Modeling of Sugar Crystallization through Knowledge Integration

This paper reports on the comparison of three modeling approaches that were applied to a fed batch evaporative sugar crystallization process. They are termed white box, black box, and grey box modeling strategies, which reflects the level of physical transparency and understanding of the model. White box models represent the traditional modeling approach, based on modeling by first principles. Black box models rely on recorded process data and knowledge collected during the normal process operation. Among various tools in this group an artificial neural networks (ANN) approach is adopted in this paper. The grey box model is obtained from a combination of first principles modeling, based on mass, energy and population balances, with an ANN to approximate three kinetic parameters ‐‐ crystal growth rate, nucleation rate and the agglomeration kernel. The results have shown that the hybrid modeling approach outperformed the other aforementioned modeling strategies.     

Continuous time Markov models for binary longitudinal data

Longitudinal data usually consist of a number of short time series. A group of subjects or groups of subjects are followed over time and observations are often taken at unequally spaced time points, and may be at different times for different subjects. When the errors and random effects are Gaussian, the likelihood of these unbalanced linear mixed models can be directly calculated, and nonlinear optimization used to obtain maximum likelihood estimates of the fixed regression coefficients and parameters in the variance components. For binary longitudinal data, a two state, non-homogeneous continuous time Markov process approach is used to model serial correlation within subjects. Formulating the model as a continuous time Markov process allows the observations to be equally or unequally spaced. Fixed and time varying covariates can be included in the model, and the continuous time model allows the estimation of the odds ratio for an exposure variable based on the steady state distribution. Exact likelihoods can be calculated. The initial probability distribution on the first observation on each subject is estimated using logistic regression that can involve covariates, and this estimation is embedded in the overall estimation. These models are applied to an intervention study designed to reduce children's sun exposure.     

Heterogeneity in multistage carcinogenesis and mixture modeling

Carcinogenesis is commonly described as a multistage process, in which stem cells are transformed into cancer cells via a series of mutations. In this article, we consider extensions of the multistage carcinogenesis model by mixture modeling. This approach allows us to describe population heterogeneity in a biologically meaningful way. We focus on finite mixture models, for which we prove identifiability. These models are applied to human lung cancer data from several birth cohorts. Maximum likelihood estimation does not perform well in this application due to the heavy censoring in our data. We thus use analytic graduation instead. Very good fits are achieved for models that combine a small high risk group with a large group that is quasi immune.     

Process flexibility and inventory flexibility via product substitution

This paper studies the optimal control of and interaction between two types of flexibility under Markov models of demand and production: process flexibility and inventory flexibility. In our model, process flexibility is generated by a multi-functional production facility that can produce two types of products, and inventory flexibility is manifested in firm-driven one-way product substitution. Both process flexibility and inventory flexibility are important drivers of supply chain performance and are strategic design considerations. To analyze the interaction between these two types of flexibility, we model a dynamically controlled two-product, make-to-stock system with stochastic processing times and stochastic demand. We characterize the complex joint optimal production and post-production policy for a special case and numerically show that a simply structured multi-threshold policy is a near-optimal heuristic policy for the general case. We gain further insight into the impact of system parameters on the value of process flexibility and inventory flexibility via a comprehensive numerical study. We find that for a wide range of capacity and cost parameters, process flexibility and inventory flexibility complement each other, so pursuing both forms of flexibility is effective.     

Information Sets and Excess Zeros in Random Effects Modeling of Longitudinal Data

Marginal regression via generalized estimating equations is widely used in biostatistics to model longitudinal data from subjects whose outcomes and covariates are observed at several time points. In this paper we consider two issues that have been raised in the literature concerning the marginal regression approach. The first is that even though the past history may be predictive of outcome, the marginal approach does not use this history. Although marginal regression has the flexibility of allowing between-subject variations in the observation times, it may lose substantial prediction power in comparison with the transitional modeling approach that relates the responses to the covariate and outcome histories. We address this issue by using the concept of “information sets” for prediction to generalize the “partly conditional mean” approach of Pepe and Couper (J. Am. Stat. Assoc. 92:991–998, 1997). This modeling approach strikes a balance between the flexibility of the marginal approach and the predictive power of transitional modeling. Another issue is the problem of excess zeros in the outcomes over what the underlying model for marginal regression implies. We show how our predictive modeling approach based on information sets can be readily modified to handle the excess zeros in the longitudinal time series. By synthesizing the marginal, transitional, and mixed effects modeling approaches in a predictive framework, we also discuss how their respective advantages can be retained while their limitations can be circumvented for modeling longitudinal data.     

Discriminant analysis for longitudinal data with multiple continuous responses and possibly missing data

Summary .  Multiple outcomes are often used to properly characterize an effect of interest. This article discusses model-based statistical methods for the classification of units into one of two or more groups where, for each unit, repeated measurements over time are obtained on each outcome. We relate the observed outcomes using multivariate nonlinear mixed-effects models to describe evolutions in different groups. Due to its flexibility, the random-effects approach for the joint modeling of multiple outcomes can be used to estimate population parameters for a discriminant model that classifies units into distinct predefined groups or populations. Parameter estimation is done via the expectation-maximization algorithm with a linear approximation step. We conduct a simulation study that sheds light on the effect that the linear approximation has on classification results. We present an example using data from a study in 161 pregnant women in Santiago, Chile, where the main interest is to predict normal versus abnormal pregnancy outcomes.     

Ecological niche variation in the Wilson's warbler Cardellina pusilla complex

Wilson's warbler comprises three subspecies separated into two geographic groups: C. p. pusilla that breeds in eastern North America; and C. p. pileolata and C. p. chryseola that breed in western North America. Given the differences between the groups in genetics, morphology, habitat use, and population decline, we tested for ecological niche similarity in both their breeding and wintering distribution using niche modeling based on temperature and precipitation data. We first conducted an inter‐prediction approach considering the percent of summer and winter localities of one group that are predicted by the potential distribution of the alternate group. We also applied a null model approach that compares self‐predictions and pseudoreplicates of each group to indicate similarity, divergence, or indeterminate niche overlap. Finally, we compared ecological distances between and within groups using the Gower similarity equation. We found that the western group had an ecological niche of broader climatic conditions, while the eastern group had a narrower ecological niche. The inter‐prediction approach showed that, for both summering and wintering ranges, ecological niche models of the western group predicted ～50% of the observed distribution of the eastern group, whereas eastern group models predicted < 18% of the western group distribution. The null model approach found that similarity in ecological niches was indeterminate, possibly due to the large area occupied by the two groups; but it suggests a more restricted set of climatic conditions of the eastern group distribution. However, the Gower coefficients demonstrated that the ecological distance between the two geographic groups was larger than the ecological distance within groups, indicating distinct ecological niches. Overall, our results support the hypothesis that the eastern and western groups of Wilson's warbler are two cryptic species; this should be taken into consideration for future analyses, particularly with respect to vulnerability categorization and conservation efforts.     

Stochastic functional data analysis: a diffusion model-based approach

This article presents a new modeling strategy in functional data analysis. We consider the problem of estimating an unknown smooth function given functional data with noise. The unknown function is treated as the realization of a stochastic process, which is incorporated into a diffusion model. The method of smoothing spline estimation is connected to a special case of this approach. The resulting models offer great flexibility to capture the dynamic features of functional data, and allow straightforward and meaningful interpretation. The likelihood of the models is derived with Euler approximation and data augmentation. A unified Bayesian inference method is carried out via a Markov chain Monte Carlo algorithm including a simulation smoother. The proposed models and methods are illustrated on some prostate-specific antigen data, where we also show how the models can be used for forecasting.     

Modeling repeated count data subject to informative dropout

In certain diseases, outcome is the number of morbid events over the course of follow-up. In epilepsy, e.g., daily seizure counts are often used to reflect disease severity. Follow-up of patients in clinical trials of such diseases is often subject to censoring due to patients dying or dropping out. If the sicker patients tend to be censored in such trials, estimates of the treatment effect that do not incorporate the censoring process may be misleading. We extend the shared random effects approach of Wu and Carroll (1988, Biometrics 44, 175-188) to the setting of repeated counts of events. Three strategies are developed. The first is a likelihood-based approach for jointly modeling the count and censoring processes. A shared random effect is incorporated to introduce dependence between the two processes. The second is a likelihood-based approach that conditions on the dropout times in adjusting for informative dropout. The third is a generalized estimating equations (GEE) approach, which also conditions on the dropout times but makes fewer assumptions about the distribution of the count process. Estimation procedures for each of the approaches are discussed, and the approaches are applied to data from an epilepsy clinical trial. A simulation study is also conducted to compare the various approaches. Through analyses and simulations, we demonstrate the flexibility of the likelihood-based conditional model for analyzing data from the epilepsy trial.     

Fragment-based modelling of single stranded RNA bound to RNA recognition motif containing proteins

Protein-RNA complexes are important for many biological processes. However, structural modeling of such complexes is hampered by the high flexibility of RNA. Particularly challenging is the docking of single-stranded RNA (ssRNA). We have developed a fragment-based approach to model the structure of ssRNA bound to a protein, based on only the protein structure, the RNA sequence and conserved contacts. The conformational diversity of each RNA fragment is sampled by an exhaustive library of trinucleotides extracted from all known experimental protein–RNA complexes. The method was applied to ssRNA with up to 12 nucleotides which bind to dimers of the RNA recognition motifs (RRMs), a highly abundant eukaryotic RNA-binding domain. The fragment based docking allows a precise de novo atomic modeling of protein-bound ssRNA chains. On a benchmark of seven experimental ssRNA–RRM complexes, near-native models (with a mean heavy-atom deviation of <3 Å from experiment) were generated for six out of seven bound RNA chains, and even more precise models (deviation < 2 Å) were obtained for five out of seven cases, a significant improvement compared to the state of the art. The method is not restricted to RRMs but was also successfully applied to Pumilio RNA binding proteins.     

Modeling the Impact of Alternative Immunization Strategies: Using Matrices as Memory Lanes

Existing modeling approaches are divided between a focus on the constitutive (micro) elements of systems or on higher (macro) organization levels. Micro-level models enable consideration of individual histories and interactions, but can be unstable and subject to cumulative errors. Macro-level models focus on average population properties, but may hide relevant heterogeneity at the micro-scale. We present a framework that integrates both approaches through the use of temporally structured matrices that can take large numbers of variables into account. Matrices are composed of several bidimensional (time×age) grids, each representing a state (e.g. physiological, immunological, socio-demographic). Time and age are primary indices linking grids. These matrices preserve the entire history of all population strata and enable the use of historical events, parameters and states dynamically in the modeling process. This framework is applicable across fields, but particularly suitable to simulate the impact of alternative immunization policies. We demonstrate the framework by examining alternative strategies to accelerate measles elimination in 15 developing countries. The model recaptured long-endorsed policies in measles control, showing that where a single routine measles-containing vaccine is employed with low coverage, any improvement in coverage is more effective than a second dose. It also identified an opportunity to save thousands of lives in India at attractively low costs through the implementation of supplementary immunization campaigns. The flexibility of the approach presented enables estimating the effectiveness of different immunization policies in highly complex contexts involving multiple and historical influences from different hierarchical levels.     

Bayesian calibration,process modeling and uncertainty quantification in biotechnology

High-throughput experimentation has revolutionized data-driven experimental sciences and opened the door to the application of machine learning techniques. Nevertheless, the quality of any data analysis strongly depends on the quality of the data and specifically the degree to which random effects in the experimental data-generating process are quantified and accounted for. Accordingly calibration, i.e. the quantitative association between observed quantities and measurement responses, is a core element of many workflows in experimental sciences.Particularly in life sciences, univariate calibration, often involving non-linear saturation effects, must be performed to extract quantitative information from measured data. At the same time, the estimation of uncertainty is inseparably connected to quantitative experimentation. Adequate calibration models that describe not only the input/output relationship in a measurement system but also its inherent measurement noise are required. Due to its mathematical nature, statistically robust calibration modeling remains a challenge for many practitioners, at the same time being extremely beneficial for machine learning applications.In this work, we present a bottom-up conceptual and computational approach that solves many problems of understanding and implementing non-linear, empirical calibration modeling for quantification of analytes and process modeling. The methodology is first applied to the optical measurement of biomass concentrations in a high-throughput cultivation system, then to the quantification of glucose by an automated enzymatic assay. We implemented the conceptual framework in two Python packages, calibr8 and murefi, with which we demonstrate how to make uncertainty quantification for various calibration tasks more accessible. Our software packages enable more reproducible and automatable data analysis routines compared to commonly observed workflows in life sciences.Subsequently, we combine the previously established calibration models with a hierarchical Monod-like ordinary differential equation model of microbial growth to describe multiple replicates of Corynebacterium glutamicum batch cultures. Key process model parameters are learned by both maximum likelihood estimation and Bayesian inference, highlighting the flexibility of the statistical and computational framework.     

A hybrid agent-based approach for modeling microbiological systems

Models for systems biology commonly adopt Differential Equations or Agent-Based modeling approaches for simulating the processes as a whole. Models based on differential equations presuppose phenomenological intracellular behavioral mechanisms, while models based on Multi-Agent approach often use directly translated, and quantitatively less precise if-then logical rule constructs. We propose an extendible systems model based on a hybrid agent-based approach where biological cells are modeled as individuals (agents) while molecules are represented by quantities. This hybridization in entity representation entails a combined modeling strategy with agent-based behavioral rules and differential equations, thereby balancing the requirements of extendible model granularity with computational tractability. We demonstrate the efficacy of this approach with models of chemotaxis involving an assay of 10³ cells and 1.2×10⁶ molecules. The model produces cell migration patterns that are comparable to laboratory observations.     

The MIAmaxent R package: Variable transformation and model selection for species distribution models

The widely used “Maxent” software for modeling species distributions from presence‐only data (Phillips et al., Ecological Modelling, 190, 2006, 231) tends to produce models with high‐predictive performance but low‐ecological interpretability, and implications of Maxent's statistical approach to variable transformation, model fitting, and model selection remain underappreciated. In particular, Maxent's approach to model selection through lasso regularization has been shown to give less parsimonious distribution models—that is, models which are more complex but not necessarily predictively better—than subset selection. In this paper, we introduce the MIAmaxent R package, which provides a statistical approach to modeling species distributions similar to Maxent's, but with subset selection instead of lasso regularization. The simpler models typically produced by subset selection are ecologically more interpretable, and making distribution models more grounded in ecological theory is a fundamental motivation for using MIAmaxent. To that end, the package executes variable transformation based on expected occurrence–environment relationships and contains tools for exploring data and interrogating models in light of knowledge of the modeled system. Additionally, MIAmaxent implements two different kinds of model fitting: maximum entropy fitting for presence‐only data and logistic regression (GLM) for presence–absence data. Unlike Maxent, MIAmaxent decouples variable transformation, model fitting, and model selection, which facilitates methodological comparisons and gives the modeler greater flexibility when choosing a statistical approach to a given distribution modeling problem.     

Robust two-stage estimation in hierarchical nonlinear models

Hierarchical models encompass two sources of variation, namely within and among individuals in the population; thus, it is important to identify outliers that may arise at each sampling level. A two-stage approach to analyzing nonlinear repeated measurements naturally allows parametric modeling of the respective variance structure for the intraindividual random errors and interindividual random effects. We propose a robust two-stage procedure based on Huber's (1981, Robust Statistics) theory of M-estimation to accommodate separately aberrant responses within an experimental unit and subjects deviating from the study population when the usual assumptions of normality are violated. A toxicology study of chronic ozone exposure in rats illustrates the impact of outliers on the population inference and hence the advantage of adopting the robust methodology. The robust weights generated by the two-stage M-estimation process also serve as diagnostics for gauging the relative influence of outliers at each level of the hierarchical model. A practical appeal of our proposal is the computational simplicity since the estimation algorithm may be implemented using standard statistical software with a nonlinear least squares routine and iterative capability.     

Modeling antitumor activity in xenograft tumor treatment

To analyze responses of solid tumors to treatment with antitumor therapy, we applied nonparametric mixed-effects models to investigate tumor volumes measured over a fixed. The population and individual response functions were approximated by penalized splines. Linear mixed-effects modeling was applied in the implementation of the estimation. We applied the approach to an analysis of a real xenograft study of a new antitumor agent, temozolomide, combined with irinotecan. The model fitted the data very well. We conducted a sensitivity analysis to determine the effect of informative dropout. We also propose an intuitive approach to a comparison of the antitumor effects of two different treatments. Biological interpretations and clinical implications are discussed.