Mark Sale* (1), Bruce G. Pollock (2), Robert R. Bies (3), Eric Sherer(3)
(1) Next Level Solutions, Raleigh NC, USA and Indiana University, Division of Clinical Pharmacology, Indianapolis, IN, USA. (2) Centre for Addiction and Mental Health, University of Toronto, Toronto, Ontario, Canada; (3) Indiana University, Division of Clinical Pharmacology, Indianapolis, IN, USA.
Objectives: Investigate multi-objective genetic algorithm (MOGA) to identify optimal NONMEM models.
Methods: MOGA is a global search algorithm that is useful when there is a tradeoff between multiple objectives, and therefore a single, strictly numerical solution isn't appropriate. Specifically for NONMEM, there is a well-known tradeoff between parsimony (number of estimated parameters) and goodness of fit, (-2ll). MOGA identifies non-dominated solutions based on several objectives. Non-dominated solutions, NONMEM models in this case, meet two criteria: 1) no models in the solution space can be superior on all objectives; and 2) the model must be superior to any other model in the solution space on at least one objective. Initially, a random "population" of NONMEM models is created. Using MOGA, models from this population can be selected based on non-domination without weighting or preference for any of the objectives. These selected "parent" models will, in general, be among the better models in the initial population of models. The parent models will then be "bred", using standard genetic algorithm methods to cross over and mutate them in a search for still better models. This is repeated until the optimal set is stable. The specific algorithm used in this example is NSGA-II (Non-dominated, Sorted Genetic Algorithm, 1). The set of non-dominated models can then be presented to the user for additional evaluation (based on biological plausibility, plots, etc.).
A model solution search space was defined for this analysis. The solution search space included: number of compartments, presence|absence of a mixture model, various covariate relationships, various between subject and residual variance structures. The objectives used for the present search were:
- Goodness of fit (-2ll)
- Number of estimated parameters
- "Quality" of solution scored as 0-3, based on convergence, covariance step and correlation test.
- Global adjusted p-value from NPDE (2)
Results: MOGA was able to identify a set of optimal models. Plots of the results demonstrate a clear inverse relationship between the different objectives. In addition, a decrease (worsening) of NPDE but a continued decline (improvement) in -2ll is seen with models having more than 15 parameters, suggesting that models exceeding that number of parameters, for the data set from this study, may be overparameterized.
Conclusions: A multi-objective genetic algorithm is capable of identifying a set of optimal NONMEM models.
References:
[1] Kalyanmoy Deb, Amrit Pratap, Sameer Agarwal, and T. Meyarivan. A Fast and Elitist Multi-objective Genetic Algorithm. NSGA-II, IEEE Transactions on Evolutionary Computation, 6, (2), 2002
[2] Emmanuelle Comets, France Mentré. Using simulations-based metrics to detect model misspecifications, PAGE meeting 2010
Reference: PAGE 21 () Abstr 2336 [www.page-meeting.org/?abstract=2336]
Poster: New Modelling Approaches