Bioequivalence and Bioavailability Forum

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

posted by d_labes  – Berlin, Germany, 2010-07-14 12:41 (5420 d 17:51 ago) – Posting: # 5621
Views: 14,375

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     s2WR    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
(µT-µR)2-theta2*sigma2WR = -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

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