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Both mathematical models and biological model systems stand as tractable representations of complex biological systems or behaviors. They facilitate research and provide insights, and they can describe general rules. Models that represent biological processes or formalize general hypotheses are essential to any broad understanding. Mathematical or biological models necessarily omit details of the natural systems and thus may ultimately be "incorrect" representations. A key challenge is that tractability requires relatively simple models but simplification can result in models that are incorrect in their qualitative, broad implications if the abstracted details matter. Our paper discusses this tension, and how we can improve our inferences from models. We advocate for further efforts dedicated to model development, improvement, and acceptance by the scientific community, all of which may necessitate a more explicit discussion of the purpose and power of models. We argue that models should play a central role in reintegrating biology as a way to test our integrated understanding of how molecules, cells, organs, organisms, populations, and ecosystems function. [ABSTRACT FROM AUTHOR]

In the genomic era, group association tests are of great interest. Due to the overwhelming number of individual genomic features, the power of testing for association of a single genomic feature at a time is often very small, as are the effect sizes for most features. Many methods have been proposed to test association of a trait with a group of features within a functional unit as a whole, e.g. all SNPs in a gene, yet few of these methods account for the fact that generally a substantial proportion of the features are not associated with the trait. In this paper, we propose to model the association for each feature in the group as a mixture of features with no association and features with non-zero associations to explicitly account for the possibility that a fraction of features may not be associated with the trait while other features in the group are. The feature-level associations are first estimated by generalized linear models; the sequence of these estimated associations is then modeled by a hidden Markov chain. To test for global association, we develop a modified likelihood ratio test based on a log-likelihood function that ignores higher order dependency plus a penalty term. We derive the asymptotic distribution of the likelihood ratio test under the null hypothesis. Furthermore, we obtain the posterior probability of association for each feature, which provides evidence of feature-level association and is useful for potential follow-up studies. In simulations and data application, we show that our proposed method performs well when compared with existing group association tests especially when there are only few features associated with the outcome. [ABSTRACT FROM AUTHOR]

Motivation: Biological networks are composed of molecular components and their interactions represented by nodes and edges, respectively, in a graph model. Based on this model, there were many studies with respect to effects of node-based mutations on the network dynamics, whereas little attention was paid to edgetic mutations so far. Results: In this paper, we defined an edgetic sensitivity measure that quantifies how likely a converging attractor is changed by edge-removal mutations in a Boolean network model. Through extensive simulations based on that measure, we found interesting properties of highly sensitive edges in both random and real signaling networks. First, the sensitive edges in random networks tend to link two end nodes both of which are susceptible to node-knockout mutations. Interestingly, it was analogous to an observation that the sensitive edges in human signaling networks are likely to connect drug-target genes. We further observed that the edgetic sensitivity predicted drug-targets better than the node-based sensitivity. In addition, the sensitive edges showed distinguished structural characteristics such as a lower connectivity, more involving feedback loops and a higher betweenness. Moreover, their gene-ontology enrichments were clearly different from the other edges. We also observed that genes incident to the highly sensitive interactions are more central by forming a considerably large connected component in human signaling networks. Finally, we validated our approach by showing that most sensitive interactions are promising edgetic drug-targets in p53 cancer and T-cell apoptosis networks. Taken together, the edgetic sensitivity is valuable to understand the complex dynamics of signaling networks. [ABSTRACT FROM AUTHOR]

This paper is motivated by a phase I-II clinical trial of a targeted agent for advanced solid tumors. We study a stylized version of this trial with the goal to determine optimal actions in each of two cycles of therapy. A design is presented that generalizes the decision-theoretic two-cycle design of Lee and others (2015. Bayesian dose-finding in two treatment cycles based on the joint utility of efficacy and toxicity. Journal of the American Statistical Association, to appear) to accommodate ordinal outcomes. Backward induction is used to jointly optimize the actions taken for each patient in each of the two cycles, with the second action accounting for the patient's cycle 1 dose and outcomes. A simulation study shows that simpler designs obtained by dichotomizing the ordinal outcomes either perform very similarly to the proposed design, or have much worse performance in some scenarios. We also compare the proposed design with the simpler approaches of optimizing the doses in each cycle separately, or ignoring the distinction between cycles 1 and 2. [ABSTRACT FROM AUTHOR]

An important use of measurement error models is to correct regression models for bias due to covariate measurement error. Most measurement error models assume that the observed error-prone covariate (WW ) is a linear function of the unobserved true covariate (X) plus other covariates (Z) in the regression model. In this paper, we consider models for W that include interactions between X and Z. We derive the conditional distribution of X given W and Z and use it to extend the method of regression calibration to this class of measurement error models. We apply the model to dietary data and test whether self-reported dietary intake includes an interaction between true intake and body mass index. We also perform simulations to compare the model to simpler approximate calibration models. [ABSTRACT FROM AUTHOR]

Advances in quantitative biology data collection and analysis across scales (molecular, cellular, organismal, and ecological) have transformed how we understand, categorize, and predict complex biological systems. This surge of quantitative data creates an opportunity to apply, develop, and evaluate mathematical models of biological systems and explore novel methods of analysis. Simultaneously, thanks to increased computational power, mathematicians, engineers and physical scientists have developed sophisticated models of biological systems at different scales. Novel modeling schemes can offer deeper understanding of principles in biology, but there is still a disconnect between modeling and experimental biology that limits our ability to fully realize the integration of mathematical modeling and biology. In this work, we explore the urgent need to expand the use of existing mathematical models across biological scales, develop models that are robust to biological heterogeneity, harness feedback loops within the iterative modeling process, and nurture a cultural shift towards interdisciplinary and cross-field interactions. Better integration of biological experimentation and robust mathematical modeling will transform our ability to understand and predict complex biological systems. [ABSTRACT FROM AUTHOR]

Interfaces play a key role on diseases development because they dictate the energy inflow of nutrients from the surrounding tissues. What is underestimated by existing mathematical models is the biological fact that cells are able to use different resources through nonlinear mechanisms. Among all nutrients, lactate appears to be a sensitive metabolic when talking about brain tumours or neurodegenerative diseases. Here we present a partial differential model to investigate the lactate exchanges between cells and the vascular network in the brain. By extending an existing kinetic model for lactate neuro-energetics, we first provide analytical proofs of the uniqueness and the derivation of precise bounds on the solutions of the problem including diffusion of lactate in a representative volume element comprising the interface between a capillary and cells. We further perform finite element simulations of the model in two test cases, discussing the relevant physical parameters governing the lactate dynamics. [ABSTRACT FROM AUTHOR]

Abstract: Batesian mimicry is characterized by phenotypic convergence between an unpalatable model and a palatable mimic. However, because convergent evolution may arise via alternative evolutionary mechanisms, putative examples of Batesian mimicry must be rigorously tested. Here, we used artificial butterfly facsimiles (N = 4000) to test the prediction that (1) palatable Limenitis lorquini butterflies should experience reduced predation when in sympatry with their putative model, Adelpha californica, (2) protection from predation on L. lorquini should erode outside of the geographical range of the model, and (3) mimetic color pattern traits are more variable in allopatry, consistent with relaxed selection for mimicry. We find support for these predictions, implying that this convergence is the result of selection for Batesian mimicry. Additionally, we conducted mark–recapture studies to examine the effect of mimicry and found that mimics survive significantly longer at sites where the model is abundant. Finally, in contrast to theoretical predictions, we found evidence that the Batesian model (A. californica) is protected from predation outside of its geographic range. We discuss these results considering the ongoing hybridization between L. lorquini and its sister species, L. weidemeyerii, and growing evidence that selection for mimicry predictably leads to a reduction in gene flow between nascent species. [ABSTRACT FROM AUTHOR]

Steady states and periodic oscillations are two important solution forms in reaction--diffusion equations. In this article, we deal with a diffusive Lotka--Volterra system with non-local delay effect and Dirichlet boundary condition. Firstly, the existence and multiplicity of spatially non-homogeneous synchronous/mirror-reflecting steady-state solutions are investigated by means of Lyapunov--Schmidt reduction. Then using centre manifold reduction, normal form analysis and equivariant bifurcation theory, we show that each of the standard Hopf bifurcations gives rise to only one branch of spatially non-homogeneous time-periodic synchronous waves, whereas each of the equivariant Hopf bifurcations gives rise to eight branches of periodic orbits, including two phase-locked oscillations, three mirrorreflecting waves and three standing waves. In particular, we derive the formula for determining the Hopf bifurcation direction and stability of these Hopf bifurcating periodic orbits. These theoretical results give an accurate picture of the bifurcation structure, in the neighbourhood of the bifurcation point, for any set of kernel functions. [ABSTRACT FROM AUTHOR]

A mathematical model of the dynamics of insulin and glucose during a frequently sampled intravenous glucose tolerance test (IVGTT) in sheep was developed that characterizes the large secondphase insulin secretion response in sheep during IVGTT. The model was fit to measurements of the glucose and insulin dynamics during standard IVGTT (n = 42) and modified IVGTT (n = 40), where insulin was injected 60 min after the initiation of the IVGTT. The correlation between log insulin sensitivity determined by hyperglycemic clamps (HGC) and standard IVGTT was r = 0.43 (P = 0.005). The correlation between log insulin sensitivity determined by HGC and modified IVGTT was r = 0.51 (P = 0.002). The model, therefore, provides a method to determine insulin sensitivity through a cheaper and more easily performed IVGTT. We validated our estimation procedure using 2 independent experiments on the effect of 1) pregnancy and 2) being born preterm and exposed to dextrose or dextrose with insulin on HGC-derived insulin sensitivity. The IVGTT-derived insulin sensitivity was significantly greater in pregnant ewes than in prepregnant ewes (difference of 0.39 ± 0.12 log10 nM ng-1 mL-1; P < 0.05), and this was consistent with the significantly greater hyperinsulinemic euglycemic clamp-derived insulin sensitivity in pregnant ewes than in prepregnant ewes (difference of 4.03 ± 0.66 μmol mL kg-1 min-1 ng-1; P < 0.001). There was no significant effect of being born preterm on IVGTT/HGC-derived insulin sensitivity. Basal insulin, insulin sensitivity, insulin production, and insulin clearance were lower in prepregnant ewes (P < 0.05). That is, prepregnant ewes have a lower insulin equilibrium status and less responsive insulin turnover. There was also a significant effect of insulin therapy on the rate of insulin clearance in preterm lambs (P < 0.05). This effect was independently significant of its covariance with all other model parameters. Therefore, it can be interpreted as a direct effect on the rate of insulin clearance by the insulin treatment. All other parameter responses to the insulin treatment effect can be regarded as being due to the covariance between these parameters. These analyses demonstrate that treatment effects on insulin sensitivity can be detected using IVGTT experiments. [ABSTRACT FROM AUTHOR]

Semiparametric methods are well established for the analysis of a progressive Markov illness-death process observed up to a noninformative right censoring time. However, often the intermediate and terminal events are censored in different ways, leading to a dual censoring scheme. In such settings, unbiased estimation of the cumulative transition intensity functions cannot be achieved without some degree of smoothing. To overcome this problem, we develop a sieve maximum likelihood approach for inference on the hazard ratio. A simulation study shows that the sieve estimator offers improved finite-sample performance over common imputation-based alternatives and is robust to some forms of dependent censoring. The proposed method is illustrated using data from cancer trials. [ABSTRACT FROM AUTHOR]

We propose a Bayesian phase I/II dose-finding trial design that simultaneously accounts for toxicity and efficacy. We model the toxicity and efficacy of investigational doses using a flexible Bayesian dynamic model, which borrows information across doses without imposing stringent parametric assumptions on the shape of the dose-toxicity and dose-efficacy curves. An intuitive utility function that reflects the desirability trade-offs between efficacy and toxicity is used to guide the dose assignment and selection. We also discuss the extension of this design to handle delayed toxicity and efficacy. We conduct extensive simulation studies to examine the operating characteristics of the proposed method under various practical scenarios. The results show that the proposed design possesses good operating characteristics and is robust to the shape of the dose-toxicity and dose-efficacy curves. [ABSTRACT FROM AUTHOR]

Meta-analysis plays an important role in summarizing and synthesizing scientific evidence derived from multiple studies. With high-dimensional data, the incorporation of variable selection into meta-analysis improves model interpretation and prediction. Existing variable selection methods require direct access to raw data, which may not be available in practical situations. We propose a new approach, sparse meta-analysis (SMA), in which variable selection for meta-analysis is based solely on summary statistics and the effect sizes of each covariate are allowed to vary among studies. We show that the SMA enjoys the oracle property if the estimated covariance matrix of the parameter estimators from each study is available. We also show that our approach achieves selection consistency and estimation consistency even when summary statistics include only the variance estimators or no variance/covariance information at all. Simulation studies and applications to high-throughput genomics studies demonstrate the usefulness of our approach. [ABSTRACT FROM AUTHOR]

High-throughput time course expression profiles have been available in the last decade due to developments in measurement techniques and devices. Functional data analysis, which treats smoothed curves instead of originally observed discrete data, is effective for the time course expression profiles in terms of dimension reduction, robustness, and applicability to data measured at small and irregularly spaced time points. However, the statistical method of differential analysis for time course expression profiles has not been well established. We propose a functional logistic model based on elastic net regularization (F-Logistic) in order to identify the genes with dynamic alterations in case/control study. We employ a mixed model as a smoothing method to obtain functional data; then F-Logistic is applied to time course profiles measured at small and irregularly spaced time points. We evaluate the performance of F-Logistic in comparison with another functional data approach, i.e. functional ANOVA test (F-ANOVA), by applying the methods to real and synthetic time course data sets. The real data sets consist of the time course gene expression profiles for long-term effects of recombinant interferon β on disease progression in multiple sclerosis. F-Logistic distinguishes dynamic alterations, which cannot be found by competitive approaches such as F-ANOVA, in case/control study based on time course expression profiles. F-Logistic is effective for time-dependent biomarker detection, diagnosis, and therapy. [ABSTRACT FROM AUTHOR]

Spatial modeling of air pollution exposures is widespread in air pollution epidemiology research as a way to improve exposure assessment. However, there are key sources of exposure model uncertainty when air pollution is modeled, including estimation error and model misspecification. We examine the use of predicted air pollution levels in linear health effect models under a measurement error framework. For the prediction of air pollution exposures, we consider a universal Kriging framework, which may include land-use regression terms in the mean function and a spatial covariance structure for the residuals. We derive the bias induced by estimation error and by model misspecification in the exposure model, and we find that a misspecified exposure model can induce asymptotic bias in the effect estimate of air pollution on health. We propose a new spatial simulation extrapolation (SIMEX) procedure, and we demonstrate that the procedure has good performance in correcting this asymptotic bias. We illustrate spatial SIMEX in a study of air pollution and birthweight in Massachusetts. [ABSTRACT FROM AUTHOR]

Species richness varies widely across the tree of life, and there is great interest in identifying ecological, geographic, and other factors that affect rates of species proliferation. Recent methods for explicitly modeling the relationships among character states, speciation rates, and extinction rates on phylogenetic trees— BiSSE, QuaSSE, GeoSSE, and related models—have been widely used to test hypotheses about character state-dependent diversification rates. Here, we document the disconcerting ease with which neutral traits are inferred to have statistically significant associations with speciation rate. We first demonstrate this unfortunate effect for a known model assumption violation: shifts in speciation rate associated with a character not included in the model. We further show that for many empirical phylogenies, characters simulated in the absence of state-dependent diversification exhibit an even higher Type I error rate, indicating that the method is susceptible to additional, unknown model inadequacies. For traits that evolve slowly, the root cause appears to be a statistical framework that does not require replicated shifts in character state and diversification. However, spurious associations between character state and speciation rate arise even for traits that lack phylogenetic signal, suggesting that phylogenetic pseudoreplication alone cannot fully explain the problem. The surprising severity of this phenomenon suggests that many trait–diversification relationships reported in the literature may not be real. More generally, we highlight the need for diagnosing and understanding the consequences of model inadequacy in phylogenetic comparative methods. [ABSTRACT FROM PUBLISHER]

A model for the progression of dental caries is derived. The analysis starts at the microscopic reaction and diffusion process. The local equations are averaged to derive a set of macroscopic equations. The global system includes features such as anisotropic diffusion and local changes in the geometry due to the melting of the enamel. The equations are then solved numerically. The simulations highlight the effect of anisotropy. In addition, we draw conclusions on the progression rate of caries, and discuss them in light of a number of experiments. [ABSTRACT FROM AUTHOR]