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Likelihood-ratio test statistic for the finite-sample case in nonlinear ordinary differential equation models
Christian Tönsing1,2,3, Bernhard Steiert1, Jens Timmer1,2,3
1Institute of Physics, University of Freiburg, Germany.
Plos Computational Biology
|September 22, 2023
Summary
Statistical tests using likelihood ratios in nonlinear ordinary differential equation (ODE) models often rely on large datasets. This study shows that limited data requires corrections to avoid inaccurate conclusions.
Area of Science:
- Statistics
- Computational Biology
- Mathematical Modeling
Background:
- Likelihood ratios are fundamental in statistical inference for tests, model selection, and uncertainty quantification.
- Translating likelihood ratios to p-values or confidence intervals typically requires knowledge of the test statistic's distribution, often approximated using asymptotic (large-data) settings.
- Quantitative molecular biology and dynamical systems modeling frequently involve nonlinear ordinary differential equation (ODE) models with limited sample sizes, posing challenges for standard statistical approaches.
Purpose of the Study:
- To investigate the behavior of empirical likelihood ratios for parameters in nonlinear ODE models under finite-sample conditions.
- To compare the distributions of empirical likelihood ratios with asymptotic approximations.
- To assess the conservativeness of statistical thresholds derived from asymptotic theory in realistic, small-data scenarios.
Main Methods:
- Empirical likelihood ratios were calculated for parameters of 19 published nonlinear ODE benchmark models.
- A resampling approach was applied using the original data designs.
- The empirical distributions were compared against the standard asymptotic approximation.
Main Results:
- The distributions of empirical likelihood ratios in finite-sample applications deviate from the asymptotic approximation.
- Standard statistical thresholds derived for large samples were found to be potentially anti-conservative when applied to small datasets.
- Corrections to likelihood ratios are necessary for valid statistical inference in finite-sample ODE models.
Conclusions:
- The asymptotic approximation for likelihood ratios is often inadequate for nonlinear ODE models with limited data.
- Finite-sample corrections are crucial to ensure the validity and conservativeness of statistical tests and confidence intervals in these models.
- This research highlights the need for adjusted statistical methodologies in quantitative biology and related fields dealing with small datasets.
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