Bioequivalence and Bioavailability Forum • Error tests between/within

Error tests between/within [Software]

posted by Helmut – Vienna, Austria, 2008-05-06 23:33 (6207 d 01:57 ago) – Posting: # 1826
Views: 23,601

Dear Eva & Ohlbe!

❝ Helmut, I will let you explain why subject(sequence) should be used as an error term ;-)

OK, sequences are a between subject effect and therefore need to be compared to the between subject residual error (or F=0.6105/0.2623=2.327). In other words we compare (the group of) subjects in sequence TR to (the group of) subjects in sequence RT.

If you compare the sequence against the within subject residual error (0.2481) you certainly will get a different – and wrong! – answer. Using the within subject residual actually overestimates the effect of sequence leading to a greater chance of concluding a sequence effect.

Since in my first post I showed identical results for SAS and WinNonlin, I would expect a coding issue in the SAS program you are using.
Results in WinNonlin-versions don't differ. Unfortunately it’s not possible to have different versions running on the same machine – I re-run ‘old’ evaluations everytime I update to a newer version – and did not get differences since v4.0.1 (3.3 and earlier versions used ANOVA instead of linear mixed effects modeling).

Just to be more comfortable about the results – a little roundup of your dataset:
WinNonlin5.2 (2007)

----------------------------------------------------------

Hypothesis       DF  SS        MS        F_stat    P_value

Sequence          1  0.61054   0.61054   2.32748   0.1780

Sequence*Subject  6  1.57391   0.262318  1.05726   0.4739

Treatment         1  0.536468  0.536468  2.1622    0.1918

Period            1  0.077422  0.077422  0.312045  0.5966

Error             6  1.48867   0.248112

Chow & Liu (2001) – coded in Excel

-------------------------------------------------------

Analysis of Variance                     

Source of variation df  SS      MS       F      P-value

Inter-subjects            

  Carry-over         1  0.6105  0.61054  2.327  0.17795

  Residuals          6  1.5739  0.26232  1.057  0.47392

Intra-subjects

  Direct drug        1  0.5365  0.53647  2.162  0.19184

  Period             1  0.0774  0.07742  0.312  0.59664

  Residuals          6  1.4887  0.24811

Total               15  4.2870

EquivTest/PK (2006)

------------------------------------------------

Analysis of variance table:

               df  SS      MS     F      P-Value

Inter-Subjects

  Carry-over    1  0.6105  0.6105 2.3274 0.1779

  Residuals     6  1.5739  0.2623 1.0572 0.4739

Intra-Subjects

  Drug          1  0.5364  0.5364 2.1622 0.1918

  Period        1  0.0774  0.0774 0.3120 0.5966

  Residuals     6  1.4886  0.2481

Total          15  4.2870

Ref [3] (2001) from this post; coded in R2.7.0 (2008)

-------------------------------------------------------

Error: subf

          Df  Sum Sq Mean Sq F value Pr(>F)

seqf       1 0.61054 0.61054  2.3275 0.1780

Residuals  6 1.57391 0.26232



Error: Within

          Df  Sum Sq Mean Sq F value Pr(>F)

treatment  1 0.53647 0.53647  2.1622 0.1918

Between    1 0.07742 0.07742  0.3120 0.5966

Residuals  6 1.48867 0.24811

NCSS (2001) (Cross-Over Analysis)

-----------------------------------------------

           Estimated  Standard  T Value  Prob

Parameter  Effect     Error     (DF=6)   Level

Treatment  0.3662     0.2491    1.4704   0.1918

Period     0.1391     0.2491    0.5586   0.5966

Carryover  0.7814     0.5122    1.5256   0.1780

Kinetica 4.4.1 (2007)

--------------------------------------------------------

SOURCE      D.F  SS        MS        F          p

Period        1  0.077422  0.077422  0.312045  0.5966 NS

Subject(Seq)  6  1.57391   0.262318  1.05726   0.4739 NS

Formulation   1  0.536468  0.536468  2.1622    0.1918 NS

Sequence      1  0.61054   0.61054   2.46074   0.1678 NS

Error         6  1.48867   0.248112

Total        15  4.28701

Besides your SAS code only Kinetica tests against the within-subject residual error; this a well known bug since v1.1 (‼) – and I would expect Thermo_Scientific never to correct it… :angry:

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Complete thread:

SAS vs. WinNonlin: different sequence effect results Eva 2008-05-06 14:04 [Software]
- SAS vs. WinNonlin: different sequence effect results Ohlbe 2008-05-06 15:56
- imbalanced design? Helmut 2008-05-06 16:13
  - Sample data & results Eva 2008-05-06 17:42
    - Error factor Ohlbe 2008-05-06 19:25
      - Error tests between/withinHelmut 2008-05-06 21:33
        
        Error tests between/within Helmut 2008-05-07 18:18
        The power to know d_labes 2008-05-08 11:16
        
        The power to know Helmut 2008-05-08 17:18
        
        The power to know d_labes 2008-05-09 09:35
        
        The power to know Nirali 2008-05-09 11:00
        
        The power to know d_labes 2008-05-16 08:54
        
        The power to know kevan 2009-05-25 15:46
        
        Bogus statement for 2,2,2-BE ElMaestro 2009-05-25 22:25
        
        Bogus? What? d_labes 2009-05-27 08:57
        
        Linear model on steroids ElMaestro 2009-05-28 19:12
        
        Fixed nowadays what? d_labes 2009-05-27 09:03
        
        Kinetica 5.0 bug Helmut 2008-12-31 16:42