Compound Regression Models for Ordered Categorical Data

A general class of sequential models for the analysis of ordered categorical variables is developed and discussed. The models apply if the ordinal response may be subdivided into two or more meaningful sets of response categories. The parametrization explicitly makes use of this subdivision. The models furnish a linear alternative to non-linear models which incorporate a scale parameter. They are shown to be special cases of multivariate generalized linear models. Applications are discussed with the use of several examples.     

A bivariate cure-mixture approach for modeling familial association in diseases

For modeling correlation in familial diseases with variable ages at onset, we propose a bivariate model that incorporates two types of pairwise association, one between the lifetime risk or the overall susceptibility of two individuals and one between the ages at onset between two susceptible individuals. For estimation, we consider a two-stage estimation procedure similar to that of Shih (1998, Biometrics 54, 1115-1128). We evaluate the properties of the estimators through simulations and compare the performance with that from a bivariate survival model that allows correlation between ages at onset only. We apply the methodology to breast cancer using the kinship data from the Washington Ashkenazi Study. We also discuss potential applications of the proposed method in the area of cure modeling.     

Measures of Imbalance for Unbalanced Models

In this paper we present a procedure to measure the degree of imbalance of an unbalanced data set. The procedure is based on choosing an appropriate loglinear model for the subclass frequencies of the data. A measure of imbalance is then introduced as some function of the chi-squared statistic used in the goodness-of-fit test for the loglinear model. The proposed procedure can also be used to measure departures from certain types of balance, such as proportionality of subclass frequencies, partial balance, and last-stage uniformity.     

Multi-patch deterministic and stochastic models for wildlife diseases

Spatial heterogeneity and host demography have a direct impact on the persistence or extinction of a disease. Natural or human-made landscape features such as forests, rivers, roads, and crops are important to the persistence of wildlife diseases. Rabies, hantaviruses, and plague are just a few examples of wildlife diseases where spatial patterns of infection have been observed. We formulate multi-patch deterministic and stochastic epidemic models and use these models to investigate problems related to disease persistence and extinction. We show in some special cases that a unique disease-free equilibrium exists. In these cases, a basic reproduction number ?₀ can be computed and shown to be bounded below and above by the minimum and maximum patch reproduction numbers ? _j , j=1, …, n. The basic reproduction number has a simple form when there is no movement or when all patches are identical or when the movement rate approaches infinity. Numerical examples of the deterministic and stochastic models illustrate the disease dynamics for different movement rates between three patches.     

Estimating amino acid substitution models for metazoan evolutionary studies

Amino acid substitution models represent the substitution rates among amino acids during the evolution of protein sequences. The models are a prerequisite for maximum likelihood or Bayesian methods to analyse the phylogenetic relationships among species based on their protein sequences. Estimating amino acid substitution models requires large protein datasets and intensive computation. In this paper, we presented the estimation of both time-reversible model (Q.met) and time non-reversible model (NQ.met) for multicellular animals (Metazoa). Analyses showed that the Q.met and NQ.met models were significantly better than existing models in analysing metazoan protein sequences. Moreover, the time non-reversible model NQ.met enables us to reconstruct the rooted phylogenetic tree for Metazoa. We recommend researchers to employ the Q.met and NQ.met models in analysing metazoan protein sequences.     

Generalized parametric cure models for relative survival

Cure models are used in time-to-event analysis when not all individuals are expected to experience the event of interest, or when the survival of the considered individuals reaches the same level as the general population. These scenarios correspond to a plateau in the survival and relative survival function, respectively. The main parameters of interest in cure models are the proportion of individuals who are cured, termed the cure proportion, and the survival function of the uncured individuals. Although numerous cure models have been proposed in the statistical literature, there is no consensus on how to formulate these. We introduce a general parametric formulation of mixture cure models and a new class of cure models, termed latent cure models, together with a general estimation framework and software, which enable fitting of a wide range of different models. Through simulations, we assess the statistical properties of the models with respect to the cure proportion and the survival of the uncured individuals. Finally, we illustrate the models using survival data on colon cancer, which typically display a plateau in the relative survival. As demonstrated in the simulations, mixture cure models which are not guaranteed to be constant after a finite time point, tend to produce accurate estimates of the cure proportion and the survival of the uncured. However, these models are very unstable in certain cases due to identifiability issues, whereas LC models generally provide stable results at the price of more biased estimates.     

A Two-Level Regression Model for Growth Curves with Correlated Outcomes

We propose a mixed-effect linear model, as a particular case of the two-level regression model, for analyzing repeated measures made at completely irregular time points. The model allows for subject-level covariates, so as to study the trend and the variability of the individual growth curves. Application of this model is illustrated on a published data set.     

A joint mixed effects dispersion model for menstrual cycle length and time-to-pregnancy

Menstrual cycle patterns are often used as indicators of female fecundity and are associated with hormonally dependent diseases such as breast cancer. A question of considerable interest is in identifying menstrual cycle patterns, and their association with fecundity. A source of data for addressing this question is prospective pregnancy studies that collect detailed information on reproductive aged women. However, methodological challenges exist in ascertaining the association between these two processes as the number of longitudinally measured menstrual cycles is relatively small and informatively censored by time to pregnancy (TTP), as well as the cycle length distribution being highly skewed. We propose a joint modeling approach with a mixed effects dispersion model for the menstrual cycle lengths and a discrete survival model for TTP to address this question. This allows us to assess the effect of important characteristics of menstrual cycle that are associated with fecundity. We are also able to assess the effect of fecundity predictors such as age at menarche, age, and parity on both these processes. An advantage of the proposed approach is the prediction of the TTP, thus allowing us to study the efficacy of menstrual cycle characteristics in predicting fecundity. We analyze two prospective pregnancy studies to illustrate our proposed method by building a model based on the Oxford Conception Study, and predicting for the New York State Angler Cohort Prospective Pregnancy Study. Our analysis has relevant findings for assessing fecundity.     

Measures of Imbalance for Higher Order Designs

In this paper we consider a generalization of the measures of imbalance given by AHRENS and PINCUS (1981) considering the cases: m-fold hierarchical model and m-way classification model in order to quantify the degree of imbalance in an unbalanced design. These measures of imbalance satisfy the same properties as those for the one-way classification model.     

Zero‐inflated spatio‐temporal models for disease mapping

In this paper, our aim is to analyze geographical and temporal variability of disease incidence when spatio‐temporal count data have excess zeros. To that end, we consider random effects in zero‐inflated Poisson models to investigate geographical and temporal patterns of disease incidence. Spatio‐temporal models that employ conditionally autoregressive smoothing across the spatial dimension and B‐spline smoothing over the temporal dimension are proposed. The analysis of these complex models is computationally difficult from the frequentist perspective. On the other hand, the advent of the Markov chain Monte Carlo algorithm has made the Bayesian analysis of complex models computationally convenient. Recently developed data cloning method provides a frequentist approach to mixed models that is also computationally convenient. We propose to use data cloning, which yields to maximum likelihood estimation, to conduct frequentist analysis of zero‐inflated spatio‐temporal modeling of disease incidence. One of the advantages of the data cloning approach is that the prediction and corresponding standard errors (or prediction intervals) of smoothing disease incidence over space and time is easily obtained. We illustrate our approach using a real dataset of monthly children asthma visits to hospital in the province of Manitoba, Canada, during the period April 2006 to March 2010. Performance of our approach is also evaluated through a simulation study.     

Mixed effects models with bivariate and univariate association parameters for longitudinal bivariate binary response data

When two binary responses are measured for each study subject across time, it may be of interest to model how the bivariate associations and marginal univariate risks involving the two responses change across time. To achieve such a goal, marginal models with bivariate log odds ratio and univariate logit components are extended to include random effects for all components. Specifically, separate normal random effects are specified on the log odds ratio scale for bivariate responses and on the logit scale for univariate responses. Assuming conditional independence given the random effects facilitates the modeling of bivariate associations across time with missing at random incomplete data. We fit the model to a dataset for which such structures are feasible: a longitudinal randomized trial of a cardiovascular educational program where the responses of interest are change in hypertension and hypercholestemia status. The proposed model is compared to a naive bivariate model that assumes independence between time points and univariate mixed effects logit models.     

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.     

A mover-stayer model for longitudinal marker data

Studies of chronic disease often focus on estimating prevalence and incidence in which the presence of active disease is based on dichotomizing a continuous marker variable measured with error. Examples include hypertension, asthma, and depression, where active disease is defined by setting a threshold on a continuous measure of blood pressure, respiratory function, and mood, respectively. This paper proposes a model for inference about prevalence and incidence when active disease is determined by dichotomizing a continuous marker variable in a population-based study. In this formulation, it is postulated that there are three groups of people, those that are not susceptible to the disease, those who are always in the disease state, and those who have the potential to transition between the disease and the disease-free states over time. The model is used to estimate the prevalence and incidence of the disease in the population while accounting for measurement error in the marker. An EM algorithm is used for parameter estimation and the methodology is illustrated on Framingham heart study hypertension data. A simulation study is conducted in order to demonstrate the importance of accounting for measurement error in estimating prevalence and incidence for this example.     

Three dimensional printing as an effective method of producing anatomically accurate models for studies in thermal ecology

Hollow copper models painted to match the reflectance of the animal subject are standard in thermal ecology research. While the copper electroplating process results in accurate models, it is relatively time consuming, uses caustic chemicals, and the models are often anatomically imprecise. Although the decreasing cost of 3D printing can potentially allow the reproduction of highly accurate models, the thermal performance of 3D printed models has not been evaluated. We compared the cost, accuracy, and performance of both copper and 3D printed lizard models and found that the performance of the models were statistically identical in both open and closed habitats. We also find that 3D models are more standard, lighter, durable, and inexpensive, than the copper electroformed models.     

A computational tool for the simulation and optimization of microbial strains accounting integrated metabolic/regulatory information

Background and scope

Recently, a number of methods and tools have been proposed to allow the use of genome-scale metabolic models for the phenotype simulation and optimization of microbial strains, within the field of Metabolic Engineering (ME). One of the limitations of most of these algorithms and tools is the fact that only metabolic information is taken into account, disregarding knowledge on regulatory events.

Implementation and performances

This work proposes a novel software tool that implements methods for the phenotype simulation and optimization of microbial strains using integrated models, encompassing both metabolic and regulatory information. This tool is developed as a plug-in that runs over OptFlux, a computational platform that aims to be a reference tool for the ME community.

Availability

The plug-in is made available in the OptFlux web site (www.optflux.org) together with examples and documentation.     

Pharmacokinetic requirements for successful site-directed targeting of drugs

Targeted drugs can be defined as those in which features of the molecule, additional to those required for receptor interaction, substantially improve the concentration ratio of active substance at the site of action compared to the site where side-effects occur.These requirements for successful targeting of systemically administered drugs can be determined by pharmacokinetic modeling. The requirements depend on the mechanism of targeting and on whether targeting is to be achieved for continuous therapy or for acute treatment. For continuous therapy (lasting several days) the success of targeting using a prodrug which is locally activated and has linear pharmacokinetics is proportional to the clearance of active drug from the body and inversely proportional the rate constant for leaving the site of action and to the volume of the tissue. The relationship can be mapped graphically and typical values for these parameters are considered so that situations where targeting can be successful can be identified. The prodrug must also have properties which result in sufficient concentration of drug being formed at the site of action. These properties can also be described by simple proportionality relationships and the conditions for success illustrated graphically.Kinetic considerations are also important for targeting. For continuous therapy it is desirable that steady drug concentrations should be reached rapidly. This is best achieved by using molecules which rapidly exchange between body compartments and have low tissue binding. For acute therapy the rules for targeting can be quite different and an example is given where binding can be responsible for a form of targeting.The results emphasise the need for careful consideration of the properties of targeted system taking into account transport, binding and clearance of both prodrug and drug. Specific details of the disease are also critical both in terms of local tissue properties and the desired time course of drug action.     

Objective prior distributions for Jolly-Seber models of zero-augmented data

Statistical models of capture-recapture data that are used to estimate the dynamics of a population are known collectively as Jolly-Seber (JS) models. State-space versions of these models have been developed for the analysis of zero-augmented data that include the capture histories of the observed individuals and an arbitrarily large number of all-zero capture histories. The number of all-zero capture histories must be sufficiently large to include the unknown number N of individuals in the population that were ever alive during all sampling periods. This definition of N is equivalent to the “superpopulation” of individuals described in several JS models. To fit JS models of zero-augmented data, practitioners often assume a set of independent, uniform prior distributions for the recruitment parameters. However, if the number of capture histories is small compared to N, these uniform priors can exert considerable influence on the posterior distributions of N and other parameters because the uniform priors induce a highly skewed prior on N. In this article, I derive a class of prior distributions for the recruitment parameters of the JS model that can be used to specify objective prior distributions for N, including the discrete-uniform and the improper scale priors as special cases. This class of priors also may be used to specify prior knowledge about recruitment while still preserving the conditions needed to induce an objective prior on N. I use analyses of simulated and real data to illustrate the inferential benefits of this class of prior distributions and to identify circumstances where these benefits are most likely to be realized.