Variability as constant coefficient of variation: Can we right two decades in error?
Jeroen Elassaiss-Schaap and Siem Heisterkamp
Schering-Plough Research Institute
Objectives: Derive mathematically correct equations that express variability components of PK-PD models as constant coefficients of variation
Introduction: The variability estimates that are reported by analysis software such as NONMEM are difficult to interpret for general audiences. Students of population PK-PD modeling are therefore routinely taught to calculate constant coefficients of variation by taking the square root of such estimates. Application of this method is widespread and can for example be found in contributions to the nmusers mailing list, in peer-reviewed papers on NONMEM analyses and in software packages. The square-root method is an approximation of the exponential variability transformation, which in practice is used as the default way to specify inter-individual variability in PK-PD models.
Methods: In this presentation it is shown how the mathematically correct equations for variability components as constant coefficients of variation (CCV) are derived. Expressions for the standard error and confidence intervals thereof are also provided.
Results: Differences between the approximation and the correct method are negligible when variability is small, e.g. for 10% CCV the difference is smaller than 0.5%. Unfortunately, biased results are obtained when variability becomes large. Calculation of CCV as square root of variability values results in a 10% downward bias at values of 64% and higher. This result is also valid for additive residual error in the logarithmic transform-both-sides (TBS) approach.
Conclusion: It is advised to consider correct equations instead of the usual approximation in calculating CCV of exponentially defined variability components as estimated by NONMEM or other software tools. This is especially important when reporting on data with high intrinsic variability such as encountered in population PK-PD analyses.
