Gordon Graham, Leon Aarons
School of Pharmacy, University of Manchester, Oxford Road, Manchester, M13 9PL
The design of pharmacokinetic studies using a range of optimality criteria has been described in the pharmacokinetic and statistical literature. Papers from D?Argenio (1981) to Mentre et al. (1997) have contributed to the literature for individual nonlinear regression to random effects regression, respectively. These methods have been applied to pharmacokinetic models, as well as continuous measure pharmacodynamic models. The emphasis of these papers has been on continuous random variables in nonlinear regression. When the response variable is on a non-continuous scale, e.g. a categorical variable, drug is effective/drug not effective, problems arise in the estimation of efficient designs.
All of the work on categorical optimal design reported in the literature has been carried on binary or binomial response measures. These optimal designs usually work from the assumption that the data are from a binomial distribution and are to be modelled using either logistic or probit linear regression. The optimal design is often for the purpose of estimating certain parameters such as ED50 or the intercept and gradient term in the logistic regression model. D-optimality is a frequently used criteria for optimising the design but other methods have been reported for binary data such as A-optimality and prior uncertainty optimal criteria. Sequential designs have also been reported for these types of models but they will not be considered here.
There is very little work if any in the literature on optimal design for categorical data with three or more categories. For a categorical response, a Gaussian assumption on the logit transformed scale is not a sensible assumption to make as it leads to inefficient designs. The optimal design is derived from a multinomial distribution as this is the usual likelihood assumption made for categorical data. A generalisation from the results for binary data will be presented when the categorical data are to be modelled using a proportional odds model. The D-optimality criteria was used to derive the optimal designs for the proportional odds models, developed from McCullagh?s (1980) parameterisation of the multinomial distribution. This work corresponds to fixed effects regression and does not include between subject variability into the optimal design.
D’Argenio DZ. Optimal sampling times for pharmacokinetic experiments. Journal of Pharmacokinetics and Biopharmaceutics. 9: 739-756 (1981).
Mentre F, Mallet A, Baccar D. Optimal design in random-effects regression models. Biometrika. 84: 429-442 (1997).
McCullagh P. Regression models for ordinal data. Journal of the Royal Statistical Society B. 42: 109-142 (1980).
Reference: PAGE 8 () Abstr 131 [www.page-meeting.org/?abstract=131]
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