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Confidence and Prediction Intervals for Pharmacometric Models.

ABSTRACT: Supporting decision making in drug development is a key purpose of pharmacometric models. Pharmacokinetic models predict exposures under alternative posologies or in different populations. Pharmacodynamic models predict drug effects based on exposure to drug, disease, or other patient characteristics. Estimation uncertainty is commonly reported for model parameters; however, prediction uncertainty is the key quantity for clinical decision making. This tutorial reviews confidence and prediction intervals with associated calculation methods, encouraging pharmacometricians to report these routinely.

SUBMITTER: Kummel A

PROVIDER: S-EPMC6027739 | biostudies-literature | 2018 Jun

REPOSITORIES: biostudies-literature

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Confidence and Prediction Intervals for Pharmacometric Models.

Kümmel Anne A Bonate Peter L PL Dingemanse Jasper J Krause Andreas A

CPT: pharmacometrics & systems pharmacology 20180325 6

Supporting decision making in drug development is a key purpose of pharmacometric models. Pharmacokinetic models predict exposures under alternative posologies or in different populations. Pharmacodynamic models predict drug effects based on exposure to drug, disease, or other patient characteristics. Estimation uncertainty is commonly reported for model parameters; however, prediction uncertainty is the key quantity for clinical decision making. This tutorial reviews confidence and prediction i ...[more]

PMID: 29388347

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Project description:BackgroundThe dynamics of gene regulation play a crucial role in a cellular control: allowing the cell to express the right proteins to meet changing needs. Some needs, such as correctly anticipating the day-night cycle, require complicated oscillatory features. In the analysis of gene regulatory networks, mathematical models are frequently used to understand how a network's structure enables it to respond appropriately to external inputs. These models typically consist of a set of ordinary differential equations, describing a network of biochemical reactions, and unknown kinetic parameters, chosen such that the model best captures experimental data. However, since a model's parameter values are uncertain, and since dynamic responses to inputs are highly parameter-dependent, it is difficult to assess the confidence associated with these in silico predictions. In particular, models with complex dynamics - such as oscillations - must be fit with computationally expensive global optimization routines, and cannot take advantage of existing measures of identifiability. Despite their difficulty to model mathematically, limit cycle oscillations play a key role in many biological processes, including cell cycling, metabolism, neuron firing, and circadian rhythms.ResultsIn this study, we employ an efficient parameter estimation technique to enable a bootstrap uncertainty analysis for limit cycle models. Since the primary role of systems biology models is the insight they provide on responses to rate perturbations, we extend our uncertainty analysis to include first order sensitivity coefficients. Using a literature model of circadian rhythms, we show how predictive precision is degraded with decreasing sample points and increasing relative error. Additionally, we show how this method can be used for model discrimination by comparing the output identifiability of two candidate model structures to published literature data.ConclusionsOur method permits modellers of oscillatory systems to confidently show that a model's dynamic characteristics follow directly from experimental data and model structure, relaxing assumptions on the particular parameters chosen. Ultimately, this work highlights the importance of continued collection of high-resolution data on gene and protein activity levels, as they allow the development of predictive mathematical models.

Project description:BackgroundValidation by data truncation is a common practice in genetic evaluations because of the interest in predicting the genetic merit of a set of young selection candidates. Two of the most used validation methods in genetic evaluations use a single data partition: predictivity or predictive ability (correlation between pre-adjusted phenotypes and estimated breeding values (EBV) divided by the square root of the heritability) and the linear regression (LR) method (comparison of "early" and "late" EBV). Both methods compare predictions with the whole dataset and a partial dataset that is obtained by removing the information related to a set of validation individuals. EBV obtained with the partial dataset are compared against adjusted phenotypes for the predictivity or EBV obtained with the whole dataset in the LR method. Confidence intervals for predictivity and the LR method can be obtained by replicating the validation for different samples (or folds), or bootstrapping. Analytical confidence intervals would be beneficial to avoid running several validations and to test the quality of the bootstrap intervals. However, analytical confidence intervals are unavailable for predictivity and the LR method.ResultsWe derived standard errors and Wald confidence intervals for the predictivity and statistics included in the LR method (bias, dispersion, ratio of accuracies, and reliability). The confidence intervals for the bias, dispersion, and reliability depend on the relationships and prediction error variances and covariances across the individuals in the validation set. We developed approximations for large datasets that only need the reliabilities of the individuals in the validation set. The confidence intervals for the ratio of accuracies and predictivity were obtained through the Fisher transformation. We show the adequacy of both the analytical and approximated analytical confidence intervals and compare them versus bootstrap confidence intervals using two simulated examples. The analytical confidence intervals were closer to the simulated ones for both examples. Bootstrap confidence intervals tend to be narrower than the simulated ones. The approximated analytical confidence intervals were similar to those obtained by bootstrapping.ConclusionsEstimating the sampling variation of predictivity and the statistics in the LR method without replication or bootstrap is possible for any dataset with the formulas presented in this study.

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Confidence and Prediction Intervals for Pharmacometric Models.

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Confidence and Prediction Intervals for Pharmacometric Models.

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