Liu ANOVA PtC [RSABE / ABEL]

posted by d_labes  – Berlin, Germany, 2010-03-11 12:07 (5131 d 11:34 ago) – Posting: # 4894
Views: 24,103

Dear Helmut, dear All,

Meanwhile I have experimented a little bit with the ANOVA described in the Liu paper. I have taken Example 4.4 from the book

Patterson, Jones
"BIOEQUIVALENCE and STATISTICS in CLINICAL PHARMACOLOGY"
Chapman & Hall / CRC 2006

a 4-period study with the sequences TRTR and RTRT as the dataset (to be found here).
[edit: /CRC WEB PAGE/chapter4/exam44.dat (Helmut)]

The subjects with missing data were left out from the analyses.

It took me some headache (and some beer :-D) to figure out how to formulate a Proc GLM ANOVA with the effects sequence, subject (within sequence), formulation, period and subject-by-formulation interaction. "Simple" attempts catched me often in the Type III sum-of-squares trap.

Here comes the code that worked without curiosities:
Proc GLM data=four;
  class sequence subject period formula;
  model ln_AUC = sequence subject(sequence) formula period
                 subject(sequence*formula) / CLparm alpha=0.1;
  random subject(sequence) subject(sequence*formula) /Test;
  Estimate 'T-R' formula -1 1;
*without subjects with missings;
 where subject not in(3 27);
quit;


The random statement is only for letting SAS figure out the "appropriate" F-tests for the effects, because we all know meanwhile that Proc GLM is fitting the model as if all effects are fixed and the random statement only affects the F-tests, which in an all-fixed model always have MS(error) as denominator.

Results:
...
                             The GLM Procedure

Dependent Variable: ln_auc

                                   Sum of
 Source                  DF       Squares   Mean Square  F Value  Pr > F

 Model                  105   55.42179511    0.52782662     5.33  <.0001
 Error                  102   10.10810776    0.09909910
 Corrected Total        207   65.52990287

           R-Square     Coeff Var      Root MSE    ln_auc Mean
           0.845748      5.349792      0.314800       5.884343

*-----------------------------------------------------------------------
the all effects fixed part;

 Source                    DF     Type I SS   Mean Square  F Value  Pr > F

 sequence                   1    0.17364001    0.17364001     1.75  0.1886
 subject(sequence)         50   49.37630741    0.98752615     9.97  <.0001
 formula                    1    0.56857602    0.56857602     5.74  0.0184
 period                     3    0.30656009    0.10218670     1.03  0.3821
 subje(sequen*formul)      50    4.99671158    0.09993423     1.01  0.4752


 Source                    DF   Type III SS   Mean Square  F Value  Pr > F

 sequence                   1    0.17364001    0.17364001     1.75  0.1886
 subject(sequence)         50   49.37630741    0.98752615     9.97  <.0001
 formula                    1    0.56857602    0.56857602     5.74  0.0184
 period                     2    0.27974027    0.13987013     1.41  0.2485
 subje(sequen*formul)      50    4.99671158    0.09993423     1.01  0.4752

*-----------------------------------------------------------------------
expected mean square from the MIXED model;

Source                Type III Expected Mean Square

sequence              Var(Error) + 2 Var(subje(sequen*formul)) +
                      4 Var(subject(sequence)) + Q(sequence)

subject(sequence)     Var(Error) + 2 Var(subje(sequen*formul)) +
                      4 Var(subject(sequence))

formula               Var(Error) + 2 Var(subje(sequen*formul)) + Q(formula)

period                Var(Error) + Q(period)

subje(sequen*formul)  Var(Error) + 2 Var(subje(sequen*formul))

*----------------------------------------------------------------------
appropriate (for the MIXED model) F-tests;

         Tests of Hypotheses for Mixed Model Analysis of Variance

Dependent Variable: ln_auc

 Source                    DF   Type III SS   Mean Square  F Value  Pr > F

 sequence                   1      0.173640      0.173640     0.18  0.6768
 Error                     50     49.376307      0.987526
 Error: MS(subject(sequence))

 subject(sequence)         50     49.376307      0.987526     9.88  <.0001
 formula                    1      0.568576      0.568576     5.69  0.0209
 Error                     50      4.996712      0.099934
 Error: MS(subje(sequen*formul))

 period                     2      0.279740      0.139870     1.41  0.2485
 subje(sequen*formul)      50      4.996712      0.099934     1.01  0.4752
 Error: MS(Error)         102     10.108108      0.099099

*--------------------------------------------------------------
estimated treatment effect, 90% CIs in log domain

Parameter  Estimate       Error    t Value    Pr > |t| 90% Confidence Limits

T-R      0.10456651    0.04365492   2.40      0.0184   0.03210240   0.17703061
...


Some points to consider:
BTW: Excuse this very long post, but I had no idea how to shorten.
BTW2: The fixed effects story gets more and more curious for me.
BTW3: If this ANOVA would be sufficient for the EMA we had also in SAS to follow Helmut's SOP with the adaption "delete Mixed model" :-D.

Regards,

Detlew

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