Semiparametric distributions with estimated shape parameters

Pharm Res. 2009 Sep;26(9):2174-85. doi: 10.1007/s11095-009-9931-1. Epub 2009 Jul 1.


Purpose: To investigate the use of adaptive transformations to assess the parameter distributions in population modeling.

Methods: The logit, box-cox, and heavy tailed transformations were investigated. Each one was used in conjunction with the standard (exponential) transformation for PK and PD parameters. The shape parameters of these transformations were estimated to allow the parameter distributions to more accurately resemble a wider range of parameter distributions. The transformations were tested both in simulated settings where the true distributions were known and in 30 models developed from real data.

Results: In the simulated setting the transformations were better than the standard lognormal distribution at characterizing the true distributions. Improvement could also be seen in objective function value (OFV) and in simulation based diagnostics. In the real datasets, significant model improvement based on OFV could be seen in 22, 18, and 22 out of the 30 models for the three transformations respectively.

Conclusion: Transformations with estimated shape parameters are a promising approach to relax the often erroneous assumption of a known shape of the parameter distribution. They offer a simple and straightforward way of handling and characterizing parameter distributions.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Models, Theoretical
  • Pharmacokinetics*
  • Pharmacology*