Chapter 29 Weighting Data

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Bayesian Analysis

An Example of Bayesian Analysis using Boomer

Consider a drug which has been studies extensively. For future data analysis a one compartment model with first order elimination is considered suitable. Estimated population values (± standard deviation) for the elimination rate constant and the apparent volume of distribution were 0.085 ± 0.025 hr^-1 and 42 ± 17 L, respectively. Consider Figure 29.9.1 representing a simulation of concentrations after a 100 mg IV Bolus dose. Included on the figure are two potential data points from another subject.

Figure 29.9.1 Simulated Concentration Time Data with Two Data Points

Combining these data points with our prior information about the pharmacokinetic model and model parameters we can perform a Bayesian analysis of the data.

 Enter type# for parameter  1 (-5 to 51) 1
 Enter parameter name Dose
 Enter Dose value 100
 0) fixed, 1) adjustable, 2) single dependence
                    or 3) double dependence 0
 Enter component to receive dose 1
 Enter component for F-dependence ( 1 to - 1 or 0 for no dependence) 

 Input summary for Dose                 (type  1)

     Fixed value is    100.0    
     Dose/initial amount added to     1

 Enter 0 if happy with input, 1 if not, 2 to start over 

 Enter -3 to see choices, -1 or -4 (save model) to exit this section 
 Enter type# for parameter  2 (-5 to 51)  2
 Enter parameter name kel
 Enter kel value 0.085
 0) fixed, 1) adjustable, 2) single dependence
                    or 3) double dependence 1
 Enter lower limit 0
 Enter upper limit 1
 Enter mean parameter value 0.085
 Enter standard deviation 0.025
 Enter component to receive flux 0
 Enter component to lose flux 1

 Input summary for kel                  (type  2)

     Initial value   0.8500E-01 float between    0.000     and    1.000    
     Population mean   0.8500E-01 with std-dev   0.2500E-01
     Transfer from     1 to     0

 Enter 0 if happy with input, 1 if not, 2 to start over 

 Enter -3 to see choices, -1 or -4 (save model) to exit this section 
 Enter type# for parameter  3 (-5 to 51)  18
 Enter parameter name V
 Enter V value 42
 0) fixed, 1) adjustable, 2) single dependence
                    or 3) double dependence 1
 Enter lower limit 1
 Enter upper limit 100
 Enter mean parameter value 42
 Enter standard deviation 17
 Enter data set (line) number 1
 Enter line description Cp
 Enter component number (0 for obs x) 1

 Input summary for V                    (type 18)

     Initial value    42.00     float between    1.000     and    100.0    
     Population mean    42.00     with std-dev    17.00    
     Component     1 added to line     1

 Enter 0 if happy with input, 1 if not, 2 to start over 

 Enter -3 to see choices, -1 or -4 (save model) to exit this section 
 Enter type# for parameter  4 (-5 to 51)  -1

Figure 29.9.2 Defining Parameters and Initial Estimates using Boomer, v3.4.7 (Feb 2021)

The results of this analysis are shown in Figure 22.3.4

                    ** FINAL PARAMETER VALUES ***

  #  Name                  Value       S.D.       C.V. %  Lower <-Limit-> Upper
              Population mean         S.D.        (Weight)  Weighted residual

  1) kel                   0.84658E-01  0.208E-02   2.5       0.0       1.0    
                       0.8500E-01   0.2500E-01     40.00      -0.1369E-01
  2) V                      42.175       1.25       3.0       1.0      0.10E+03
                        42.00        17.00        0.5882E-01   0.1030E-01

 Final WSS =   0.143082E-01  R^2 =    1.000     Corr. Coeff =    1.000    
 AIC =   -4.49385            AICc =    0.00000    
 Log likelihood =   2.10     Schwarz Criteria =   -7.10755    
 R^2 and R - jp1      1.000         1.000    
 R^2 and R - jp2     0.8809        0.9386    
 RMSE =     0.1425     or          8.371 % RMSE
 MAE  =     0.1359     ME =     0.4267E-01

 Model and Parameter Definition

  #  Name                    Value       Type From To     Dep  Start Stop

  1) Dose                =   100.0        1    0    1       0    0    0
  2) kel                 =  0.8466E-01    2    1    0       0    0    0
  3) V                   =   42.18       18    1    1       0    0    0

 Data for Cp :-

 DATA #   Time       Observed      Calculated    (Weight)  Weighted residual

     1    1.000       2.00000       2.17860      0.500000     -0.892979E-01
     2    9.000       1.20000       1.10674      0.833333      0.777201E-01

Figure 29.9.3 Results from Bayesian Analysis using Boomer, v3.4.7 (Feb 2021)

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