# Identifiability - Definitions

The identifiability problem or question is: Can all the parameters in the model be estimated accurately with the data provided? Parameters can be described as identifiable, non-identifiable or non-observable.

Identifiable parameters are those which effect the value of the data and can be estimated with some degree of certainty.

Non-identifiable parameters are those which effect the value of the data but which cannot be estimated accurately

Non-observable parameters are those which don't have an effect on the data.

Figure 20.2.1 Identifiable, Non-identifiable and Non-observable Parameters

Parameters can be defined using the model shown in Figure 20.2.1. Note that only one sample site is used to provide data. Drug concentration in plasma (or blood). The apparent volume of distribution, V, is identifiable. We can determine a good value of V from the Y-intercept of the data plotted on semi-log graph paper. The parameter, kel (not shown but equal to ke plus km) is identifiable from the slope of line on the semi-log plot. Note that changing either V or kel will change the value of the data collected, Cp. Although kel can be readily determined, neither ke nor km can be determined separately. Thus these parameters can be termed non-identifiability. They are observable because if we change the value of either of these parameters the data, Cp, will be altered. There are two other parameters in this model. Both kmu and Vm are non-identifiable and they have not effect on the data. They are both non-observable.

Identifiability can also be define in terms of global or local identifiability. A parameter is globally identifiable or non-identifiable if this is independent of dose or scale. Local identifiability refers to identifiability dependent on dose or scale. For example, if a parameter is identifiable at one dose level but is non-identifiable at another dose level then this would be a local identifiability.