Bioequivalence and Bioavailability Forum

Dear HS, d_labes and ElMaestro,

Thank all of you for your great discussion on LSM comparison between WNL and SAS. The concept of "real mixed effects" in WNL or SAS is key factor that leads to different SE, and thus 90%CI for LSM.

Now let me go on with the story of Proc GLM and Proc Mixed in SAS.
Let me begin the story with my test results in SAS.

All tests are performed using untransformed data.

----GLM 1 and GLM 2----Start--------------------------------------------------------
proc glm data=dose_equivalence;
class subject sequence period formulation;
model AUC=sequence subject(sequence) period formulation;
random subject(sequence) / test;
lsmeans formulation/stderr pdiff cl alpha=0.1;
run;
quit;

proc glm data=dose_equivalence;
class subject sequence period formulation;
model AUC=sequence subject(sequence) period formulation;
lsmeans formulation/stderr pdiff cl alpha=0.1;
run;
quit;
                                  The GLM Procedure

                                 Least Squares Means

                                                                    H0:LSMean1=
                                         Standard    H0:LSMEAN=0      LSMean2
      formulation      AUC LSMEAN           Error       Pr > |t|       Pr > |t|
      1                235.152143        7.344914         <.0001         0.7564
      2                231.866667        7.344914         <.0001


      formulation      AUC LSMEAN      90% Confidence Limits
      1                235.152143     222.215471   248.088815
      2                231.866667     218.929995   244.803339


                     Least Squares Means for Effect formulation

                             Difference
                                Between    90% Confidence Limits for
                 i    j           Means       LSMean(i)-LSMean(j)
                 1    2        3.285476      -15.009741    21.580693
----GLM 1 and GLM 2---End---------------------------------------------------------

----GLM 3 and GLM 4----Start--------------------------------------------------------
proc glm data=dose_equivalence;
class subject sequence period formulation;
model AUC=sequence period formulation;
random subject(sequence) / test;
lsmeans formulation/stderr pdiff cl alpha=0.1;
run;
quit;

proc glm data=dose_equivalence;
class subject sequence period formulation;
model AUC=sequence period formulation;
lsmeans formulation/stderr pdiff cl alpha=0.1;
run;
quit;
                                  The GLM Procedure
                                 Least Squares Means

                                                                    H0:LSMean1=
                                         Standard    H0:LSMEAN=0      LSMean2
      formulation      AUC LSMEAN           Error       Pr > |t|       Pr > |t|
      1                235.152143       12.746266         <.0001         0.8567
      2                231.866667       12.746266         <.0001


      formulation      AUC LSMEAN      90% Confidence Limits
      1                235.152143     213.469076   256.835210
      2                231.866667     210.183600   253.549734


                      Least Squares Means for Effect formulation

                             Difference
                                Between    90% Confidence Limits for
                 i    j           Means       LSMean(i)-LSMean(j)
                 1    2        3.285476      -27.379011    33.949964
----GLM 3 and GLM 4---End---------------------------------------------------------

----Mixed 1--Start------------------------------------------------------------------------

proc mixed data=dose_equivalence;
class subject sequence period formulation;
model AUC=sequence subject(sequence) period formulation;
random subject(sequence) / subject=subject;
lsmeans formulation/cl diff alpha=0.1;
run;
quit;

                                 The Mixed Procedure

                                 Least Squares Means
                  Effect         formulation       Lower       Upper

                  formulation    1                222.22      248.09
                  formulation    2                218.93      244.80


                         Differences of Least Squares Means

                                               Standard
Effect      formulation _formulation Estimate    Error DF t Value Pr > |t| Alpha
formulation 1           2              3.2855  10.3873 14   0.32   0.7564    0.1

                          Differences of Least Squares Means

             Effect       formulation  _formulation     Lower       Upper
             formulation  1            2             -15.0097     21.5807

----Mixed 1--End------------------------------------------------------------------------