Subject-specific observed profiles of change from baseline vs week trt=10000u
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1 Mean of age 1 The MEANS Procedure Analysis Variable : age N Mean Std Dev Minimum Maximum ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Subject-specific observed profiles of change from baseline vs week trt=10000u diff week Subject-specific observed profiles of change from baseline vs week trt=5000u diff week
2 Subject-specific observed profiles of change from baseline vs week trt=placebo diff week Raw Data: Change scores vs Age diff age
3 diff Boxplots of raw data (change scores) by gender F sex M
4 Model M1: Full model 2 Unspecified var-cov structure Model Information Data Set Dependent Variable Covariance Structures Subject Effects Estimation Method Residual Variance Method Fixed Effects SE Method Degrees of Freedom Method WORK.THREE diff Variance Components, Unstructured site, id(site) REML None Kenward-Roger Kenward-Roger Class Level Information Class Levels Values id trt U 5000U Placebo site sex 2 F M week measocc Dimensions Covariance Parameters 16 Columns in X 98 Columns in Z Per Subject 1 Subjects 9 Max Obs Per Subject 95 Number of Observations Number of Observations Read 545 Number of Observations Used 522 Number of Observations Not Used 23 Iteration History Iteration Evaluations -2 Res Log Like Criterion
5 Model M1: Full model 3 Unspecified var-cov structure Convergence criteria met. Estimated R Matrix for id(site) 1 1 Row Col1 Col2 Col3 Col4 Col Estimated R Correlation Matrix for id(site) 1 1 Row Col1 Col2 Col3 Col4 Col Covariance Parameter Estimates Z Cov Parm Subject Estimate Error Value Pr Z Intercept site UN(1,1) id(site) <.0001 UN(2,1) id(site) <.0001 UN(2,2) id(site) <.0001 UN(3,1) id(site) UN(3,2) id(site) <.0001 UN(3,3) id(site) <.0001 UN(4,1) id(site) UN(4,2) id(site) UN(4,3) id(site) <.0001 UN(4,4) id(site) <.0001 UN(5,1) id(site) UN(5,2) id(site) UN(5,3) id(site) UN(5,4) id(site) <.0001 UN(5,5) id(site) <.0001
6 Model M1: Full model 4 Unspecified var-cov structure Fit Statistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) agec sex agec*sex trt agec*trt week <.0001 agec*week trt*week agec*trt*week trt*sex sex*week trt*sex*week Least Squares Means Effect trt week Estimate Error DF t Value Pr > t trt 10000U <.0001 trt 5000U <.0001 trt Placebo week <.0001 week <.0001 week <.0001 week week trt*week 10000U <.0001 trt*week 10000U <.0001 trt*week 10000U <.0001 trt*week 10000U trt*week 10000U trt*week 5000U <.0001 trt*week 5000U <.0001 trt*week 5000U <.0001 trt*week 5000U trt*week 5000U trt*week Placebo
7 Model M1: Full model 5 Unspecified var-cov structure Least Squares Means Effect trt week Estimate Error DF t Value Pr > t trt*week Placebo trt*week Placebo trt*week Placebo trt*week Placebo Group by time profile plots for model M1 Estimate week trt 10000U 5000U Placebo
8 AIC values for variants of model M1 with a variety of var-cov structures 6 Obs Descr Value 1 AIC (smaller is better) AIC (smaller is better) AIC (smaller is better) AIC (smaller is better) AIC (smaller is better) AIC (smaller is better) AIC (smaller is better) AIC (smaller is better) AIC (smaller is better) AIC (smaller is better) AIC (smaller is better) AIC (smaller is better) AIC (smaller is better)
9 M4 is best among models considered so far 7 Convergence criteria met. Covariance Parameter Estimates Z Cov Parm Subject Estimate Error Value Pr Z Intercept site 4.53E AR(1) id(site) <.0001 Residual <.0001 Fit Statistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) age sex age*sex trt age*trt week age*week trt*week age*trt*week trt*sex sex*week trt*sex*week
10 M4a: same as M4 without site effect 8 Convergence criteria met. Covariance Parameter Estimates Z Cov Parm Subject Estimate Error Value Pr Z AR(1) id(site) <.0001 Residual <.0001 Fit Statistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) age sex age*sex trt age*trt week age*week trt*week age*trt*week trt*sex sex*week trt*sex*week
11 Model M4b has ar(1) residual var-cov matrix with trt-specific parameters 9 Convergence criteria met. Estimated R Matrix for id(site) 1 1 Row Col1 Col2 Col3 Col4 Col Estimated R Correlation Matrix for id(site) 1 1 Row Col1 Col2 Col3 Col4 Col Estimated R Matrix for id(site) 2 1 Row Col1 Col2 Col3 Col4 Col Estimated R Correlation Matrix for id(site) 2 1 Row Col1 Col2 Col3 Col4 Col
12 Model M4b has ar(1) residual var-cov matrix with trt-specific parameters 10 Estimated R Matrix for id(site) 8 1 Row Col1 Col2 Col3 Col4 Col Estimated R Correlation Matrix for id(site) 8 1 Row Col1 Col2 Col3 Col4 Col Covariance Parameter Estimates Z Cov Parm Subject Group Estimate Error Value Pr Z Variance id(site) trt 10000U <.0001 AR(1) id(site) trt 10000U <.0001 Variance id(site) trt 5000U <.0001 AR(1) id(site) trt 5000U <.0001 Variance id(site) trt Placebo <.0001 AR(1) id(site) trt Placebo <.0001 Fit Statistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) age sex age*sex trt
13 Model M4b has ar(1) residual var-cov matrix with trt-specific parameters 11 age*trt week age*week trt*week age*trt*week trt*sex sex*week trt*sex*week
14 Model M4c has AR(1) residual var-cov matrix with sex-specific parameters 12 Convergence criteria met. Estimated R Matrix for id(site) 1 1 Row Col1 Col2 Col3 Col4 Col Estimated R Correlation Matrix for id(site) 1 1 Row Col1 Col2 Col3 Col4 Col Estimated R Matrix for id(site) 7 1 Row Col1 Col2 Col3 Col4 Col Estimated R Correlation Matrix for id(site) 7 1 Row Col1 Col2 Col3 Col4 Col
15 Model M4c has AR(1) residual var-cov matrix with sex-specific parameters 13 Covariance Parameter Estimates Z Cov Parm Subject Group Estimate Error Value Pr Z Variance id(site) sex F <.0001 AR(1) id(site) sex F <.0001 Variance id(site) sex M <.0001 AR(1) id(site) sex M <.0001 Fit Statistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) age sex age*sex trt age*trt week age*week trt*week age*trt*week trt*sex sex*week trt*sex*week
16 Model M4b-9. Same as previous model but drop age 14 This is final model when week is a factor Convergence criteria met. Covariance Parameter Estimates Z Cov Parm Subject Group Estimate Error Value Pr Z Variance id(site) trt 10000U <.0001 AR(1) id(site) trt 10000U <.0001 Variance id(site) trt 5000U <.0001 AR(1) id(site) trt 5000U <.0001 Variance id(site) trt Placebo <.0001 AR(1) id(site) trt Placebo <.0001 Fit Statistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) trt week <.0001 trt*week Least Squares Means Effect trt week Estimate Error DF t Value Pr > t trt 10000U <.0001 trt 5000U <.0001 trt Placebo week <.0001 week <.0001 week <.0001 week week trt*week 10000U <.0001 trt*week 10000U <.0001 trt*week 10000U <.0001 trt*week 10000U
17 Model M4b-9. Same as previous model but drop age 15 This is final model when week is a factor Least Squares Means Effect trt week Estimate Error DF t Value Pr > t trt*week 10000U trt*week 5000U <.0001 trt*week 5000U <.0001 trt*week 5000U <.0001 trt*week 5000U trt*week 5000U trt*week Placebo trt*week Placebo trt*week Placebo trt*week Placebo trt*week Placebo Group by time profile plots for model M4b-9 Estimate week trt 10000U 5000U Placebo
18 Model M4b-9(ML). Model M4b-9 fit with ML estimation 16 Convergence criteria met. Covariance Parameter Estimates Z Cov Parm Subject Group Estimate Error Value Pr Z Variance id(site) trt 10000U <.0001 AR(1) id(site) trt 10000U <.0001 Variance id(site) trt 5000U <.0001 AR(1) id(site) trt 5000U <.0001 Variance id(site) trt Placebo <.0001 AR(1) id(site) trt Placebo <.0001 Fit Statistics -2 Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) trt week <.0001 trt*week
19 Model M5(ML). Same var-cov as m4b-9, but linear effect of time in each trt 17 Convergence criteria met. Covariance Parameter Estimates Z Cov Parm Subject Group Estimate Error Value Pr Z Variance id(site) trt 10000U <.0001 AR(1) id(site) trt 10000U <.0001 Variance id(site) trt 5000U <.0001 AR(1) id(site) trt 5000U <.0001 Variance id(site) trt Placebo <.0001 AR(1) id(site) trt Placebo <.0001 Fit Statistics -2 Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Solution for Fixed Effects Effect trt Estimate Error DF t Value Pr > t Intercept trt 10000U <.0001 trt 5000U trt Placebo week week*trt 10000U week*trt 5000U week*trt Placebo trt week <.0001 week*trt
20 Model M5. Refit model M5 with REML and test hypotheses 18 Convergence criteria met. Covariance Parameter Estimates Z Cov Parm Subject Group Estimate Error Value Pr Z Variance id(site) trt 10000U <.0001 AR(1) id(site) trt 10000U <.0001 Variance id(site) trt 5000U <.0001 AR(1) id(site) trt 5000U <.0001 Variance id(site) trt Placebo <.0001 AR(1) id(site) trt Placebo <.0001 Fit Statistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Solution for Fixed Effects Effect trt Estimate Error DF t Value Pr > t Intercept trt 10000U <.0001 trt 5000U trt Placebo week week*trt 10000U week*trt 5000U week*trt Placebo trt week <.0001 week*trt
21 Model M5. Refit model M5 with REML and test hypotheses 19 Convergence criteria met. Covariance Parameter Estimates Z Cov Parm Subject Group Estimate Error Value Pr Z Variance id(site) trt 10000U <.0001 AR(1) id(site) trt 10000U <.0001 Variance id(site) trt 5000U <.0001 AR(1) id(site) trt 5000U <.0001 Variance id(site) trt Placebo <.0001 AR(1) id(site) trt Placebo <.0001 Fit Statistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Solution for Fixed Effects Effect trt Estimate Error DF t Value Pr > t Intercept trt 10000U <.0001 trt 5000U trt Placebo week week2*trt 10000U week2*trt 5000U week2*trt Placebo trt week <.0001 week2*trt
22 Model M5. Refit model M5 with REML and test hypotheses 20 Least Squares Means Effect trt week2 Estimate Error DF t Value Pr > t trt 10000U <.0001 trt 5000U <.0001 trt Placebo Differences of Least Squares Means Effect trt _trt week2 Estimate Error DF t Value Pr > t Adjustment trt 10000U Placebo <.0001 Dunnett trt 5000U Placebo Dunnett Differences of Least Squares Means Effect trt _trt Adj P trt 10000U Placebo trt 5000U Placebo
23 Model M5. Refit model M5 with REML and test hypotheses 21 Convergence criteria met. Covariance Parameter Estimates Z Cov Parm Subject Group Estimate Error Value Pr Z Variance id(site) trt 10000U <.0001 AR(1) id(site) trt 10000U <.0001 Variance id(site) trt 5000U <.0001 AR(1) id(site) trt 5000U <.0001 Variance id(site) trt Placebo <.0001 AR(1) id(site) trt Placebo <.0001 Fit Statistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Solution for Fixed Effects Effect trt Estimate Error DF t Value Pr > t Intercept trt 10000U trt 5000U trt Placebo week week16*trt 10000U week16*trt 5000U week16*trt Placebo trt week <.0001 week16*trt
24 Model M5. Refit model M5 with REML and test hypotheses 22 Least Squares Means Effect trt week16 Estimate Error DF t Value Pr > t trt 10000U trt 5000U trt Placebo Differences of Least Squares Means Effect trt _trt week16 Estimate Error DF t Value Pr > t Adjustment trt 10000U Placebo Dunnett trt 5000U Placebo Dunnett Differences of Least Squares Means Effect trt _trt Adj P trt 10000U Placebo trt 5000U Placebo
25 Model M5a. Refit model M5 but add site effect and test 23 Convergence criteria met. Covariance Parameter Estimates Z Cov Parm Subject Group Estimate Error Value Pr Z Intercept site 0... Variance id(site) trt 10000U <.0001 AR(1) id(site) trt 10000U <.0001 Variance id(site) trt 5000U <.0001 AR(1) id(site) trt 5000U <.0001 Variance id(site) trt Placebo <.0001 AR(1) id(site) trt Placebo <.0001 Fit Statistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) trt week <.0001 week*trt
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