Using the Adapted Levenberg-Marquardt method to determine the validity of ignoring insulin and glucose data that is affected by mixing

Abstract

Most parameter ID methods use least squares criterion to fit parameter values to observed behavior. However, the least squares criterion can be heavily influenced by outlying data or un-modelled effects. In such cases, least squares estimation can yield poor results. Outlying data is often manually removed to avoid inaccurate outcomes, but this process is complex, tedious and operator dependent.

This research presents an adaptation of the Levenberg-Marquardt (L-M) parameter identification method that effectively ignores least-square contributions from outlying data. The adapted method (aL-M) is capable of ignoring outlier data in accordance with the coefficient of variation of the residuals and was thus, capable of operator independent omission of outlier data using the 3 standard deviation rule. The aL-M was compared to the original Levenberg-Marquardt (L-M) method in C-peptide, insulin and glucose data. In total three cases were tested: L-M in the full dataset, L-M in the same data where the points that were suspected to be affected by incomplete mixing at the depot site were removed, and the aL-M in the full data set.

There were strong correlations between the aL-M and the reduced dataset from [0.85, 0.71] for the clinically valuable glucose parameters. In contrast, the unreduced data yielded poor residuals and poor correlations with the aL-M [0.44, 0.33]. The aL-M approach provided strong justification for consistent removal of data that was deemed to be affected by mixing.