Bioequivalence and Bioavailability Forum

lme() answer and beyond ... [General Statistics]

posted by d_labes – Berlin, Germany, 2010-07-14 12:41 (5815 d 20:00 ago) – Posting: # 5621
Views: 16,984

Dear Helmut!

❝ OK, I end up after 7 iterations at:

❝ -2* REML log(likelihood) 251.724

❝ Same result if use the default convergence criterion (10^-10),

❝ yours ((10^-8), or approach numeric resolution.

Here the results using R's lme().
Code used:

model2 <- lme(log(Cmax) ~ tmt + period + sequence,

              random=list(subject=pdSymm(form= ~tmt-1)),

              weights=varIdent(form = ~ 1 | tmt), 

              data=PKparms, method="REML", na.action=na.omit) 

summary(model2)

Answer:

Linear mixed-effects model fit by REML

 Data: PKparms 

      AIC     BIC   logLik

  291.654 320.096 -135.827  # -2*LL = 271.654! Seems WNL computes different. 



Random effects:

 Formula: ~tmt - 1 | subject

 Structure: General positive-definite

         StdDev   Corr 

tmtR     0.574772 tmtR 

tmtT     0.705001 0.642

Residual 0.431758           # s2=0.186415



Variance function:

 Structure: Different standard deviations per stratum

 Formula: ~1 | tmt 

 Parameter estimates:

       R        T 

1.000000 0.993312           # very interesting: variability of T lower then R.



Fixed effects: log(Cmax) ~ tmt + period + sequence 

               Value Std.Error DF  t-value p-value

(Intercept)  5.60475 0.1867666 86 30.00937  0.0000

tmtT        -0.14753 0.1153259 86 -1.27927  0.2042

period       0.08578 0.0534769 86  1.60402  0.1124

sequenceRTR  0.17906 0.2209845 41  0.81027  0.4225

sequenceTRR -0.28646 0.2297086 41 -1.24704  0.2195

Ok the random effects parameters can't directly compared, only via th G matrix.


getVarCov(model2)

Random effects variance covariance matrix

        tmtR    tmtT

tmtR 0.33036 0.26032          # SAS: 0.3313  0.2581

tmtT 0.26032 0.49703          #      0.2581  0.3596



intervals(model2,which="var-cov",level=0.95)

Error in intervals.lme(model2, which = "var-cov", level = 0.95) : 

  Cannot get confidence intervals on var-cov components: Non-positive

  definite approximate variance-covariance

Seems that the difference in intra-subject variability is absorbed by the G matrix, with no loss in the fit (nearly identical -2*LL).

Quintessence for scABE using the EMA approach:


                                              -- Widened (EMA)

             ----- 90% CIs -----              acceptance range --

           point est.  lower  upper     s²_WR    lower   upper

FDA (MoM)   0.8746    0.7216  1.0605  0.14332   0.7500  1.3334

SAS (FDA)   0.8632    0.7037  1.0498  0.1862    0.7204  1.3881

WNL             ?                     0.18616   0.7204  1.3881

lme()       0.8628    0.7123  1.0452  0.18642   0.7203  1.3884

Confusion

: scABE not proven.

Astonishing enough the 95% upper confidence interval of the linearized scABE criterion
(µ_T-µ_R)²-theta²*sigma²_WR = -0.03751
is negative if theta=0.76 (EMA and recommended by Tothfalusi et.al.) and the MOM terms are used, if I calculated right. And this would indicate scABE proven.

Tothfalusi et.al.
Evaluation of Bioequivalence for Highly Variable Drugs with Scaled Average Bioequivalence
Clin. Pharmacokinet. 2009; 48 (11): 725-743

—
Regards,

Detlew

Complete thread:

SABE Reference Variability and CI Computation preyes323 2010-07-12 17:12 [General Statistics]
- Dataset Helmut 2010-07-12 17:26
  - Dataset preyes323 2010-07-12 18:20
    - Data format Helmut 2010-07-12 18:38
      - Data format preyes323 2010-07-13 01:16
        
        SAS and/or Phoenix/WinNonlin-experts around? Helmut 2010-07-13 02:29
        
        Phoenix/WinNonlin-experts around? d_labes 2010-07-13 12:15
        
        Phoenix/WinNonlin-experts around? Helmut 2010-07-13 13:42
        
        Mixed interest d_labes 2010-07-13 15:11
        
        Mixed interest Helmut 2010-07-13 19:19
        
        lme() answer and beyond ...d_labes 2010-07-14 10:41
        
        lme() answer and beyond ... Helmut 2010-07-14 13:47
        
        AIC, BIC and that all ... d_labes 2010-07-15 12:01
        
        To Err is Human d_labes 2010-07-13 11:51
        
        To Err is Human, but... Helmut 2010-07-13 13:45
        
        ... to Arr is Pirate d_labes 2010-07-13 15:47
        
        Brilliant page!!! ElMaestro 2010-07-14 21:03
        
        To Err is Human preyes323 2010-07-14 14:45
        
        Heads up! Helmut 2010-07-14 15:17
        To Err is Teacher d_labes 2010-07-15 11:05
        
        To Err is Human preyes323 2010-07-16 02:28
        
        To Err is Human d_labes 2010-07-16 10:42
        
        To Err is Human preyes323 2010-07-17 11:14
        
        Regulatory constants d_labes 2010-07-19 10:00
        
        Data format ElMaestro 2011-02-06 11:54
        
        SAS System Viewer Helmut 2011-02-06 13:02

lme() answer and beyond ... [General Sta­tis­tics]

Complete thread:

lme() answer and beyond ... [General Statistics]