(640f) Parameter Estimation and Estimability Analysis in Pharmaceutical Models with Uncertain Inputs

A new methodology is proposed to aid parameter estimation in fundamental models when there are too many parameters to be estimated reliably using the available data and there are large uncertainties in some independent variables (model inputs). During traditional Weighted-Least-Squares (WLS) parameter estimation, all model inputs are assumed to be perfectly known. However, when uncertainties in independent variables are large compared to uncertainties in dependent variables, unreliable parameter estimates and model predictions can be obtained.^1-4 In this type of situation, it is beneficial to use estimability analysis to determine which parameters can and should be estimated and an Error-in-Variables Model (EVM) approach to account for uncertain inputs during parameter estimation.

The proposed methodology extends parameter estimability analysis techniques so that they can be readily applied when model inputs are uncertain. First, a sensitivity-based parameter ranking algorithm is extended so that unknown parameters and inputs can be ranked from most estimable to least estimable based on their independent influence on model outputs.^5,6 Second, a mean-squared-error (MSE) criterion is extended so it can be used to select an appropriate number of parameters and inputs for estimation from the ranked list to prevent overfitting.⁷ The proposed methodologies rely on an augmented scaled sensitivity matrix, which contains additional columns and rows to account for the uncertain inputs.

A pharmaceutical case study using experimental data provided by Merck & Co., Inc. is used to illustrate the proposed methods. This case study involves several reactions used to produce an intermediate for the AIDS drug Islatravir. In this batch process, the initial concentration of one of the reagents (trimethylamine ()) is uncertain due to variability and imprecision in its feed rate and feeding time prior to the start of the reaction. Data from two experimental runs conducted at two temperatures are available for model fitting. The proposed ranking method is used to determine that the unknown initial concentrations of in the experimental runs have more important influence on the model predictions than four of the six kinetic parameters in the model. The proposed MSE-based method is then used to show that these uncertain inputs should be estimated along with the three highest-ranked model parameters. The remaining three model parameters, which were not selected for estimation, were held constant at their initial values to prevent overfitting. Parameter estimates obtained from the proposed method result in an excellent fit to the data. Comparisons with model predictions obtained using WLS parameter estimates confirm that the EVM fit to the data is much better. For example, there is a noticeable offset between the data and the model predictions obtained using WLS parameter estimates assuming that the inputs were perfectly known, especially at long reaction times. This offset is not present in the fit to the data obtained using the proposed EVM-based methodology. The proposed extended parameter ranking and subset selection methods should be useful in a wide range of pharmaceutical and chemical process models in which some independent variables are subject to error and the available data are insufficient to reliably estimate all the unknown parameters and uncertain inputs.

References

1. Abdi K, Celse B, McAuley KB. Propagating Input Uncertainties into Parameter Uncertainties an Model Prediction Uncertainties- A Review. Submitted to Industrial and Engineering Chemistry Research. 2022.
2. Abdi K, McAuley KB. Estimation of Output Measurement Variances for EVM Parameter Estimation. AIChE Journal. 2022:e17735.
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