Effects of Political Instability in Venezuela on Malaria Resurgence at Ecuador-Peru Border, 2018.

Mass migration from Venezuela has increased malaria resurgence risk across South America. During 2018, migrants from Venezuela constituted 96% of imported malaria cases along the Ecuador-Peru border. Plasmodium vivax predominated (96%). Autochthonous malaria cases emerged in areas previously malaria-free. Heightened malaria control and a response to this humanitarian crisis are imperative.

A Bayesian random partition model for sequential refinement and coagulation.

We analyze time-course protein activation data to track the changes in protein expression over time after exposure to drugs such as protein inhibitors. Protein expression is expected to change over time in response to the intervention in different ways due to biological pathways. We therefore allow for clusters of proteins with different treatment effects, and allow these clusters to change over time. As the effect of the drug wears off, protein expression may revert back to the level before treatment. In addition, different drugs, doses, and cell lines may have different effects in altering the protein expression. To model and understand this process we develop random partitions that define a refinement and coagulation of protein clusters over time. We demonstrate the approach using a time-course reverse phase protein array (RPPA) dataset consisting of protein expression measurements under different drugs, dose levels, and cell lines. The proposed model can be applied in general to time-course data where clustering of the experimental units is expected to change over time in a sequence of refinement and coagulation.

Bayesian inference for longitudinal data with non-parametric treatment effects.

We consider inference for longitudinal data based on mixed-effects models with a non-parametric Bayesian prior on the treatment effect. The proposed non-parametric Bayesian prior is a random partition model with a regression on patient-specific covariates. The main feature and motivation for the proposed model is the use of covariates with a mix of different data formats and possibly high-order interactions in the regression. The regression is not explicitly parameterized. It is implied by the random clustering of subjects. The motivating application is a study of the effect of an anticancer drug on a patient's blood pressure. The study involves blood pressure measurements taken periodically over several 24-h periods for 54 patients. The 24-h periods for each patient include a pretreatment period and several occasions after the start of therapy.

On species sampling sequences induced by residual allocation models.

We discuss fully Bayesian inference in a class of species sampling models that are induced by residual allocation (sometimes called stick-breaking) priors on almost surely discrete random measures. This class provides a generalization of the well-known Ewens sampling formula that allows for additional flexibility while retaining computational tractability. In particular, the procedure is used to derive the exchangeable predictive probability functions associated with the generalized Dirichlet process of Hjort (2000) and the probit stick-breaking prior of Chung and Dunson (2009) and Rodriguez and Dunson (2011). The procedure is illustrated with applications to genetics and nonparametric mixture modeling.

Defining Predictive Probability Functions for Species Sampling Models.

We review the class of species sampling models (SSM). In particular, we investigate the relation between the exchangeable partition probability function (EPPF) and the predictive probability function (PPF). It is straightforward to define a PPF from an EPPF, but the converse is not necessarily true. In this paper we introduce the notion of putative PPFs and show novel conditions for a putative PPF to define an EPPF. We show that all possible PPFs in a certain class have to define (unnormalized) probabilities for cluster membership that are linear in cluster size. We give a new necessary and sufficient condition for arbitrary putative PPFs to define an EPPF. Finally, we show posterior inference for a large class of SSMs with a PPF that is not linear in cluster size and discuss a numerical method to derive its PPF.

DPpackage: Bayesian Non- and Semi-parametric Modelling in R.

Data analysis sometimes requires the relaxation of parametric assumptions in order to gain modeling flexibility and robustness against mis-specification of the probability model. In the Bayesian context, this is accomplished by placing a prior distribution on a function space, such as the space of all probability distributions or the space of all regression functions. Unfortunately, posterior distributions ranging over function spaces are highly complex and hence sampling methods play a key role. This paper provides an introduction to a simple, yet comprehensive, set of programs for the implementation of some Bayesian non- and semi-parametric models in R, DPpackage. Currently DPpackage includes models for marginal and conditional density estimation, ROC curve analysis, interval-censored data, binary regression data, item response data, longitudinal and clustered data using generalized linear mixed models, and regression data using generalized additive models. The package also contains functions to compute pseudo-Bayes factors for model comparison, and for eliciting the precision parameter of the Dirichlet process prior. To maximize computational efficiency, the actual sampling for each model is carried out using compiled FORTRAN.

Logistic regression when covariates are random effects from a non-linear mixed model.

In many studies, the association of longitudinal measurements of a continuous response and a binary outcome are often of interest. A convenient framework for this type of problems is the joint model, which is formulated to investigate the association between a binary outcome and features of longitudinal measurements through a common set of latent random effects. The joint model, which is the focus of this article, is a logistic regression model with covariates defined as the individual-specific random effects in a non-linear mixed-effects model (NLMEM) for the longitudinal measurements. We discuss different estimation procedures, which include two-stage, best linear unbiased predictors, and various numerical integration techniques. The proposed methods are illustrated using a real data set where the objective is to study the association between longitudinal hormone levels and the pregnancy outcome in a group of young women. The numerical performance of the estimating methods is also evaluated by means of simulation.

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

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.

Bayesian Nonparametric Longitudinal Data Analysis.

Practical Bayesian nonparametric methods have been developed across a wide variety of contexts. Here, we develop a novel statistical model that generalizes standard mixed models for longitudinal data that include flexible mean functions as well as combined compound symmetry (CS) and autoregressive (AR) covariance structures. AR structure is often specified through the use of a Gaussian process (GP) with covariance functions that allow longitudinal data to be more correlated if they are observed closer in time than if they are observed farther apart. We allow for AR structure by considering a broader class of models that incorporates a Dirichlet Process Mixture (DPM) over the covariance parameters of the GP. We are able to take advantage of modern Bayesian statistical methods in making full predictive inferences and about characteristics of longitudinal profiles and their differences across covariate combinations. We also take advantage of the generality of our model, which provides for estimation of a variety of covariance structures. We observe that models that fail to incorporate CS or AR structure can result in very poor estimation of a covariance or correlation matrix. In our illustration using hormone data observed on women through the menopausal transition, biology dictates the use of a generalized family of sigmoid functions as a model for time trends across subpopulation categories.

A Simple Class of Bayesian Nonparametric Autoregression Models.

We introduce a model for a time series of continuous outcomes, that can be expressed as fully nonparametric regression or density regression on lagged terms. The model is based on a dependent Dirichlet process prior on a family of random probability measures indexed by the lagged covariates. The approach is also extended to sequences of binary responses. We discuss implementation and applications of the models to a sequence of waiting times between eruptions of the Old Faithful Geyser, and to a dataset consisting of sequences of recurrence indicators for tumors in the bladder of several patients.

Semi-parametric Bayesian Inference for Multi-Season Baseball Data.

We analyze complete sequences of successes (hits, walks, and sacrifices) for a group of players from the American and National Leagues, collected over 4 seasons. The goal is to describe how players' performances vary from season to season. In particular, we wish to assess and compare the effect of available occasion-specific covariates over seasons. The data are binary sequences for each player and each season. We model dependence in the binary sequence by an autoregressive logistic model. The model includes lagged terms up to a fixed order. For each player and season we introduce a different set of autologistic regression coefficients, i.e., the regression coefficients are random effects that are specific to each season and player. We use a nonparametric approach to define a random effects distribution. The nonparametric model is defined as a mixture with a Dirichlet process prior for the mixing measure. The described model is justified by a representation theorem for order-k exchangeable sequences. Besides the repeated measurements for each season and player, multiple seasons within a given player define an additional level of repeated measurements. We introduce dependence at this level of repeated measurements by relating the season-specific random effects vectors in an autoregressive fashion. We ultimately conclude that while some covariates like the ERA of the opposing pitcher are always relevant, others like an indicator for the game being into the seventh inning may be significant only for certain seasons, and some others, like the score of the game, can safely be ignored.

A Semiparametric Bayesian Model for Repeatedly Repeated Binary Outcomes.

We discuss the analysis of data from single nucleotide polymorphism (SNP) arrays comparing tumor and normal tissues. The data consist of sequences of indicators for loss of heterozygosity (LOH) and involve three nested levels of repetition: chromosomes for a given patient, regions within chromosomes, and SNPs nested within regions. We propose to analyze these data using a semiparametric model for multi-level repeated binary data. At the top level of the hierarchy we assume a sampling model for the observed binary LOH sequences that arises from a partial exchangeability argument. This implies a mixture of Markov chains model. The mixture is defined with respect to the Markov transition probabilities. We assume a nonparametric prior for the random mixing measure. The resulting model takes the form of a semiparametric random effects model with the matrix of transition probabilities being the random effects. The model includes appropriate dependence assumptions for the two remaining levels of the hierarchy, i.e., for regions within chromosomes and for chromosomes within patient. We use the model to identify regions of increased LOH in a dataset coming from a study of treatment-related leukemia in children with an initial cancer diagnostic. The model successfully identifies the desired regions and performs well compared to other available alternatives.

A model-based approach to Bayesian classification with applications to predicting pregnancy outcomes from longitudinal beta-hCG profiles.

This paper discusses Bayesian statistical methods for the classification of observations into two or more groups based on hierarchical models for nonlinear longitudinal profiles. Parameter estimation for a discriminant model that classifies individuals into distinct predefined groups or populations uses appropriate posterior simulation schemes. The methods are illustrated with data from a study involving 173 pregnant women. The main objective in this study is to predict normal versus abnormal pregnancy outcomes from beta human chorionic gonadotropin data available at early stages of pregnancy.

Semiparametric bayesian inference for multilevel repeated measurement data.

We discuss inference for data with repeated measurements at multiple levels. The motivating example is data with blood counts from cancer patients undergoing multiple cycles of chemotherapy, with days nested within cycles. Some inference questions relate to repeated measurements over days within cycle, while other questions are concerned with the dependence across cycles. When the desired inference relates to both levels of repetition, it becomes important to reflect the data structure in the model. We develop a semiparametric Bayesian modeling approach, restricting attention to two levels of repeated measurements. For the top-level longitudinal sampling model we use random effects to introduce the desired dependence across repeated measurements. We use a nonparametric prior for the random effects distribution. Inference about dependence across second-level repetition is implemented by the clustering implied in the nonparametric random effects model. Practical use of the model requires that the posterior distribution on the latent random effects be reasonably precise.

Semiparametric Bayesian classification with longitudinal markers.

We analyse data from a study involving 173 pregnant women. The data are observed values of the ß human chorionic gonadotropin hormone measured during the first 80 days of gestational age, including from one up to six longitudinal responses for each woman. The main objective in this study is to predict normal versus abnormal pregnancy outcomes from data that are available at the early stages of pregnancy. We achieve the desired classification with a semiparametric hierarchical model. Specifically, we consider a Dirichlet process mixture prior for the distribution of the random effects in each group. The unknown random-effects distributions are allowed to vary across groups but are made dependent by using a design vector to select different features of a single underlying random probability measure. The resulting model is an extension of the dependent Dirichlet process model, with an additional probability model for group classification. The model is shown to perform better than an alternative model which is based on independent Dirichlet processes for the groups. Relevant posterior distributions are summarized by using Markov chain Monte Carlo methods.