Drug Targeting Organ-Specific Strategies

348 13 Pharmacokinetic/Pharmacodynamic Modelling in Drug Targeting
13.2.8.5 Goodness-of-Fit
After fitting the parameters of a model to a set of measurement data, criteria for the goodness-of-fit
are required. There will always be some differences between the measured data
and the values calculated from the model. These differences may be due to the following
causes:
• Measurement errors in the data, for example, inevitable analytical errors implicit in the
chosen analytical method. In general, measurement errors are random errors, and their order
of magnitude may be known from the precision of the assay, as assessed during the validation
of the assay. If the magnitude of the measurement errors is comparable to the precision
of the assay, the goodness-of-fit is acceptable.The possibility of problems in the case
of measurements close to the detection limit of the assay should be taken into account. In
this case, the relative errors in the analysis may be significantly larger than over the usual
range.
• Model mis-specification. If an inappropriate model is chosen (for example, a model with
too small a number of compartments, or an incorrect structure), it will not be able to describe
the measurements adequately, resulting in systematic deviations between the measurements
(for example, plasma or tissue concentrations) and the values calculated from
the model. Such systematic deviation can be detected by the visual methods described below.
• Other errors in the procedure, such as failure to distinguish between carrier-bound and unbound
drug, as well as errors in dosing, deviations in the time of measurement, incorrect
sampling procedure, exchange of samples, mistakes in dilution during sample treatment, and so
forth.These types of error are the most problematic, and no general solution can be given.
There are several methods available for the assessment of goodness-of-fit, however, there are
no exact and objective criteria for its evaluation.This is due to the following: (1) goodness-offit
is not a single property, and cannot be expressed in a single value, and (2) numerical measures
of goodness-of-fit do no have an absolute meaning.Therefore there is a dependence on
somewhat subjective criteria.To ensure maximal objectivity, the criteria for accepting a set of
model parameters obtained by the fitting procedure as a valid result should be defined explicitly
before the analysis is initiated. In practice, however, this condition is hardly applicable
during the development of new drug targeting preparations, taking into account the complexity
of the modelling procedure.
The following criteria could be used to ensure an acceptable goodness-of-fit:
• Visual inspection of the observed and calculated data should not reveal any significant
lack of fit.
• Residuals (difference between observed and calculated data) or normalized residuals
(residuals divided by the corresponding standard deviation) should be scattered randomly
around zero, by visual inspection.
• Normalized residuals should be neither diverging nor converging when plotted against
time or plotted against (logarithm of) concentration, by visual inspection.
• Residuals should not be serially correlated, as identified by visual inspection or by an appropriate
statistical test (for example a Run’s test).