Likelihood based observability analysis and confidence intervals for predictions of dynamic models

Mechanistic dynamic models of biochemical networks such as Ordinary Differential Equations (ODEs) contain unknown parameters like the reaction rate constants and the initial concentrations of the compounds. The large number of parameters as well as their nonlinear impact on the model responses hamper the determination of confidence regions for parameter estimates. At the same time, classical approaches translating the uncertainty of the parameters into confidence intervals for model predictions are hardly feasible. In this article it is shown that a so-called prediction profile likelihood yields reliable confidence intervals for model predictions, despite arbitrarily complex and high-dimensional shapes of the confidence regions for the estimated parameters. Prediction confidence intervals of the dynamic states allow a data-based observability analysis. The approach renders the issue of sampling a high-dimensional parameter space into evaluating one-dimensional prediction spaces. The method is also applicable if there are non-identifiable parameters yielding to some insufficiently specified model predictions that can be interpreted as non-observability. Moreover, a validation profile likelihood is introduced that should be applied when noisy validation experiments are to be interpreted. The properties and applicability of the prediction and validation profile likelihood approaches are demonstrated by two examples, a small and instructive ODE model describing two consecutive reactions, and a realistic ODE model for the MAP kinase signal transduction pathway. The presented general approach constitutes a concept for observability analysis and for generating reliable confidence intervals of model predictions, not only, but especially suitable for mathematical models of biological systems

Constructing Exact Confidence Regions on Parameter Manifolds of Non-Linear Models

Using the mathematical framework of information geometry, we introduce a novel method which allows one to efficiently determine the exact shape of simultaneous confidence regions for non-linearly parametrised models. Furthermore, we show how pointwise confidence bands around the model predictions can be constructed from detailed knowledge of the exact confidence region with little additional computational effort. We exemplify our methods using inference problems in cosmology and epidemic modelling. An open source implementation of the developed schemes is publicly available via the InformationGeometry.jl package for the Julia programming language.Comment: 24 page

A statistical approach to latent dynamic modeling with differential equations

Ordinary differential equations (ODEs) can provide mechanistic models of temporally local changes of processes, where parameters are often informed by external knowledge. While ODEs are popular in systems modeling, they are less established for statistical modeling of longitudinal cohort data, e.g., in a clinical setting. Yet, modeling of local changes could also be attractive for assessing the trajectory of an individual in a cohort in the immediate future given its current status, where ODE parameters could be informed by further characteristics of the individual. However, several hurdles so far limit such use of ODEs, as compared to regression-based function fitting approaches. The potentially higher level of noise in cohort data might be detrimental to ODEs, as the shape of the ODE solution heavily depends on the initial value. In addition, larger numbers of variables multiply such problems and might be difficult to handle for ODEs. To address this, we propose to use each observation in the course of time as the initial value to obtain multiple local ODE solutions and build a combined estimator of the underlying dynamics. Neural networks are used for obtaining a low-dimensional latent space for dynamic modeling from a potentially large number of variables, and for obtaining patient-specific ODE parameters from baseline variables. Simultaneous identification of dynamic models and of a latent space is enabled by recently developed differentiable programming techniques. We illustrate the proposed approach in an application with spinal muscular atrophy patients and a corresponding simulation study. In particular, modeling of local changes in health status at any point in time is contrasted to the interpretation of functions obtained from a global regression. This more generally highlights how different application settings might demand different modeling strategies.Comment: 29 pages, 6 figure

Prevalence of and risk factors for prostatitis in African American men: The Flint Men's Health Study

INTRODUCTION Prostatitis is a common, yet ill-defined condition without clear diagnostic criteria and treatment strategies. Previous studies examining the prevalence and correlates of prostatitis are limited in their inclusion of primarily white populations. The objective of the current study was to identify prevalence of and risk factors for prostatitis in a population-based sample of African-American men. METHODS In 1996, a probability sample of 703 African-American men, aged 40–79, residing in Genesee County, Michigan without a prior history of prostate cancer/surgery provided responses to a structured interview-administered questionnaire which elicited information regarding sociodemographics, current stress and health ratings, and past medical history, including history of physician diagnosed prostatitis, BPH and sexually transmitted diseases. Logistic regression was used to identify predictors of prostatitis after adjustment for age. RESULTS Forty-seven (6.7%) of the 703 men reported a history of prostatitis. Increased frequency of sexual activity and physical activity were significantly associated with decreased odds of disease. Moderate to severe lower urinary tract symptoms (LUTS) and a history of BPH were significantly associated with prostatitis after adjustment for age. CONCLUSION After adjustment for age, LUTS severity and history of BPH were associated with increased odds of prostatitis. BMI, physical activity and sexual frequency were associated with decreased odds of prostatitis. Finally, poor emotional and physical health, high perceived stress and low social support were associated with an increased risk of prostatitis history. Importantly, these findings suggest that the primary risk factors for this condition are largely modifiable and highlight potential targets for future prevention. Prostate 69: 24–32, 2009. © 2008 Wiley–Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/61311/1/20846_ftp.pd

Dealing with prognostic signature instability : a strategy illustrated for cardiovascular events in patients with end-stage renal disease

Background Identification of prognostic gene expression markers from clinical cohorts might help to better understand disease etiology. A set of potentially important markers can be automatically selected when linking gene expression covariates to a clinical endpoint by multivariable regression models and regularized parameter estimation. However, this is hampered by instability due to selection from many measurements. Stability can be assessed by resampling techniques, which might guide modeling decisions, such as choice of the model class or the specific endpoint definition. Methods We specifically propose a strategy for judging the impact of different endpoint definitions, endpoint updates, different approaches for marker selection, and exclusion of outliers. This strategy is illustrated for a study with end-stage renal disease patients, who experience a yearly mortality of more than 20 %, with almost 50 % sudden cardiac death or myocardial infarction. The underlying etiology is poorly understood, and we specifically point out how our strategy can help to identify novel prognostic markers and targets for therapeutic interventions. Results For markers such as the potentially prognostic platelet glycoprotein IIb, the endpoint definition, in combination with the signature building approach is seen to have the largest impact. Removal of outliers, as identified by the proposed strategy, is also seen to considerably improve stability. Conclusions As the proposed strategy allowed us to precisely quantify the impact of modeling choices on the stability of marker identification, we suggest routine use also in other applications to prevent analysis-specific results, which are unstable, i.e. not reproducible

Benchmarking of analysis strategies for data-independent acquisition proteomics using a large-scale dataset comprising inter-patient heterogeneity

Numerous software tools exist for data-independent acquisition (DIA) analysis of clinical samples, necessitating their comprehensive benchmarking. We present a benchmark dataset comprising real-world inter-patient heterogeneity, which we use for in-depth benchmarking of DIA data analysis workflows for clinical settings. Combining spectral libraries, DIA software, sparsity reduction, normalization, and statistical tests results in 1428 distinct data analysis workflows, which we evaluate based on their ability to correctly identify differentially abundant proteins. From our dataset, we derive bootstrap datasets of varying sample sizes and use the whole range of bootstrap datasets to robustly evaluate each workflow. We find that all DIA software suites benefit from using a gas-phase fractionated spectral library, irrespective of the library refinement used. Gas-phase fractionation-based libraries perform best against two out of three reference protein lists. Among all investigated statistical tests non-parametric permutation-based statistical tests consistently perform best

Benchmarking of analysis strategies for data-independent acquisition proteomics using a large-scale dataset comprising inter-patient heterogeneity

Numerous software tools exist for data-independent acquisition (DIA) analysis of clinical samples, necessitating their comprehensive benchmarking. We present a benchmark dataset comprising real-world inter-patient heterogeneity, which we use for in-depth benchmarking of DIA data analysis workflows for clinical settings. Combining spectral libraries, DIA software, sparsity reduction, normalization, and statistical tests results in 1428 distinct data analysis workflows, which we evaluate based on their ability to correctly identify differentially abundant proteins. From our dataset, we derive bootstrap datasets of varying sample sizes and use the whole range of bootstrap datasets to robustly evaluate each workflow. We find that all DIA software suites benefit from using a gas-phase fractionated spectral library, irrespective of the library refinement used. Gas-phase fractionation-based libraries perform best against two out of three reference protein lists. Among all investigated statistical tests non-parametric permutation-based statistical tests consistently perform best

Division of labor by dual feedback regulators controls JAK2/STAT5 signaling over broad ligand range

Quantitative analysis of time-resolved data in primary erythroid progenitor cells reveals that a dual negative transcriptional feedback mechanism underlies the ability of STAT5 to respond to the broad spectrum of physiologically relevant Epo concentrations