PK1 - One-compartment iv bolus dosing

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pk1.csv

### read the dataset
> pk1<-read.csv("C:/data/pk1.csv")

### conc-time profile

> coplot(conc~time|factor(subject), data=pk1)

### subject 1

   subject time conc
1        1   10  920
2        1   20  800
3        1   30  750
4        1   40  630
5        1   50  610
6        1   60  530
7        1   70  520
8        1   90  380
9        1  110  350
10       1  150  200

### estimate inital values with linear regression with log-transformation

> lm.beta<-coef(lm(log(conc)~time, data=pk1, subset=subject==1))
> lm.beta
(Intercept)        time
 6.91891347 -0.01044090

## conc = C0 * exp(-K*time)
> beta0<-c(exp(lm.beta[1]),-lm.beta[2])
> out1<-nls(conc~C0*exp(-K*time), data=pk1, start=list(C0=beta0[1],K=beta0[2]), subset=subject==1)

> summary(out1)

Formula: conc ~ C0 * exp(-K * time)

Parameters:
    Estimate Std. Error t value Pr(>|t|)   
C0 1.002e+03  2.059e+01   48.68 3.51e-11 ***
K  1.026e-02  4.329e-04   23.69 1.07e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 23.26 on 8 degrees of freedom

Number of iterations to convergence: 2
Achieved convergence tolerance: 6.187e-08

## conc = X0/V * exp(-K*time)

> beta0<-c(exp(lm.beta[1])/10000 ,-lm.beta[2])
> out2<-nls(conc~10000/V*exp(-K*time), data=pk1, start=list(V=beta0[1],K=beta0[2]), subset=subject==1)

> summary(out2)

Formula: conc ~ 10000/V * exp(-K * time)

Parameters:
   Estimate Std. Error t value Pr(>|t|)   
V 9.9784334  0.2049941   48.68 3.51e-11 ***
K 0.0102561  0.0004329   23.69 1.07e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 23.26 on 8 degrees of freedom

Number of iterations to convergence: 11
Achieved convergence tolerance: 2.810e-08

## conc = X0/V * exp(-Cl/V*time)

> beta0<-c(10000/exp(lm.beta[1]) ,-10000*lm.beta[2]/exp(lm.beta[1]))
> out3<-nls(conc~10000/V*exp(-Cl/V*time), data=pk1, start=list(V=beta0[1],Cl=beta0[2]), subset=subject==1)

> summary(out3)

Formula: conc ~ 10000/V * exp(-Cl/V * time)

Parameters:
   Estimate Std. Error t value Pr(>|t|)   
V  9.978433   0.204994   48.68 3.51e-11 ***
Cl 0.102340   0.002902   35.26 4.58e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 23.26 on 8 degrees of freedom

Number of iterations to convergence: 2
Achieved convergence tolerance: 1.464e-06