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data analysis approach
fit the data by a proper equation for a 3 compartment model: 
c= a1*e^b1*t + a2*e^b2*t + a3...


data analysis: fitting procedure
pharmacokinetic models are nonlinear with respect to optimized parameters, ie: 
the dependent variable c cannot be described as the sum of functions of independent variables (time t) multiplied by the optimized parameters


initial estimates can be obtained by the:

methods of risiduals (peeling, feathering)


the best model is selected using statistical criteria that include the quality of the fit:

x^2, sum of squares of deviations (the smaller the better, but cannot be smaller than the experimental error. does not consider the number of parameters)
the correlation coefficient r (percentage of explained variance = r^2. the closer to 1 the better) the Ftest criterion 

another criterion: the deviations between the model and the experimental points need to be distributed:

homogeneously
see slide page 1 

if several models are of equal quality, the simplest model (containing the smallest number of optimized parameters) is selected. The rule is called:

Occam's Razor


data analysis: summary

 method of residuals used to get initial estimates of the model parameters
 the parameter values are refined using nonlinear regression analysis  for single dose, number of exponentials = number of compartments if the exponents are sufficiently different. 