Fuzzy least squares for identification of individual pharmacokinetic parameters.

Abstract

In this paper, we examined the added value of fuzzy nonlinear regression to identify individual pharmacokinetic parameters in the case of noisy fuzzy data and/or small sample sizes. We first described three approaches that use least squares of errors as a fitting criterion for parameter estimation by fuzzy regression. Next, we compared the estimation and prediction capability of fuzzy least squares (FLS) and ordinary least squares (OLS) regressions via a simulation experiment, so as to determine the conditions of data size and variability under which one approach could be deemed superior over the other. We considered two empirical pharmacokinetic models. Our results showed that OLS regression outperformed FLS regression when the sample size was larger and/or there existed more outliers in the data. Overall, FLS regression was more powerful as the dataset size decreased. When the data were smaller in size and contained more variability, FLS regression's performance remained better than that of the OLS regression. Although the accuracy of the three FLS regression approaches was very close in almost all instances, those that estimated fuzzy parameters were superior in terms of predictive capability. These findings could aid in selecting the proper regression technique to employ in the presence of fuzzy data.