lambda_z estimation [🇷 for BE/BA]

posted by yjlee168 Homepage – Kaohsiung, Taiwan, 2008-09-23 14:13 (6113 d 20:17 ago) – Posting: # 2387
Views: 72,796

Dear Ace,

We've tried to implement your methods (codes) into bear now. But we find that the difference between your method and WinNonlin. Here is your method as R code:
b<-c(0,0.25,0.5,0.75,1,1.5,2,3,4,8,12,24)
c<-c(0,36.1,125,567,963,1343,1739,1604,1460,797,383,72)
dat <- data.frame(time=b,conc=c)
n_lambda=1
r.adj=0

for (i in (nrow(dat)-3):which.max(dat$conc)) {
if (r.adj - round(summary(lm(log(conc)~time,dat[i:nrow(dat),]))$adj.r.squared,4) <
(0.0001)) {
n_lambda <- nrow(dat)-i+1
r.adj <- summary(lm(log(conc)~time,dat[i:nrow(dat),]))$adj.r.squared
 }
}

And we got

Call:
lm(formula = log(conc) ~ time, data = dat[i:nrow(dat), ])

Residuals:
        7         8         9        10        11        12
-0.057481  0.009958  0.064143  0.051802 -0.088021  0.019598

Coefficients:
             Estimate Std. Error t value Pr(>|t|)   
(Intercept)  7.815044   0.042438  184.15 5.22e-09 ***
time        -0.148249   0.003646  -40.66 2.19e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.0677 on 4 degrees of freedom
Multiple R-squared: 0.9976,     Adjusted R-squared: 0.997
F-statistic:  1654 on 1 and 4 DF,  p-value: 2.186e-06

Your method picked 6 data points for this example. However, WinNonlin
picked 5 data points as follows:

Model:  Plasma Data, Extravascular Administration
Number of nonmissing observations:   12
Dose time:      0.00
Dose amount:    80000.00
Calculation method:  Linear Trapezoidal with Linear/Log Interpolation
Weighting for lambda_z calculations:  Uniform weighting
Lambda_z method:  Find best fit for lambda_z,  Log regression


Summary Table
-------------
      Time         Conc.      Pred.    Residual      AUC       AUMC      Weight
-------------------------------------------------------------------------------
     0.0000       0.0000                           0.0000     0.0000
     0.2500        36.10                            4.513      1.128
     0.5000        125.0                            24.65      10.07
     0.7500        567.0                            111.2      71.04
      1.000        932.0                            298.5      240.7
      1.500        1343.                            867.3      977.3
      2.000        1739.                            1638.      2350.
      3.000 *      1604.      1625.     -21.46      3309.      6495.      1.000
      4.000 *      1460.      1399.      60.79      4841. 1.182e+004      1.000
      8.000 *      797.0      768.3      28.73      9355. 3.625e+004      1.000
      12.00 *      383.0      421.8     -38.84 1.172e+004 5.820e+004      1.000
      24.00 *      72.00      69.83      2.172 1.445e+004 9.614e+004      1.000


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


Final Parameters
---------------
Rsq                                                       0.9979
Rsq_adjusted                                              0.9972
Corr_XY                                                  -0.9990
No_points_lambda_z                                        5
Lambda_z                                                  0.1499
Lambda_z_lower                                            3.0000
Lambda_z_upper                                           24.0000
HL_Lambda_z                                               4.6246
Tlag                                                      0.0000
Tmax                                                      2.0000
... (truncated after this line)


What are we missing here? Thanks.
—
All the best,
-- Yung-jin Lee
bear v2.9.2:- created by Hsin-ya Lee & Yung-jin Lee
Kaohsiung, Taiwan https://www.pkpd168.com/bear
Download link (updated) -> here
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