Dataset Information

Bayesian data integration for quantifying the contribution of diverse measurements to parameter estimates.

ABSTRACT:

Motivation

Computational models in biology are frequently underdetermined, due to limits in our capacity to measure biological systems. In particular, mechanistic models often contain parameters whose values are not constrained by a single type of measurement. It may be possible to achieve better model determination by combining the information contained in different types of measurements. Bayesian statistics provides a convenient framework for this, allowing a quantification of the reduction in uncertainty with each additional measurement type. We wished to explore whether such integration is feasible and whether it can allow computational models to be more accurately determined.

Results

We created an ordinary differential equation model of cell cycle regulation in budding yeast and integrated data from 13 different studies covering different experimental techniques. We found that for some parameters, a single type of measurement, relative time course mRNA expression, is sufficient to constrain them. Other parameters, however, were only constrained when two types of measurements were combined, namely relative time course and absolute transcript concentration. Comparing the estimates to measurements from three additional, independent studies, we found that the degradation and transcription rates indeed matched the model predictions in order of magnitude. The predicted translation rate was incorrect however, thus revealing a deficiency in the model. Since this parameter was not constrained by any of the measurement types separately, it was only possible to falsify the model when integrating multiple types of measurements. In conclusion, this study shows that integrating multiple measurement types can allow models to be more accurately determined.

Availability and implementation

The models and files required for running the inference are included in the Supplementary information.

Contact

l.wessels@nki.nl.

Supplementary information

Supplementary data are available at Bioinformatics online.

SUBMITTER: Thijssen B

PROVIDER: S-EPMC6192208 | biostudies-literature | 2018 Mar

REPOSITORIES: biostudies-literature

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Publications

Bayesian data integration for quantifying the contribution of diverse measurements to parameter estimates.

Thijssen Bram B Dijkstra Tjeerd M H TMH Heskes Tom T Wessels Lodewyk F A LFA

Bioinformatics (Oxford, England) 20180301 5

<h4>Motivation</h4>Computational models in biology are frequently underdetermined, due to limits in our capacity to measure biological systems. In particular, mechanistic models often contain parameters whose values are not constrained by a single type of measurement. It may be possible to achieve better model determination by combining the information contained in different types of measurements. Bayesian statistics provides a convenient framework for this, allowing a quantification of the redu ...[more]

PMID: 29069283

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Project description:BackgroundOrdinary differential equations (ODEs) are often used to understand biological processes. Since ODE-based models usually contain many unknown parameters, parameter estimation is an important step toward deeper understanding of the process. Parameter estimation is often formulated as a least squares optimization problem, where all experimental data points are considered as equally important. However, this equal-weight formulation ignores the possibility of existence of relative importance among different data points, and may lead to misleading parameter estimation results. Therefore, we propose to introduce weights to account for the relative importance of different data points when formulating the least squares optimization problem. Each weight is defined by the uncertainty of one data point given the other data points. If one data point can be accurately inferred given the other data, the uncertainty of this data point is low and the importance of this data point is low. Whereas, if inferring one data point from the other data is almost impossible, it contains a huge uncertainty and carries more information for estimating parameters.ResultsG1/S transition model with 6 parameters and 12 parameters, and MAPK module with 14 parameters were used to test the weighted formulation. In each case, evenly spaced experimental data points were used. Weights calculated in these models showed similar patterns: high weights for data points in dynamic regions and low weights for data points in flat regions. We developed a sampling algorithm to evaluate the weighted formulation, and demonstrated that the weighted formulation reduced the redundancy in the data. For G1/S transition model with 12 parameters, we examined unevenly spaced experimental data points, strategically sampled to have more measurement points where the weights were relatively high, and fewer measurement points where the weights were relatively low. This analysis showed that the proposed weights can be used for designing measurement time points.ConclusionsGiving a different weight to each data point according to its relative importance compared to other data points is an effective method for improving robustness of parameter estimation by reducing the redundancy in the experimental data.

Project description:Audits are often performed to assess the quality of clinical trial data, but beyond detecting fraud or sloppiness, the audit data are generally ignored. In an earlier study, using data from a nonrandomized study, Shepherd and Yu developed statistical methods to incorporate audit results into study estimates and demonstrated that audit data could be used to eliminate bias.In this article, we examine the usefulness of audit-based error-correction methods in clinical trial settings where a continuous outcome is of primary interest.We demonstrate the bias of multiple linear regression estimates in general settings with an outcome that may have errors and a set of covariates for which some may have errors and others, including treatment assignment, are recorded correctly for all subjects. We study this bias under different assumptions, including independence between treatment assignment, covariates, and data errors (conceivable in a double-blinded randomized trial) and independence between treatment assignment and covariates but not data errors (possible in an unblinded randomized trial). We review moment-based estimators to incorporate the audit data and propose new multiple imputation estimators. The performance of estimators is studied in simulations.When treatment is randomized and unrelated to data errors, estimates of the treatment effect using the original error-prone data (i.e., ignoring the audit results) are unbiased. In this setting, both moment and multiple imputation estimators incorporating audit data are more variable than standard analyses using the original data. In contrast, in settings where treatment is randomized but correlated with data errors and in settings where treatment is not randomized, standard treatment-effect estimates will be biased. And in all settings, parameter estimates for the original, error-prone covariates will be biased. The treatment and covariate effect estimates can be corrected by incorporating audit data using either the multiple imputation or moment-based approaches. Bias, precision, and coverage of confidence intervals improve as the audit size increases.The extent of bias and the performance of methods depend on the extent and nature of the error as well as the size of the audit. This study only considers methods for the linear model. Settings much different than those considered here need further study.In randomized trials with continuous outcomes and treatment assignment independent of data errors, standard analyses of treatment effects will be unbiased and are recommended. However, if treatment assignment is correlated with data errors or other covariates, naive analyses may be biased. In these settings, and when covariate effects are of interest, approaches for incorporating audit results should be considered.

Dataset Information

Bayesian data integration for quantifying the contribution of diverse measurements to parameter estimates.

Motivation

Results

Availability and implementation

Contact

Supplementary information

Publications

Bayesian data integration for quantifying the contribution of diverse measurements to parameter estimates.

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