depression scale. Researchers measure  depression score and brain-chemical levels at three subsequent time points: at 2  months, 3 months, and 6 months post-baseline. Here are the data in broad form:
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4 Turn the data to long form… data long4; set new4; time= 0 ; score=time1; chem=chem1; output ; time= 2 ; score=time2; chem=chem2; output ; time= 3 ; score=time3; chem=chem3; output ; time= 6 ; score=time4; chem=chem4; output ; run ; Note that time is being treated as a continuous  variable—here measured in months.  If patients were measured at different times, this is  easily incorporated too; e.g. time can be 3.5 for  subject A’s fourth measurement and 9.12 for  subject B’s fourth measurement. (we’ll do this in  the lab on Wednesday).
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Data in long  form: id time score chem 1 0 20 1000 1 2 18 1100 1 3 15 1200 1 6 20 1300 2 0 22 1000 2 2 24 1000 2 3 18 1005 2 6 22 950 3 0 14 1000 3 2 10 1999 3 3 24 800 3 6 10 1700 4 0 38 1000 4 2 34 1100 4 3 32 1150 4 6 34 1100 5 0 25 1000 5 2 29 1000 5 3 25 1050 5 6 29 1010 6 0 30 1000 6 2 28 1100 6 3 26 1109 6 6 14 150
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Graphically, let’s see what’s going on: First, by subject.
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All 6 subjects at once:
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Mean chemical levels compared with mean  depression scores:
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14 How do you analyze these  data? Using repeated-measures ANOVA?  The only way to force a rANOVA here is… data forcedanova; set broad; avgchem=(chem1+chem2+chem3+chem4)/ 4 ; if avgchem< 1100 then group= "low" ; if avgchem> 1100 then group= "high" ; run ; proc glm data =forcedanova; class group; model time1-time4= group/ nouni ; repeated time / summary ; run ; quit ; Gives no  significant  results!
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15 How do you analyze these  data?
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