Repeated Measures Part 4: Blood Flow data

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Repeated Measures Part 4: Blood Flow data /* bloodflow.sas */ options linesize=79 pagesize=100 noovp formdlim='_'; title 'Two within-subjecs factors: Blood flow data (NWK p. 1181)'; proc format; value ynfmt 0 = 'No' 1 = 'Yes'; data blood; infile 'bloodflow.dat' firstobs=2; /* Skip the first line */ input row1 iflow1 patient1 DrugA1 DrugB1 row2 iflow2 patient2 DrugA2 DrugB2 row3 iflow3 patient3 DrugA3 DrugB3 row4 iflow4 patient4 DrugA4 DrugB4 ; format druga1-druga4 drugb1-drugb4 ynfmt.; proc means n mean stddev; var iflow1-iflow4; proc glm; title2 ''; model iflow1-iflow4 = ; /* No IV (just intercepts) */ repeated Drug_A 2, Drug_B 2 / short summary; /* Variable on the right changes fastest */ data uvblood; infile 'bloodflow.dat' firstobs=2; /* Skip the first line */ input row iflow patient DrugA DrugB; label iflow = 'Increase in Blood Flow'; format DrugA DrugB ynfmt.; proc mixed; title2 'Covariance Structure Approach with proc mixed'; class DrugA DrugB; model iflow = DrugA DrugB; repeated / type=un subject=patient r; Two within-subjecs factors: Blood flow data (NWK p. 1181) 1 The MEANS Procedure Variable N Mean Std Dev ---------------------------------------------- iflow1 12 0.5000000 2.1105794 iflow2 12 10.0000000 3.1908961 iflow3 12 8.5000000 2.0225996 iflow4 12 25.0000000 3.4377583 ---------------------------------------------- Page 1 of 8

Joint Effects of Drug A and Drug B on Increase in Blood Flow 30 25 20 Flow Increase 15 Drug A = No Drug A = Yes 10 5 0 No Drug B Yes

Two within-subjecs factors: Blood flow data (NWK p. 1181) 2 Number of observations 12 Two within-subjecs factors: Blood flow data (NWK p. 1181) 3 Dependent Variable: iflow1 Sum of Source DF Squares Mean Square F Value Pr > F Model 1 3.00000000 3.00000000 0.67 0.4293 Error 11 49.00000000 4.45454545 Uncorrected Total 12 52.00000000 R-Square Coeff Var Root MSE iflow1 Mean 0.000000 422.1159 2.110579 0.500000 Source DF Type I SS Mean Square F Value Pr > F Intercept 1 3.00000000 3.00000000 0.67 0.4293 Intercept 1 3.00000000 3.00000000 0.67 0.4293 Standard Parameter Estimate Error t Value Pr > t Intercept 0.5000000000 0.60927180 0.82 0.4293 Page 2 of 8

Two within-subjecs factors: Blood flow data (NWK p. 1181) 4 Dependent Variable: iflow2 Sum of Source DF Squares Mean Square F Value Pr > F Model 1 1200.000000 1200.000000 117.86 <.0001 Error 11 112.000000 10.181818 Uncorrected Total 12 1312.000000 R-Square Coeff Var Root MSE iflow2 Mean 0.000000 31.90896 3.190896 10.00000 Source DF Type I SS Mean Square F Value Pr > F Intercept 1 1200.000000 1200.000000 117.86 <.0001 Intercept 1 1200.000000 1200.000000 117.86 <.0001 Standard Parameter Estimate Error t Value Pr > t Intercept 10.00000000 0.92113237 10.86 <.0001 Two within-subjecs factors: Blood flow data (NWK p. 1181) 5 Dependent Variable: iflow3 Sum of Source DF Squares Mean Square F Value Pr > F Model 1 867.0000000 867.0000000 211.93 <.0001 Error 11 45.0000000 4.0909091 Page 3 of 8

Uncorrected Total 12 912.0000000 R-Square Coeff Var Root MSE iflow3 Mean 0.000000 23.79529 2.022600 8.500000 Source DF Type I SS Mean Square F Value Pr > F Intercept 1 867.0000000 867.0000000 211.93 <.0001 Intercept 1 867.0000000 867.0000000 211.93 <.0001 Standard Parameter Estimate Error t Value Pr > t Intercept 8.500000000 0.58387421 14.56 <.0001 Two within-subjecs factors: Blood flow data (NWK p. 1181) 6 Dependent Variable: iflow4 Sum of Source DF Squares Mean Square F Value Pr > F Model 1 7500.000000 7500.000000 634.62 <.0001 Error 11 130.000000 11.818182 Uncorrected Total 12 7630.000000 R-Square Coeff Var Root MSE iflow4 Mean 0.000000 13.75103 3.437758 25.00000 Source DF Type I SS Mean Square F Value Pr > F Intercept 1 7500.000000 7500.000000 634.62 <.0001 Intercept 1 7500.000000 7500.000000 634.62 <.0001 Page 4 of 8

Standard Parameter Estimate Error t Value Pr > t Intercept 25.00000000 0.99239533 25.19 <.0001 Two within-subjecs factors: Blood flow data (NWK p. 1181) 7 Repeated Measures Analysis of Variance Repeated Measures Level Information Dependent Variable iflow1 iflow2 iflow3 iflow4 Level of Drug_A 1 1 2 2 Level of Drug_B 1 2 1 2 Manova Test Criteria and Exact F Statistics for the Hypothesis of no Drug_A Effect H = Type III SSCP Matrix for Drug_A E = Error SSCP Matrix S=1 M=-0.5 N=4.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.01397950 775.87 1 11 <.0001 Pillai's Trace 0.98602050 775.87 1 11 <.0001 Hotelling-Lawley Trace 70.53333333 775.87 1 11 <.0001 Roy's Greatest Root 70.53333333 775.87 1 11 <.0001 Manova Test Criteria and Exact F Statistics for the Hypothesis of no Drug_B Effect H = Type III SSCP Matrix for Drug_B E = Error SSCP Matrix S=1 M=-0.5 N=4.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.02052644 524.89 1 11 <.0001 Pillai's Trace 0.97947356 524.89 1 11 <.0001 Hotelling-Lawley Trace 47.71764706 524.89 1 11 <.0001 Roy's Greatest Root 47.71764706 524.89 1 11 <.0001 Page 5 of 8

Manova Test Criteria and Exact F Statistics for the Hypothesis of no Drug_A*Drug_B Effect H = Type III SSCP Matrix for Drug_A*Drug_B E = Error SSCP Matrix S=1 M=-0.5 N=4.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.07836991 129.36 1 11 <.0001 Pillai's Trace 0.92163009 129.36 1 11 <.0001 Hotelling-Lawley Trace 11.76000000 129.36 1 11 <.0001 Roy's Greatest Root 11.76000000 129.36 1 11 <.0001 Two within-subjecs factors: Blood flow data (NWK p. 1181) 8 Repeated Measures Analysis of Variance Univariate Tests of Hypotheses for Within Subject Effects Drug_A 1 1587.000000 1587.000000 775.87 <.0001 Error(Drug_A) 11 22.500000 2.045455 Drug_B 1 2028.000000 2028.000000 524.89 <.0001 Error(Drug_B) 11 42.500000 3.863636 Drug_A*Drug_B 1 147.0000000 147.0000000 129.36 <.0001 Error(Drug_A*Drug_B) 11 12.5000000 1.1363636 Skip the analysis of contrast variables. Page 6 of 8

Two within-subjecs factors: Blood flow data (NWK p. 1181) 12 Covariance Structure Approach with proc mixed The Mixed Procedure Model Information Data Set Dependent Variable Covariance Structure Subject Effect Estimation Method Residual Variance Method Fixed Effects SE Method Degrees of Freedom Method WORK.UVBLOOD iflow Unstructured patient REML None Model-Based Between-Within Class Level Information Class Levels Values DrugA 2 No Yes DrugB 2 No Yes Dimensions Covariance Parameters 10 Columns in X 9 Columns in Z 0 Subjects 12 Max Obs Per Subject 4 Observations Used 48 Observations Not Used 0 Total Observations 48 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 224.25476467 1 1 179.84564795 0.00000000 Convergence criteria met. Estimated R Matrix for Subject 1 Row Col1 Col2 Col3 Col4 1 4.4545 4.0000 2.7273 4.0909 2 4.0000 10.1818 5.2727 9.3636 3 2.7273 5.2727 4.0909 6.2727 4 4.0909 9.3636 6.2727 11.8182 Page 7 of 8

Covariance Parameter Estimates Cov Parm Subject Estimate UN(1,1) patient 4.4545 UN(2,1) patient 4.0000 UN(2,2) patient 10.1818 UN(3,1) patient 2.7273 UN(3,2) patient 5.2727 UN(3,3) patient 4.0909 UN(4,1) patient 4.0909 UN(4,2) patient 9.3636 UN(4,3) patient 6.2727 UN(4,4) patient 11.8182 Fit Statistics -2 Res Log Likelihood 179.8 AIC (smaller is better) 199.8 AICC (smaller is better) 206.5 BIC (smaller is better) 204.7 Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 9 44.41 <.0001 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F DrugA 1 11 775.87 <.0001 DrugB 1 11 524.89 <.0001 DrugA*DrugB 1 11 129.36 <.0001 Page 8 of 8

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