A constrained-likelihood approach to marker-trait association studies

Marker-trait association analysis is an important statistical tool for detecting DNA variants responsible for genetic traits. In such analyses, an analysis model of the mean genetic effects of the genotypes is often specified. For instance, the effect of the disease allele on the trait is often specified to be dominant, recessive, additive, or multiplicative. Although this model-based approach is powerful when the analysis model is correctly specified, it has been found to have low power sometimes when the specified model is incorrect. We introduce an approach that does not require the specification of a particular genetic model. This approach is built upon a constrained maximum likelihood in which the mean genetic effect of the heterozygous genotype is required to not exceed those of the two homozygous genotypes. The asymptotic distribution of the likelihood-ratio statistic is derived for two special cases. A simulation study suggests that this new approach has power comparable to that of the model-based method when the analysis model is correctly specified. This approach uses one marker at a time (i.e., it is a single-marker analysis). However, given the latest findings that powerful inferential procedures for haplotype analyses can be constructed from single-marker analyses, we expect this approach to be useful for haplotype analyses.     

Survival analysis using auxiliary variables via multiple imputation, with application to AIDS clinical trial data

We develop an approach, based on multiple imputation, to using auxiliary variables to recover information from censored observations in survival analysis. We apply the approach to data from an AIDS clinical trial comparing ZDV and placebo, in which CD4 count is the time-dependent auxiliary variable. To facilitate imputation, a joint model is developed for the data, which includes a hierarchical change-point model for CD4 counts and a time-dependent proportional hazards model for the time to AIDS. Markov chain Monte Carlo methods are used to multiply impute event times for censored cases. The augmented data are then analyzed and the results combined using standard multiple-imputation techniques. A comparison of our multiple-imputation approach to simply analyzing the observed data indicates that multiple imputation leads to a small change in the estimated effect of ZDV and smaller estimated standard errors. A sensitivity analysis suggests that the qualitative findings are reproducible under a variety of imputation models. A simulation study indicates that improved efficiency over standard analyses and partial corrections for dependent censoring can result. An issue that arises with our approach, however, is whether the analysis of primary interest and the imputation model are compatible.     

On Estimating the Relationship between Longitudinal Measurements and Time‐to‐Event Data Using a Simple Two‐Stage Procedure

Summary Ye, Lin, and Taylor (2008, Biometrics 64 , 1238–1246) proposed a joint model for longitudinal measurements and time‐to‐event data in which the longitudinal measurements are modeled with a semiparametric mixed model to allow for the complex patterns in longitudinal biomarker data. They proposed a two‐stage regression calibration approach that is simpler to implement than a joint modeling approach. In the first stage of their approach, the mixed model is fit without regard to the time‐to‐event data. In the second stage, the posterior expectation of an individual's random effects from the mixed‐model are included as covariates in a Cox model. Although Ye et al. (2008) acknowledged that their regression calibration approach may cause a bias due to the problem of informative dropout and measurement error, they argued that the bias is small relative to alternative methods. In this article, we show that this bias may be substantial. We show how to alleviate much of this bias with an alternative regression calibration approach that can be applied for both discrete and continuous time‐to‐event data. Through simulations, the proposed approach is shown to have substantially less bias than the regression calibration approach proposed by Ye et al. (2008) . In agreement with the methodology proposed by Ye et al. (2008) , an advantage of our proposed approach over joint modeling is that it can be implemented with standard statistical software and does not require complex estimation techniques.     

Errors-in-variables in joint population pharmacokinetic/pharmacodynamic modeling

Pharmacokinetic (PK) models describe the relationship between the administered dose and the concentration of drug (and/or metabolite) in the blood as a function of time. Pharmacodynamic (PD) models describe the relationship between the concentration in the blood (or the dose) and the biologic response. Population PK/PD studies aim to determine the sources of variability in the observed concentrations/responses across groups of individuals. In this article, we consider the joint modeling of PK/PD data. The natural approach is to specify a joint model in which the concentration and response data are simultaneously modeled. Unfortunately, this approach may not be optimal if, due to sparsity of concentration data, an overly simple PK model is specified. As an alternative, we propose an errors-in-variables approach in which the observed-concentration data are assumed to be measured with error without reference to a specific PK model. We give an example of an analysis of PK/PD data obtained following administration of an anticoagulant drug. The study was originally carried out in order to make dosage recommendations. The prior for the distribution of the true concentrations, which may incorporate an individual's covariate information, is derived as a predictive distribution from an earlier study. The errors-in-variables approach is compared with the joint modeling approach and more naive methods in which the observed concentrations, or the separately modeled concentrations, are substituted into the response model. Throughout, a Bayesian approach is taken with implementation via Markov chain Monte Carlo methods.     

Cell-Specific Cardiac Electrophysiology Models

The traditional cardiac model-building paradigm involves constructing a composite model using data collected from many cells. Equations are derived for each relevant cellular component (e.g., ion channel, exchanger) independently. After the equations for all components are combined to form the composite model, a subset of parameters is tuned, often arbitrarily and by hand, until the model output matches a target objective, such as an action potential. Unfortunately, such models often fail to accurately simulate behavior that is dynamically dissimilar (e.g., arrhythmia) to the simple target objective to which the model was fit. In this study, we develop a new approach in which data are collected via a series of complex electrophysiology protocols from single cardiac myocytes and then used to tune model parameters via a parallel fitting method known as a genetic algorithm (GA). The dynamical complexity of the electrophysiological data, which can only be fit by an automated method such as a GA, leads to more accurately parameterized models that can simulate rich cardiac dynamics. The feasibility of the method is first validated computationally, after which it is used to develop models of isolated guinea pig ventricular myocytes that simulate the electrophysiological dynamics significantly better than does a standard guinea pig model. In addition to improving model fidelity generally, this approach can be used to generate a cell-specific model. By so doing, the approach may be useful in applications ranging from studying the implications of cell-to-cell variability to the prediction of intersubject differences in response to pharmacological treatment.     

A real time hyperelastic tissue model

Real-time soft tissue modeling has a potential application in medical training, procedure planning and image-guided therapy. This paper characterizes the mechanical properties of organ tissue using a hyperelastic material model, an approach which is then incorporated into a real-time finite element framework. While generalizable, in this paper we use the published mechanical properties of pig liver to characterize an example application. Specifically, we calibrate the parameters of an exponential model, with a least-squares method (LSM) using the assumption that the material is isotropic and incompressible in a uniaxial compression test. From the parameters obtained, the stress–strain curves generated from the LSM are compared to those from the corresponding computational model solved by ABAQUS and also to experimental data, resulting in mean errors of 1.9 and 4.8%, respectively, which are considerably better than those obtained when employing the Neo-Hookean model. We demonstrate our approach through the simulation of a biopsy procedure, employing a tetrahedral mesh representation of human liver generated from a CT image. Using the material properties along with the geometric model, we develop a nonlinear finite element framework to simulate the behaviour of liver during an interventional procedure with a real-time performance achieved through the use of an interpolation approach.     

A real time hyperelastic tissue model

Real-time soft tissue modeling has a potential application in medical training, procedure planning and image-guided therapy. This paper characterizes the mechanical properties of organ tissue using a hyperelastic material model, an approach which is then incorporated into a real-time finite element framework. While generalizable, in this paper we use the published mechanical properties of pig liver to characterize an example application. Specifically, we calibrate the parameters of an exponential model, with a least-squares method (LSM) using the assumption that the material is isotropic and incompressible in a uniaxial compression test. From the parameters obtained, the stress-strain curves generated from the LSM are compared to those from the corresponding computational model solved by ABAQUS and also to experimental data, resulting in mean errors of 1.9 and 4.8%, respectively, which are considerably better than those obtained when employing the Neo-Hookean model. We demonstrate our approach through the simulation of a biopsy procedure, employing a tetrahedral mesh representation of human liver generated from a CT image. Using the material properties along with the geometric model, we develop a nonlinear finite element framework to simulate the behaviour of liver during an interventional procedure with a real-time performance achieved through the use of an interpolation approach.     

Binomial regression with misclassification

Motivated by a study of human papillomavirus infection in women, we present a Bayesian binomial regression analysis in which the response is subject to an unconstrained misclassification process. Our iterative approach provides inferences for the parameters that describe the relationships of the covariates with the response and for the misclassification probabilities. Furthermore, our approach applies to any meaningful generalized linear model, making model selection possible. Finally, it is straightforward to extend it to multinomial settings.     

New understanding on phloem physiology and possible consequences for modelling long-distance carbon transport

Most current models of assimilate carbohydrate partitioning are based on growth patterns observed under a range of experimental conditions, from which a set of empirical rules are derived to simulate partitioning. As a result, they are not good at extrapolating to other conditions; this requires a mechanistic approach, which only transport-resistance (TR) models currently provide. We examine an approach to incorporating recent progress in phloem physiology into the TR approach, which leads to a 'minimalist' Munch model of a branched system with competing sinks. In vivo whole-plant measurements have demonstrated that C-flow rates are dependent not only on the properties of the sink, but also on the properties of the whole transport system, and the detailed dynamics of this behaviour is mimicked by the proposed model. This model provides a sound theoretical framework for an unambiguous definition of sink and source strengths, with sink priority being an emergent property of the model. Further developments are proposed, some of which have already had limited application, to cope with the complexity of plants; the emphasis is on a modular approach, together with the importance of choosing the appropriate scale level for both structure and function. Whole-plant experiments with in vivo measurement of the phloem dynamics will be needed to help with this choice.     

COEVOLUTION AS AN EVOLUTIONARY GAME

Coevolution is modeled as a continuous game where the fitness-maximizing strategy of an individual is assumed to be a function of the strategy of other individuals who are also under selection to maximize fitness. An evolutionary stable strategy (ESS) is sought such that no rare alternative strategies can invade the community. The approach can be used to model coevolution because the ESS may be composed of a coalition of more than one strategy. This work, by modeling frequency-dependent selection, extends the approach of Roughgarden (1976) which only considered density-dependent selection. In particular, we show that the coevolutionary model of Rummel and Roughgarden (1985) does contain frequency-dependent selection, and thus, their application of Roughgarden's criterion for evolutionary stability to a model for which it is not applicable leads to the erroneous conclusion that the ecological and evolutionary processes are in conflict. The utility of the game theoretic approach is illustrated by two examples. The first considers an ESS composed of a single strategy, the second an ESS composed of a coalition of two strategies. Evolution occurs on a frequency-dependent adaptive landscape. For this reason, the approach is appropriate for modeling competitive speciation (Rosenzweig, 1978). Also, the game theoretic approach is designed to combine the interplay between the background environment (including the biotic components) and the evolutionary potential of the populations or organisms. The actual application of this theory will require knowledge of both.     

Integrating Evolution into Ecological Modelling: Accommodating Phenotypic Changes in Agent Based Models

Evolutionary change is a characteristic of living organisms and forms one of the ways in which species adapt to changed conditions. However, most ecological models do not incorporate this ubiquitous phenomenon. We have developed a model that takes a ‘phenotypic gambit’ approach and focuses on changes in the frequency of phenotypes (which differ in timing of breeding and fecundity) within a population, using, as an example, seasonal breeding. Fitness per phenotype calculated as the individual’s contribution to population growth on an annual basis coincide with the population dynamics per phenotype. Simplified model variants were explored to examine whether the complexity included in the model is justified. Outputs from the spatially implicit model underestimated the number of individuals across all phenotypes. When no phenotype transitions are included (i.e. offspring always inherit their parent’s phenotype) numbers of all individuals are always underestimated. We conclude that by using a phenotypic gambit approach evolutionary dynamics can be incorporated into individual based models, and that all that is required is an understanding of the probability of offspring inheriting the parental phenotype.     

A Two-Stage Algorithm for Origin-Destination Matrices Estimation Considering Dynamic Dispersion Parameter for Route Choice

This paper proposes a two-stage algorithm to simultaneously estimate origin-destination (OD) matrix, link choice proportion, and dispersion parameter using partial traffic counts in a congested network. A non-linear optimization model is developed which incorporates a dynamic dispersion parameter, followed by a two-stage algorithm in which Generalized Least Squares (GLS) estimation and a Stochastic User Equilibrium (SUE) assignment model are iteratively applied until the convergence is reached. To evaluate the performance of the algorithm, the proposed approach is implemented in a hypothetical network using input data with high error, and tested under a range of variation coefficients. The root mean squared error (RMSE) of the estimated OD demand and link flows are used to evaluate the model estimation results. The results indicate that the estimated dispersion parameter theta is insensitive to the choice of variation coefficients. The proposed approach is shown to outperform two established OD estimation methods and produce parameter estimates that are close to the ground truth. In addition, the proposed approach is applied to an empirical network in Seattle, WA to validate the robustness and practicality of this methodology. In summary, this study proposes and evaluates an innovative computational approach to accurately estimate OD matrices using link-level traffic flow data, and provides useful insight for optimal parameter selection in modeling travelers’ route choice behavior.     

Stochastic modeling for the expression of a gene regulated by competing transcription factors

It is widely accepted that gene expression regulation is a stochastic event. The common approach for its computer simulation requires detailed information on the interactions of individual molecules, which is often not available for the analyses of biological experiments. As an alternative approach, we employed a more intuitive model to simulate the experimental result, the Markov-chain model, in which a gene is regulated by activators and repressors, which bind the same site in a mutually exclusive manner. Our stochastic simulation in the presence of both activators and repressors predicted a Hill-coefficient of the dose-response curve closer to the experimentally observed value than the calculated value based on the simple additive effects of activators alone and repressors alone. The simulation also reproduced the heterogeneity of gene expression levels among individual cells observed by Fluorescence Activated Cell Sorting analysis. Therefore, our approach may help to apply stochastic simulations to broader experimental data.     

Optimization-based metabolic control analysis

In this work, a novel optimization-based metabolic control analysis (OMCA) method is introduced for reducing data requirement for metabolic control analysis (MCA). It is postulated that using the optimal control approach, the fluxes in a metabolic network are correlated to metabolite concentrations and enzyme activities as a state-feedback control system that is optimal with respect to a homeostasis objective. It is then shown that the optimal feedback gains are directly related to the elasticity coefficients (ECs) of MCA. This approach requires determination of the relative "importance" of metabolites and fluxes for the system, which is possible with significantly reduced experimental data, as compared with typical MCA requirements. The OMCA approach is applied to a top-down control model of glycolysis in hepatocytes. It is statistically demonstrated that the OMCA model is capable of predicting the ECs observed experimentally with few exceptions. Further, an OMCA-based model reconciliation study shows that the modification of four assumed stoichiometric coefficients in the model can explain most of the discrepancies, with the exception of elasticities with respect to the NADH/NAD ratio.     

Bayesian design for minimizing prediction uncertainty in bivariate spatial responses with applications to air quality monitoring

Model-based geostatistical design involves the selection of locations to collect data to minimize an expected loss function over a set of all possible locations. The loss function is specified to reflect the aim of data collection, which, for geostatistical studies, could be to minimize the prediction uncertainty at unobserved locations. In this paper, we propose a new approach to design such studies via a loss function derived through considering the entropy about the model predictions and the parameters of the model. The approach includes a multivariate extension to generalized linear spatial models, and thus can be used to design experiments with more than one response. Unfortunately, evaluating our proposed loss function is computationally expensive so we provide an approximation such that our approach can be adopted to design realistically sized geostatistical studies. This is demonstrated through a simulated study and through designing an air quality monitoring program in Queensland, Australia. The results show that our designs remain highly efficient in achieving each experimental objective individually, providing an ideal compromise between the two objectives. Accordingly, we advocate that our approach could be adopted more generally in model-based geostatistical design.