lambda_z estimation [🇷 for BE/BA]

posted by yjlee168 Homepage – Kaohsiung, Taiwan, 2008-09-29 15:32 (5686 d 12:54 ago) – Posting: # 2437
Views: 55,748

Dear Ace,

This is my second post replied to your previous post. In my first replied message, I said that the three examples (Ex. 01-03) that we tested before were all matched the data points picked by WinNonlin (WNL). Then we go further to test three more examples (Ex. 04-06) and we find that both your method and WNL may pick (Tmax, Cmax) to estimate lambdaz with Ex. 04 and Ex. 06. Please see the following results.

Ace -Ex. 04
b<-c(0,0.25,0.5,0.75,1,1.5,2,3,4,8,12,24)
c<-c(0,30.1,211,1221,1485,1837,1615,1621,1411,763,424,109)
dat <- data.frame(time=b,conc=c)
...truncated here (due to limited characters; plz see previous posts)
Call:
lm(formula = log(conc) ~ time, data = dat[(nrow(dat) - n_lambda +
    1):nrow(dat), ])

Residuals:
       6        7        8        9       10       11       12
0.01135 -0.05373  0.07742  0.06613 -0.03889 -0.11662  0.05434

Coefficients:
             Estimate Std. Error t value Pr(>|t|)   
(Intercept)  7.695712   0.043288  177.78 1.07e-10 ***
time        -0.127446   0.004011  -31.77 5.80e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.07931 on 5 degrees of freedom
Multiple R-squared: 0.9951,     Adjusted R-squared: 0.9941
F-statistic:  1010 on 1 and 5 DF,  p-value: 5.8e-07

WNL - Ex. 04
...truncated here

Summary Table
-------------
      Time         Conc.      Pred.    Residual      AUC       AUMC      Weight
-------------------------------------------------------------------------------
     0.0000       0.0000                           0.0000     0.0000
     0.2500        30.10                            3.763     0.9406
     0.5000        211.0                            33.90      15.07
     0.7500        1221.                            212.9      142.7
      1.000        1485.                            551.2      442.8
      1.500 *      1837.      1816.      20.72      1382.      1503.      1.000
      2.000 *      1615.      1704.     -89.15      2245.      2999.      1.000
      3.000 *      1621.      1500.      120.8      3863.      7046.      1.000
      4.000 *      1411.      1321.      90.29      5379. 1.230e+004      1.000
      8.000 *      763.0      793.3     -30.25      9727. 3.580e+004      1.000
      12.00 *      424.0      476.4     -52.45 1.210e+004 5.818e+004      1.000
      24.00 *      109.0      103.2      5.765 1.530e+004 1.044e+005      1.000


*) Starred values were included in the estimation of Lambda_z.
...truncated here

Ace - Ex.05
b<-c(0,0.5,0.75,1,1.5,2,3,4,8,12,24)
c<-c(0,38.2,277,631,1002,1780,1776,1618,782,466,89.7)
... truncated here ...

Residuals:
        9        10        11
-0.010928  0.014570 -0.003643

Coefficients:
             Estimate Std. Error t value Pr(>|t|)   
(Intercept)  7.759117   0.025498   304.3  0.00209 **
time        -0.135792   0.001577   -86.1  0.00739 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

... truncated here

WNL - Ex. 05
[code]... truncated here
Summary Table
-------------
      Time         Conc.      Pred.    Residual      AUC       AUMC      Weight
-------------------------------------------------------------------------------
     0.0000       0.0000                           0.0000     0.0000
     0.5000        38.20                            9.550      4.775
     0.7500        277.0                            48.95      33.13
      1.000        631.0                            162.5      138.0
      1.500        1002.                            570.7      671.5
      2.000        1780.                            1266.      1937.
      3.000        1776.                            3044.      6381.
      4.000        1618.                            4741. 1.228e+004
      8.000 *      782.0      790.6     -8.592      9541. 3.774e+004      1.000
      12.00 *      466.0      459.3      6.741 1.204e+004 6.143e+004      1.000
      24.00 *      89.70      90.03    -0.3273 1.537e+004 1.079e+005      1.000
...truncated here

Ace - Ex. 06
b<-c(0,0.25,0.5,0.75,1,1.5,2,3,4,8,12,24)
c<-c(0,32.8,181,271,402,783,2073,1842,1610,883,389,75.8)
...truncated here
Call:
lm(formula = log(conc) ~ time, data = dat[(nrow(dat) - n_lambda +
    1):nrow(dat), ])

Residuals:
       7        8        9       10       11       12
-0.01308  0.02206  0.04072  0.05320 -0.15341  0.05052

Coefficients:
             Estimate Std. Error t value Pr(>|t|)   
(Intercept)  7.956404   0.055392  143.64 1.41e-08 ***
time        -0.153284   0.004759  -32.21 5.54e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.08836 on 4 degrees of freedom
Multiple R-squared: 0.9962,     Adjusted R-squared: 0.9952
F-statistic:  1038 on 1 and 4 DF,  p-value: 5.537e-06

WNL - Ex. 06
...truncated here

Summary Table
-------------
      Time         Conc.      Pred.    Residual      AUC       AUMC      Weight
-------------------------------------------------------------------------------
     0.0000       0.0000                           0.0000     0.0000
     0.2500        32.80                            4.100      1.025
     0.5000        181.0                            30.83      13.36
     0.7500        271.0                            87.33      50.08
      1.000        402.0                            171.5      125.7
      1.500        783.0                            467.7      519.9
      2.000 *      2073.      2100.     -27.30      1182.      1850.      1.000
      3.000 *      1842.      1802.      40.18      3139.      6686.      1.000
      4.000 *      1610.      1546.      64.25      4865. 1.267e+004      1.000
      8.000 *      883.0      837.3      45.74      9851. 3.968e+004      1.000
      12.00 *      389.0      453.5     -64.50 1.240e+004 6.314e+004      1.000
      24.00 *      75.80      72.07      3.734 1.518e+004 1.021e+005      1.000

*) Starred values were included in the estimation of Lambda_z.
... truncated here

Looks like that your method and WNL are quite consistent in data point selection for estimation of lambdaz now. Question is that both methods still cannot absolutely rule out the data point of Cmax (e.g. Ex 04 and Ex. 06).
—
All the best,
-- Yung-jin Lee
bear v2.9.1:- created by Hsin-ya Lee & Yung-jin Lee
Kaohsiung, Taiwan https://www.pkpd168.com/bear
Download link (updated) -> here
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