Bayesian Inference for Functional Response in a Stochastic Predator–Prey System

We present a Bayesian method for functional response parameter estimation starting from time series of field data on predator–prey dynamics. Population dynamics is described by a system of stochastic differential equations in which behavioral stochasticities are represented by noise terms affecting each population as well as their interaction. We focus on the estimation of a behavioral parameter appearing in the functional response of predator to prey abundance when a small number of observations is available. To deal with small sample sizes, latent data are introduced between each pair of field observations and are considered as missing data. The method is applied to both simulated and observational data. The results obtained using different numbers of latent data are compared with those achieved following a frequentist approach. As a case study, we consider an acarine predator–prey system relevant to biological control problems.     

A semiparametric transition model with latent traits for longitudinal multistate data

SUMMARY: We propose a general multistate transition model. The model is developed for the analysis of repeated episodes of multiple states representing different health status. Transitions among multiple states are modeled jointly using multivariate latent traits with factor loadings. Different types of state transition are described by flexible transition-specific nonparametric baseline intensities. A state-specific latent trait is used to capture individual tendency of the sojourn in the state that cannot be explained by covariates and to account for correlation among repeated sojourns in the same state within an individual. Correlation among sojourns across different states within an individual is accounted for by the correlation between the different latent traits. The factor loadings for a latent trait accommodate the dependence of the transitions to different competing states from a same state. We obtain the semiparametric maximum likelihood estimates through an expectation-maximization (EM) algorithm. The method is illustrated by studying repeated transitions between independence and disability states of activities of daily living (ADL) with death as an absorbing state in a longitudinal aging study. The performance of the estimation procedure is assessed by simulation studies.     

Evaluating the association between latent classes and competing risks outcomes with multiphenotype data

Latent class analysis is an intuitive tool to characterize disease phenotype heterogeneity. With data more frequently collected on multiple phenotypes in chronic disease studies, it is of rising interest to investigate how the latent classes embedded in one phenotype are related to another phenotype. Motivated by a cohort with mild cognitive impairment (MCI) from the Uniform Data Set (UDS), we propose and study a time-dependent structural model to evaluate the association between latent classes and competing risk outcomes that are subject to missing failure types. We develop a two-step estimation procedure which circumvents latent class membership assignment and is rigorously justified in terms of accounting for the uncertainty in classifying latent classes. The new method also properly addresses the realistic complications for competing risks outcomes, including random censoring and missing failure types. The asymptotic properties of the resulting estimator are established. Given that the standard bootstrapping inference is not feasible in the current problem setting, we develop analytical inference procedures, which are easy to implement. Our simulation studies demonstrate the advantages of the proposed method over benchmark approaches. We present an application to the MCI data from UDS, which uncovers a detailed picture of the neuropathological relevance of the baseline MCI subgroups.     

Estimating equations for a latent transition model with multiple discrete indicators

This paper proposes a two-part model for studying transitions between health states over time when multiple, discrete health indicators are available. The includes a measurement model positing underlying latent health states and a transition model between latent health states over time. Full maximum likelihood estimation procedures are computationally complex in this latent variable framework, making only a limited class of models feasible and estimation of standard errors problematic. For this reason, an estimating equations analogue of the pseudo-likelihood method for the parameters of interest, namely the transition model parameters, is considered. The finite sample properties of the proposed procedure are investigated through a simulation study and the importance of choosing strong indicators of the latent variable is demonstrated. The applicability of the methodology is illustrated with health survey data measuring disability in the elderly from the Longitudinal Study of Aging.     

Joint modeling and analysis of longitudinal data with informative observation times

Summary .  In analysis of longitudinal data, it is often assumed that observation times are predetermined and are the same across study subjects. Such an assumption, however, is often violated in practice. As a result, the observation times may be highly irregular. It is well known that if the sampling scheme is correlated with the outcome values, the usual statistical analysis may yield bias. In this article, we propose joint modeling and analysis of longitudinal data with possibly informative observation times via latent variables. A two-step estimation procedure is developed for parameter estimation. We show that the resulting estimators are consistent and asymptotically normal, and that the asymptotic variance can be consistently estimated using the bootstrap method. Simulation studies and a real data analysis demonstrate that our method performs well with realistic sample sizes and is appropriate for practical use.     

CODEX: a normalization and copy number variation detection method for whole exome sequencing

High-throughput sequencing of DNA coding regions has become a common way of assaying genomic variation in the study of human diseases. Copy number variation (CNV) is an important type of genomic variation, but detecting and characterizing CNV from exome sequencing is challenging due to the high level of biases and artifacts. We propose CODEX, a normalization and CNV calling procedure for whole exome sequencing data. The Poisson latent factor model in CODEX includes terms that specifically remove biases due to GC content, exon capture and amplification efficiency, and latent systemic artifacts. CODEX also includes a Poisson likelihood-based recursive segmentation procedure that explicitly models the count-based exome sequencing data. CODEX is compared to existing methods on a population analysis of HapMap samples from the 1000 Genomes Project, and shown to be more accurate on three microarray-based validation data sets. We further evaluate performance on 222 neuroblastoma samples with matched normals and focus on a well-studied rare somatic CNV within the ATRX gene. We show that the cross-sample normalization procedure of CODEX removes more noise than normalizing the tumor against the matched normal and that the segmentation procedure performs well in detecting CNVs with nested structures.     

Identification of causal effects with latent confounding and classical additive errors in treatment

In this paper, we discuss the identifiability and estimation of causal effects of a continuous treatment on a binary response when the treatment is measured with errors and there exists a latent categorical confounder associated with both treatment and response. Under some widely used parametric models, we first discuss the identifiability of the causal effects and then propose an approach for estimation and inference. Our approach can eliminate the biases induced by latent confounding and measurement errors by using only a single instrumental variable. Based on the identification results, we give guidelines for determining the existence of a latent categorical confounder and for selecting the number of levels of the latent confounder. We apply the proposed approach to a data set from the Framingham Heart Study to evaluate the effect of the systolic blood pressure on the coronary heart disease.     

Additive mixed effect model for clustered failure time data

We propose an additive mixed effect model to analyze clustered failure time data. The proposed model assumes an additive structure and includes a random effect as an additional component. Our model imitates the commonly used mixed effect models in repeated measurement analysis but under the context of hazards regression; our model can also be considered as a parallel development of the gamma-frailty model in additive model structures. We develop estimating equations for parameter estimation and propose a way of assessing the distribution of the latent random effect in the presence of large clusters. We establish the asymptotic properties of the proposed estimator. The small sample performance of our method is demonstrated via a large number of simulation studies. Finally, we apply the proposed model to analyze data from a diabetic study and a treatment trial for congestive heart failure.     

Estimation of false discovery proportion under general dependence

MOTIVATION: Wide-scale correlations between genes are commonly observed in gene expression data, due to both biological and technical reasons. These correlations increase the variability of the standard estimate of the false discovery rate (FDR). We highlight the false discovery proportion (FDP, instead of the FDR) as the suitable quantity for assessing differential expression in microarray data, demonstrate the deleterious effects of correlation on FDP estimation and propose an improved estimation method that accounts for the correlations. METHODS: We analyse the variation pattern of the distribution of test statistics under permutation using the singular value decomposition. The results suggest a latent FDR model that accounts for the effects of correlation, and is statistically closer to the FDP. We develop a procedure for estimating the latent FDR (ELF) based on a Poisson regression model. RESULTS: For simulated data based on the correlation structure of real datasets, we find that ELF performs substantially better than the standard FDR approach in estimating the FDP. We illustrate the use of ELF in the analysis of breast cancer and lymphoma data. AVAILABILITY: R code to perform ELF is available in http://www.meb.ki.se/~yudpaw.     

A longitudinal measurement error model with a semicontinuous covariate

Covariate measurement error in regression is typically assumed to act in an additive or multiplicative manner on the true covariate value. However, such an assumption does not hold for the measurement error of sleep-disordered breathing (SDB) in the Wisconsin Sleep Cohort Study (WSCS). The true covariate is the severity of SDB, and the observed surrogate is the number of breathing pauses per unit time of sleep, which has a nonnegative semicontinuous distribution with a point mass at zero. We propose a latent variable measurement error model for the error structure in this situation and implement it in a linear mixed model. The estimation procedure is similar to regression calibration but involves a distributional assumption for the latent variable. Modeling and model-fitting strategies are explored and illustrated through an example from the WSCS.     

Structural time series models with feedback mechanisms

Structural time series models have applications in many different fields such as biology, economics, and meteorology. A structural times series model can be represented as a state-space model where the states of the system represent the unobserved components and the structural parameters have clear interpretations. This paper introduces a class of structural time series models that incorporate feedback from the latent components of the history. An iterative procedure is proposed for estimation. These models allow flexible and robust feedback mechanisms, have clear interpretations, and have a computationally efficient estimation procedure. They are applied to hormone data to characterize hormone secretion and to explore a potential feedback mechanism.     

A general class of pattern mixture models for nonignorable dropout with many possible dropout times

Summary .   In this article we consider the problem of fitting pattern mixture models to longitudinal data when there are many unique dropout times. We propose a marginally specified latent class pattern mixture model. The marginal mean is assumed to follow a generalized linear model, whereas the mean conditional on the latent class and random effects is specified separately. Because the dimension of the parameter vector of interest (the marginal regression coefficients) does not depend on the assumed number of latent classes, we propose to treat the number of latent classes as a random variable. We specify a prior distribution for the number of classes, and calculate (approximate) posterior model probabilities. In order to avoid the complications with implementing a fully Bayesian model, we propose a simple approximation to these posterior probabilities. The ideas are illustrated using data from a longitudinal study of depression in HIV-infected women.     

Latent group detection in functional partially linear regression models

In this paper, we propose a functional partially linear regression model with latent group structures to accommodate the heterogeneous relationship between a scalar response and functional covariates. The proposed model is motivated by a salinity tolerance study of barley families, whose main objective is to detect salinity tolerant barley plants. Our model is flexible, allowing for heterogeneous functional coefficients while being efficient by pooling information within a group for estimation. We develop an algorithm in the spirit of the K-means clustering to identify latent groups of the subjects under study. We establish the consistency of the proposed estimator, derive the convergence rate and the asymptotic distribution, and develop inference procedures. We show by simulation studies that the proposed method has higher accuracy for recovering latent groups and for estimating the functional coefficients than existing methods. The analysis of the barley data shows that the proposed method can help identify groups of barley families with different salinity tolerant abilities.     

Multilevel Latent Class Models with Dirichlet Mixing Distribution

Summary Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social science and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this article, we consider multilevel latent class models, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the expectation‐maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less‐efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the obsessive compulsive disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for LCA of multilevel data.     

Latent multinomial models for extended batch-mark data

Batch marking is common and useful for many capture–recapture studies where individual marks cannot be applied due to various constraints such as timing, cost, or marking difficulty. When batch marks are used, observed data are not individual capture histories but a set of counts including the numbers of individuals first marked, marked individuals that are recaptured, and individuals captured but released without being marked (applicable to some studies) on each capture occasion. Fitting traditional capture–recapture models to such data requires one to identify all possible sets of capture–recapture histories that may lead to the observed data, which is computationally infeasible even for a small number of capture occasions. In this paper, we propose a latent multinomial model to deal with such data, where the observed vector of counts is a non-invertible linear transformation of a latent vector that follows a multinomial distribution depending on model parameters. The latent multinomial model can be fitted efficiently through a saddlepoint approximation based maximum likelihood approach. The model framework is very flexible and can be applied to data collected with different study designs. Simulation studies indicate that reliable estimation results are obtained for all parameters of the proposed model. We apply the model to analysis of golden mantella data collected using batch marks in Central Madagascar.     

Estimating linear causality in the presence of latent variables

Learning causality from data is known as the causal discovery problem, and it is an important and relatively new field. In many applications, there often exist latent variables, if such latent variables are completely ignored, which can lead to the estimation results seriously biased. In this paper, a method of combining exploratory factor analysis and path analysis (EFA-PA) is proposed to infer the causality in the presence of latent variables. Our method expands latent variables as well as their linear causal relationships with observed variables, which enhances the accuracy of causal models. Such model can be thought of as the simplest possible causal models for continuous data. The EFA-PA is very similar to that of structural equation model, but the theoretical model established by the structural equation model needs to be modified in the process of data fitting until the ideal model is established.The model gained by EFA-PA not only avoids subjectivity but also reduces estimation complexity. It is found that the EFA-PA estimation model is superior to the other models. EFA-PA can provides a basis for the correct estimation of the causal relationship between the observed variables in the presence of latent variables. The experiment shows that EFA-PA is better than the structural equation model.     

Latent class models for joint analysis of disease prevalence and high-dimensional semicontinuous biomarker data

High-dimensional biomarker data are often collected in epidemiological studies when assessing the association between biomarkers and human disease is of interest. We develop a latent class modeling approach for joint analysis of high-dimensional semicontinuous biomarker data and a binary disease outcome. To model the relationship between complex biomarker expression patterns and disease risk, we use latent risk classes to link the 2 modeling components. We characterize complex biomarker-specific differences through biomarker-specific random effects, so that different biomarkers can have different baseline (low-risk) values as well as different between-class differences. The proposed approach also accommodates data features that are common in environmental toxicology and other biomarker exposure data, including a large number of biomarkers, numerous zero values, and complex mean-variance relationship in the biomarkers levels. A Monte Carlo EM (MCEM) algorithm is proposed for parameter estimation. Both the MCEM algorithm and model selection procedures are shown to work well in simulations and applications. In applying the proposed approach to an epidemiological study that examined the relationship between environmental polychlorinated biphenyl (PCB) exposure and the risk of endometriosis, we identified a highly significant overall effect of PCB concentrations on the risk of endometriosis.     

Likelihood methods for treatment noncompliance and subsequent nonresponse in randomized trials

While several new methods that account for noncompliance or missing data in randomized trials have been proposed, the dual effects of noncompliance and nonresponse are rarely dealt with simultaneously. We construct a maximum likelihood estimator (MLE) of the causal effect of treatment assignment for a two-armed randomized trial assuming all-or-none treatment noncompliance and allowing for subsequent nonresponse. The EM algorithm is used for parameter estimation. Our likelihood procedure relies on a latent compliance state covariate that describes the behavior of a subject under all possible treatment assignments and characterizes the missing data mechanism as in Frangakis and Rubin (1999, Biometrika 86, 365-379). Using simulated data, we show that the MLE for normal outcomes compares favorably to the method-of-moments (MOM) and the standard intention-to-treat (ITT) estimators under (1) both normal and non-normal data, and (2) departures from the latent ignorability and compound exclusion restriction assumptions. We illustrate methods using data from a trial to compare the efficacy of two antipsychotics for adults with refractory schizophrenia.     

Bayesian variable selection for latent class models

In this article, we develop a latent class model with class probabilities that depend on subject-specific covariates. One of our major goals is to identify important predictors of latent classes. We consider methodology that allows estimation of latent classes while allowing for variable selection uncertainty. We propose a Bayesian variable selection approach and implement a stochastic search Gibbs sampler for posterior computation to obtain model-averaged estimates of quantities of interest such as marginal inclusion probabilities of predictors. Our methods are illustrated through simulation studies and application to data on weight gain during pregnancy, where it is of interest to identify important predictors of latent weight gain classes.     

Optimal designs for a multiresponse Emax model and efficient parameter estimation

The aim of dose finding studies is sometimes to estimate parameters in a fitted model. The precision of the parameter estimates should be as high as possible. This can be obtained by increasing the number of subjects in the study, N, choosing a good and efficient estimation approach, and by designing the dose finding study in an optimal way. Increasing the number of subjects is not always feasible because of increasing cost, time limitations, etc. In this paper, we assume fixed N and consider estimation approaches and study designs for multiresponse dose finding studies. We work with diabetes dose–response data and compare a system estimation approach that fits a multiresponse Emax model to the data to equation‐by‐equation estimation that fits uniresponse Emax models to the data. We then derive some optimal designs for estimating the parameters in the multi‐ and uniresponse Emax model and study the efficiency of these designs.