Bayesian meta-analysis for longitudinal data models using multivariate mixture priors

We propose a class of longitudinal data models with random effects that generalizes currently used models in two important ways. First, the random-effects model is a flexible mixture of multivariate normals, accommodating population heterogeneity, outliers, and nonlinearity in the regression on subject-specific covariates. Second, the model includes a hierarchical extension to allow for meta-analysis over related studies. The random-effects distributions are decomposed into one part that is common across all related studies (common measure), and one part that is specific to each study and that captures the variability intrinsic between patients within the same study. Both the common measure and the study-specific measures are parameterized as mixture-of-normals models. We carry out inference using reversible jump posterior simulation to allow a random number of terms in the mixtures. The sampler takes advantage of the small number of entertained models. The motivating application is the analysis of two studies carried out by the Cancer and Leukemia Group B (CALGB). In both studies, we record for each patient white blood cell counts (WBC) over time to characterize the toxic effects of treatment. The WBCs are modeled through a nonlinear hierarchical model that gathers the information from both studies.     

JAK2 inhibition has different therapeutic effects according to myeloproliferative neoplasm development in mice

JAK2 inhibition therapy is used to treat patients suffering from myeloproliferative neoplasms (MPN). Conflicting data on this therapy are reported possibly linked to the types of inhibitors or disease type. Therefore, we decided to compare in mice the effect of a JAK2 inhibitor, Fedratinib, in MPN models of increasing severity: polycythemia vera (PV), post‐PV myelofibrosis (PPMF) and rapid post‐essential thrombocythemia MF (PTMF). The models were generated through JAK2 activation by the JAK2^V617F mutation or MPL constant stimulation. JAK2 inhibition induced a correction of splenomegaly, leucocytosis and microcytosis in all three MPN models. However, the effects on fibrosis, osteosclerosis, granulocytosis, erythropoiesis or platelet counts varied according to the disease severity stage. Strikingly, complete blockade of fibrosis and osteosclerosis was observed in the PPMF model, linked to correction of MK hyper/dysplasia, but not in the PTMF model, suggesting that MF development may also become JAK2‐independent. Interestingly, we originally found a decreased in the JAK2^V617F allele burden in progenitor cells from the spleen but not in other cell types. Overall, this study shows that JAK2 inhibition has different effects according to disease phenotypes and can (i) normalize platelet counts, (ii) prevent the development of marrow fibrosis/osteosclerosis at an early stage and (iii) reduce splenomegaly through blockage of stem cell mobilization in the spleen.     

A two-part mixed-effects pattern-mixture model to handle zero-inflation and incompleteness in a longitudinal setting

Two-part regression models are frequently used to analyze longitudinal count data with excess zeros, where the same set of subjects is repeatedly observed over time. In this context, several sources of heterogeneity may arise at individual level that affect the observed process. Further, longitudinal studies often suffer from missing values: individuals dropout of the study before its completion, and thus present incomplete data records. In this paper, we propose a finite mixture of hurdle models to face the heterogeneity problem, which is handled by introducing random effects with a discrete distribution; a pattern-mixture approach is specified to deal with non-ignorable missing values. This approach helps us to consider overdispersed counts, while allowing for association between the two parts of the model, and for non-ignorable dropouts. The effectiveness of the proposal is tested through a simulation study. Finally, an application to real data on skin cancer is provided.     

Analysis of relation between virologic responses and immunologic responses, patient's factors in AIDS clinical trials using a semiparametric mixed-effects model

In this article we propose to use a semiparametric mixed-effects model based on an exploratory analysis of clinical trial data for a study of the relation between virologic responses and immunologic markers such as CD4+ and CD8 counts, and host-specific factors in AIDS clinical trials. The regression spline technique, used for inference for parameters in the model, reduces the unknown nonparametric components to parametric functions. It is simple and straightforward to implement the procedures using readily available software, and parameter inference can be developed from standard parametric models. We apply the model and the proposed method to an AIDS clinical study. Our findings indicate that viral load level is positively related to baseline viral load level, negatively related to CD4+ cell counts, but unrelated to CD8 cell counts and patient's age neither.     

A 30-day-ahead forecast model for grass pollen in north London, United Kingdom

A 30-day-ahead forecast method has been developed for grass pollen in north London. The total period of the grass pollen season is covered by eight multiple regression models, each covering a 10-day period running consecutively from 21 May to 8 August. This means that three models were used for each 30-day forecast. The forecast models were produced using grass pollen and environmental data from 1961 to 1999 and tested on data from 2000 and 2002. Model accuracy was judged in two ways: the number of times the forecast model was able to successfully predict the severity (relative to the 1961–1999 dataset as a whole) of grass pollen counts in each of the eight forecast periods on a scale of 1 to 4; the number of times the forecast model was able to predict whether grass pollen counts were higher or lower than the mean. The models achieved 62.5% accuracy in both assessment years when predicting the relative severity of grass pollen counts on a scale of 1 to 4, which equates to six of the eight 10-day periods being forecast correctly. The models attained 87.5% and 100% accuracy in 2000 and 2002, respectively, when predicting whether grass pollen counts would be higher or lower than the mean. Attempting to predict pollen counts during distinct 10-day periods throughout the grass pollen season is a novel approach. The models also employed original methodology in the use of winter averages of the North Atlantic Oscillation to forecast 10-day means of allergenic pollen counts.     

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.     

A statistical model for under- or overdispersed clustered and longitudinal count data

We propose a likelihood-based model for correlated count data that display under- or overdispersion within units (e.g. subjects). The model is capable of handling correlation due to clustering and/or serial correlation, in the presence of unbalanced, missing or unequally spaced data. A family of distributions based on birth-event processes is used to model within-subject underdispersion. A computational approach is given to overcome a parameterization difficulty with this family, and this allows use of common Markov Chain Monte Carlo software (e.g. WinBUGS) for estimation. Application of the model to daily counts of asthma inhaler use by children shows substantial within-subject underdispersion, between-subject heterogeneity and correlation due to both clustering of measurements within subjects and serial correlation of longitudinal measurements. The model provides a major improvement over Poisson longitudinal models, and diagnostics show that the model fits well.     

Model Diagnostic Plots for Repeated Measures Data

In the analysis of repeated measurements, multivariate regression models that account for the correlations among the observations from the same subject are widely used. Like the usual univariate regression models, these multivariate regression models also need some model diagnostic procedures. Though these models have been widely used, not many studies have been performed in model diagnostic areas. In this paper, we propose simple residual plots to investigate the goodness of model fit for repeated measures data. Here, we mainly focus on the mean model diagnostics. The proposed residual plots are based on the quantile‐quantile(Q–Q) plots of a χ² distribution and a normal distribution. In particular, the proposed model is useful in comparing several models simultaneously. The proposed method is illustrated using two examples. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evaluating the effects of rater and subject factors on measures of association

Large‐scale agreement studies are becoming increasingly common in medical settings to gain better insight into discrepancies often observed between experts' classifications. Ordered categorical scales are routinely used to classify subjects' disease and health conditions. Summary measures such as Cohen's weighted kappa are popular approaches for reporting levels of association for pairs of raters' ordinal classifications. However, in large‐scale studies with many raters, assessing levels of association can be challenging due to dependencies between many raters each grading the same sample of subjects' results and the ordinal nature of the ratings. Further complexities arise when the focus of a study is to examine the impact of rater and subject characteristics on levels of association. In this paper, we describe a flexible approach based upon the class of generalized linear mixed models to assess the influence of rater and subject factors on association between many raters' ordinal classifications. We propose novel model‐based measures for large‐scale studies to provide simple summaries of association similar to Cohen's weighted kappa while avoiding prevalence and marginal distribution issues that Cohen's weighted kappa is susceptible to. The proposed summary measures can be used to compare association between subgroups of subjects or raters. We demonstrate the use of hypothesis tests to formally determine if rater and subject factors have a significant influence on association, and describe approaches for evaluating the goodness‐of‐fit of the proposed model. The performance of the proposed approach is explored through extensive simulation studies and is applied to a recent large‐scale cancer breast cancer screening study.     

Personalized treatment plans with multivariate outcomes

In this work, we propose a novel method for individualized treatment selection when the treatment response is multivariate. Our method covers any number of treatments and it can be applied for a broad set of models. The proposed method uses a Mahalanobis-type distance measure to establish an ordering of treatments based on treatment performance measures. Our investigation in this work deals with means of responses conditional on lower dimensional composite scores based on covariates where these scores are built using single index models to approximate mean responses against patient covariates. Smoothed estimates of such conditional means are combined to construct an estimate of the aforementioned distance measure, which is then used to estimate the optimal treatment. An empirical study demonstrates the performance of the proposed method in finite samples. We also present a data analysis using an HIV clinical trial data to show the applicability of the proposed procedure for real data.     

Penalized estimation of a class of single-index varying-coefficient models for integrative genomic analysis

Recent technological advances have made it possible to collect high-dimensional genomic data along with clinical data on a large number of subjects. In the studies of chronic diseases such as cancer, it is of great interest to integrate clinical and genomic data to build a comprehensive understanding of the disease mechanisms. Despite extensive studies on integrative analysis, it remains an ongoing challenge to model the interaction effects between clinical and genomic variables, due to high dimensionality of the data and heterogeneity across data types. In this paper, we propose an integrative approach that models interaction effects using a single-index varying-coefficient model, where the effects of genomic features can be modified by clinical variables. We propose a penalized approach for separate selection of main and interaction effects. Notably, the proposed methods can be applied to right-censored survival outcomes based on a Cox proportional hazards model. We demonstrate the advantages of the proposed methods through extensive simulation studies and provide applications to a motivating cancer genomic study.     

Impact: Toward a Framework for Understanding the Ecological Effects of Invaders

Although ecologists commonly talk about the impacts of nonindigenous species, little formal attention has been given to defining what we mean by impact, or connecting ecological theory with particular measures of impact. The resulting lack of generalizations regarding invasion impacts is more than an academic problem; we need to be able to distinguish invaders with minor effects from those with large effects in order to prioritize management efforts. This paper focuses on defining, evaluating, and comparing a variety of measures of impact drawn from empirical examples and theoretical reasoning. We begin by arguing that the total impact of an invader includes three fundamental dimensions: range, abundance, and the per-capita or per-biomass effect of the invader. Then we summarize previous approaches to measuring impact at different organizational levels, and suggest some new approaches. Reviewing mathematical models of impact, we argue that theoretical studies using community assembly models could act as a basis for better empirical studies and monitoring programs, as well as provide a clearer understanding of the relationship among different types of impact. We then discuss some of the particular challenges that come from the need to prioritize invasive species in a management or policy context. We end with recommendations about how the field of invasion biology might proceed in order to build a general framework for understanding and predicting impacts. In particular, we advocate studies designed to explore the correlations among different measures: Are the results of complex multivariate methods adequately captured by simple composite metrics such as species richness? How well are impacts on native populations correlated with impacts on ecosystem functions? Are there useful bioindicators for invasion impacts? To what extent does the impact of an invasive species depend on the system in which it is measured? Three approaches would provide new insights in this line of inquiry: (1) studies that measure impacts at multiple scales and multiple levels of organization, (2) studies that synthesize currently available data on different response variables, and (3) models designed to guide empirical work and explore generalities.     

Integer‐valued functional data analysis for measles forecasting

Measles presents a unique and imminent challenge for epidemiologists and public health officials: the disease is highly contagious, yet vaccination rates are declining precipitously in many localities. Consequently, the risk of a measles outbreak continues to rise. To improve preparedness, we study historical measles data both prevaccine and postvaccine, and design new methodology to forecast measles counts with uncertainty quantification. We propose to model the disease counts as an integer‐valued functional time series: measles counts are a function of time‐of‐year and time‐ordered by year. The counts are modeled using a negative‐binomial distribution conditional on a real‐valued latent process, which accounts for the overdispersion observed in the data. The latent process is decomposed using an unknown basis expansion, which is learned from the data, with dynamic basis coefficients. The resulting framework provides enhanced capability to model complex seasonality, which varies dynamically from year‐to‐year, and offers improved multimonth‐ahead point forecasts and substantially tighter forecast intervals (with correct coverage) compared to existing forecasting models. Importantly, the fully Bayesian approach provides well‐calibrated and precise uncertainty quantification for epi‐relevant features, such as the future value and time of the peak measles count in a given year. An R package is available online.     

Geometric constraints and spatial pattern of species richness: critique of range-based null models

Abstract. Does the shape of a biogeographical region influence its spatial patterns of species richness? A complete answer must include careful distinction between the distribution of a species, which is a complex geometric object, and the range of a species, which is relatively simple, especially when reduced to one dimension. We consider range‐based models of species richness, in particular range overlap counts in one dimension, for which we give a unified mathematical treatment via the joint probability P(m,l) of midpoints and lengths of ranges. We discuss a number of difficulties, in practice and in principle, using range‐based models, and show that the so‐called mid‐domain effect, a proposed null model for the effect of geometric constraint, is qualitatively a property of all biologically realistic models based on range overlap counts. As such, range‐based models provide little insight into understanding or explaining biogeographical patterns in species richness. We characterize the quantitative null model for range overlap counts in one dimension, for which we give a simple and direct field test based on P(m,l). We apply this test to a large clade in a complete bioregion (the Proteaceae of the Cape Floristic Region): geometric constraint does not explain the spatial pattern in this case. We show that any geometric constraint on species richness, including range overlap counts, must act via edge effects. Thus, to understand biogeographical patterns, an understanding of the effects and consequences of edges is fundamental.     

Sustainable agriculture and plant diseases: an epidemiological perspective

The potential for modern biology to identify new sources for genetical, chemical and biological control of plant disease is remarkably high. Successful implementation of these methods within globally and locally changing agricultural environments demands new approaches to durable control. This, in turn, requires fusion of population genetics and epidemiology at a range of scales from the field to the landscape and even to continental deployment of control measures. It also requires an understanding of economic and social constraints that influence the deployment of control. Here I propose an epidemiological framework to model invasion, persistence and variability of epidemics that encompasses a wide range of scales and topologies through which disease spreads. By considering how to map control methods onto epidemiological parameters and variables, some new approaches towards optimizing the efficiency of control at the landscape scale are introduced. Epidemiological strategies to minimize the risks of failure of chemical and genetical control are presented and some consequences of heterogeneous selection pressures in time and space on the persistence and evolutionary changes of the pathogen population are discussed. Finally, some approaches towards embedding epidemiological models for the deployment of control in an economically plausible framework are presented.     

Optimal fishery policy: An equilibrium solution with irreversible investment

Optimal fishery policy has been derived using several different models of varying biological realism. Policy has either been assumed to be non-time-varying and static optimization techniques have been applied or dynamic techniques have been used and have in some cases resulted in constant policy. Botsford (1981) showed by applying dynamic optimization techniques to several biologically realistic models (i.e. models that included size structure and either density or food dependent growth and recruitment rates) that the constant policy solution found for simpler, less realistic models was not possible. He concluded that optimal policy was a time-varying, possibly pulse-fishing policy. We show here that when the maximum allowed fishing mortality is low enough a different kind of constant policy is optimal for these realistic models. Interpretation of this condition requires explicit consideration of fixed capital costs in addition to operating costs. Practical considerations indicate that this constant policy would apply only to fisheries with high fixed capital costs.     

A general approach for two-stage analysis of multilevel clustered non-Gaussian data

In this article, we propose a two-stage approach to modeling multilevel clustered non-Gaussian data with sufficiently large numbers of continuous measures per cluster. Such data are common in biological and medical studies utilizing monitoring or image-processing equipment. We consider a general class of hierarchical models that generalizes the model in the global two-stage (GTS) method for nonlinear mixed effects models by using any square-root-n-consistent and asymptotically normal estimators from stage 1 as pseudodata in the stage 2 model, and by extending the stage 2 model to accommodate random effects from multiple levels of clustering. The second-stage model is a standard linear mixed effects model with normal random effects, but the cluster-specific distributions, conditional on random effects, can be non-Gaussian. This methodology provides a flexible framework for modeling not only a location parameter but also other characteristics of conditional distributions that may be of specific interest. For estimation of the population parameters, we propose a conditional restricted maximum likelihood (CREML) approach and establish the asymptotic properties of the CREML estimators. The proposed general approach is illustrated using quartiles as cluster-specific parameters estimated in the first stage, and applied to the data example from a collagen fibril development study. We demonstrate using simulations that in samples with small numbers of independent clusters, the CREML estimators may perform better than conditional maximum likelihood estimators, which are a direct extension of the estimators from the GTS method.     

Incorporating Estimates of Group Size in Sightability Models for Wildlife

ABSTRACT Sightability models have been used to estimate population size of many wildlife species; however, a limitation of these models is an assumption that groups of animals observed and counted during aerial surveys are enumerated completely. Replacing these unknown counts with maximum observed counts, as is typically done, produces population size estimates that are negatively biased. This bias can be substantial depending on the degree of undercounting occurring. We first investigated a method-of-moments estimator of group sizes. We then defined a population size estimator using the method-of-moments estimator of group sizes in place of maximum counts in the traditional sightability models, thereby correcting for bias associated with undercounting group size. We also provide associated equations for calculating the variance of our estimator. This estimator is an improvement over existing sightability model techniques because it significantly reduces bias, and variance estimates provide near nominal confidence interval coverage. The data needed for this estimator can be easily collected and implemented by wildlife managers with a field crew of only 3 individuals and little additional flight or personnel time beyond the normal requirements for developing sightability models.     

Two criteria for evaluating risk prediction models

Summary We propose and study two criteria to assess the usefulness of models that predict risk of disease incidence for screening and prevention, or the usefulness of prognostic models for management following disease diagnosis. The first criterion, the proportion of cases followed PCF (q) , is the proportion of individuals who will develop disease who are included in the proportion q of individuals in the population at highest risk. The second criterion is the proportion needed to follow‐up, PNF (p) , namely the proportion of the general population at highest risk that one needs to follow in order that a proportion p of those destined to become cases will be followed. PCF (q) assesses the effectiveness of a program that follows 100q % of the population at highest risk. PNF (p) assess the feasibility of covering 100p % of cases by indicating how much of the population at highest risk must be followed. We show the relationship of those two criteria to the Lorenz curve and its inverse, and present distribution theory for estimates of PCF and PNF. We develop new methods, based on influence functions, for inference for a single risk model, and also for comparing the PCFs and PNFs of two risk models, both of which were evaluated in the same validation data.     

A coefficient of determination (R2) for generalized linear mixed models

Extensions of linear models are very commonly used in the analysis of biological data. Whereas goodness of fit measures such as the coefficient of determination (R²) or the adjusted R² are well established for linear models, it is not obvious how such measures should be defined for generalized linear and mixed models. There are by now several proposals but no consensus has yet emerged as to the best unified approach in these settings. In particular, it is an open question how to best account for heteroscedasticity and for covariance among observations present in residual error or induced by random effects. This paper proposes a new approach that addresses this issue and is universally applicable for arbitrary variance‐covariance structures including spatial models and repeated measures. It is exemplified using three biological examples.