Discovering novel cancer bio-markers in acquired lapatinib resistance using Bayesian methods.

Signalling transduction pathways (STPs) are commonly hijacked by many cancers for their growth and malignancy, but demystifying their underlying mechanisms is difficult. Here, we developed methodologies with a fully Bayesian approach in discovering novel driver bio-markers in aberrant STPs given high-throughput gene expression (GE) data. This project, namely 'PathTurbEr' (Pathway Perturbation Driver) uses the GE dataset derived from the lapatinib (an EGFR/HER dual inhibitor) sensitive and resistant samples from breast cancer cell lines (SKBR3). Differential expression analysis revealed 512 differentially expressed genes (DEGs) and their pathway enrichment revealed 13 highly perturbed singalling pathways in lapatinib resistance, including PI3K-AKT, Chemokine, Hippo and TGF-$\beta $ singalling pathways. Next, the aberration in TGF-$\beta $ STP was modelled as a causal Bayesian network (BN) using three MCMC sampling methods, i.e. Neighbourhood sampler (NS) and Hit-and-Run (HAR) sampler that potentially yield robust inference with lower chances of getting stuck at local optima and faster convergence compared to other state-of-art methods. Next, we examined the structural features of the optimal BN as a statistical process that generates the global structure using $p_1$-model, a special class of Exponential Random Graph Models (ERGMs), and MCMC methods for their hyper-parameter sampling. This step enabled key drivers identification that drive the aberration within the perturbed BN structure of STP, and yielded 34, 34 and 23 perturbation driver genes out of 80 constituent genes of three perturbed STP models of TGF-$\beta $ signalling inferred by NS, HAR and MH sampling methods, respectively. Functional-relevance and disease-relevance analyses suggested their significant associations with breast cancer progression/resistance.

A joint model for multivariate longitudinal and survival data to discover the conversion to Alzheimer's disease.

Alzheimer's disease (AD) is an incurable and progressive disease that starts from mild cognitive impairment and deteriorates over time. Examining the effects of patients' longitudinal cognitive decline on time to conversion to AD and obtaining a reliable diagnostic model are therefore critical to the evaluation of AD prognosis and early treatment. Previous studies either assess patients' cognitive impairment through a single cognitive test or assume it changes linearly across time, thereby leading to an incomplete measure of cognitive decline or overlooking the subtle trajectory pattern of patients' cognitive impairment. This study develops a new joint model to address these shortcomings. First, a dynamic factor analysis model is adopted to characterize cognitive impairment through multiple cognitive measures in a comprehensive manner. Second, a spline-based random coefficient model is proposed to reveal possibly nonlinear trajectories of patients' cognitive decline. Finally, a proportional hazard model is considered to examine the effects of time-invariant markers and time-variant cognitive impairment on AD hazards. A Bayesian approach coupled with spline approximation techniques and MCMC methods is developed to conduct statistical inference. The application of the proposed method to the Alzheimer's Disease Neuroimaging Initiative study provides new insights into the prevention of AD and shows a high prediction capacity of the proposed method.

Bayesian analysis under accelerated failure time models with error-prone time-to-event outcomes.

We consider accelerated failure time models with error-prone time-to-event outcomes. The proposed models extend the conventional accelerated failure time model by allowing time-to-event responses to be subject to measurement errors. We describe two measurement error models, a logarithm transformation regression measurement error model and an additive error model with a positive increment, to delineate possible scenarios of measurement error in time-to-event outcomes. We develop Bayesian approaches to conduct statistical inference. Efficient Markov chain Monte Carlo algorithms are developed to facilitate the posterior inference. Extensive simulation studies are conducted to assess the performance of the proposed method, and an application to a study of Alzheimer's disease is presented.

A Bayesian Mixture Cure Rate Model for Estimating Short-Term and Long-Term Recidivism.

Mixture cure rate models have been developed to analyze failure time data where a proportion never fails. For such data, standard survival models are usually not appropriate because they do not account for the possibility of non-failure. In this context, mixture cure rate models assume that the studied population is a mixture of susceptible subjects who may experience the event of interest and non-susceptible subjects that will never experience it. More specifically, mixture cure rate models are a class of survival time models in which the probability of an eventual failure is less than one and both the probability of eventual failure and the timing of failure depend (separately) on certain individual characteristics. In this paper, we propose a Bayesian approach to estimate parametric mixture cure rate models with covariates. The probability of eventual failure is estimated using a binary regression model, and the timing of failure is determined using a Weibull distribution. Inference for these models is attained using Markov Chain Monte Carlo methods under the proposed Bayesian framework. Finally, we illustrate the method using data on the return-to-prison time for a sample of prison releases of men convicted of sexual crimes against women in England and Wales and we use mixture cure rate models to investigate the risk factors for long-term and short-term survival of recidivism.

Bayesian latent factor on image regression with nonignorable missing data.

Medical imaging data have been widely used in modern health care, particularly in the prognosis, screening, diagnosis, and treatment of various diseases. In this study, we consider a latent factor-on-image (LoI) regression model that regresses a latent factor on ultrahigh dimensional imaging covariates. The latent factor is characterized by multiple manifest variables through a factor analysis model, while the manifest variables are subject to nonignorable missingness. We propose a two-stage approach for statistical inference. At the first stage, an efficient functional principal component analysis method is applied to reduce the dimension and extract useful features/eigenimages. At the second stage, a factor analysis mode is proposed to characterize the latent response variable. Moreover, an LoI model is used to detect influential risk factors, and an exponential tiling model applied to accommodate nonignoreable nonresponses. A fully Bayesian method with an adjust spike-and-slab absolute shrinkage and selection operator (lasso) procedure is developed for the estimation and selection of influential features/eigenimages. Simulation studies show the proposed method exhibits satisfactory performance. The proposed methodology is applied to a study on the Alzheimer's Disease Neuroimaging Initiative data set.

The influence of the correlation-covariance structure of measurement errors over uncertainties propagation in online monitoring: application to environmental indicators in SUDS.

This paper presents a methodology to assess the influence of the correlation-covariance structure of measurement errors in online monitoring over the propagation of uncertainties, applied to wet-weather environmental indicators in sustainable urban drainage systems (SUDSs). The effect of auto-correlated and heteroskedastic errors in measured time-series over the estimated probability density function (PDF) of different environmental indicators is analyzed for a wide variety of possible error structures in the data. For this purpose, multiple correlation-covariance structures are randomly generated from exploring the parametric space of a linear exponent autoregressive (LEAR) model, employing a Bayesian-based Markov Chain Monte Carlo sampling technique. Significant differences tests are proposed to identify the most correlated parameters of the correlation-covariance error model with statistics of the environmental indicator PDFs. The method is applied to total suspended solids (TSS) and chemical oxygen demand (COD) time-series recorded during 13 rainfall events at the inlet and outlet of a SUDS train (stormwater settling tank-horizontal constructed wetland). In this case, results showed that the total error in the estimation of the analyzed environmental indicators is mostly explained by standard uncertainties (flattening of the PDFs) rather than bias contributions (displacement of the PDFs). The correlation-covariance model parameters related to the temporal delimitation of hydrographs/pollutographs and the intensity of the autocorrelation showed to have the strongest influence in the propagation of measurement errors (flattening/displacement of the PDFs).

A Bayesian multi-risks survival (MRS) model in the presence of double censorings.

Semi-competing risks data include the time to a nonterminating event and the time to a terminating event, while competing risks data include the time to more than one terminating event. Our work is motivated by a prostate cancer study, which has one nonterminating event and two terminating events with both semi-competing risks and competing risks present as well as two censoring times. In this paper, we propose a new multi-risks survival (MRS) model for this type of data. In addition, the proposed MRS model can accommodate noninformative right-censoring times for nonterminating and terminating events. Properties of the proposed MRS model are examined in detail. Theoretical and empirical results show that the estimates of the cumulative incidence function for a nonterminating event may be biased if the information on a terminating event is ignored. A Markov chain Monte Carlo sampling algorithm is also developed. Our methodology is further assessed using simulations and also an analysis of the real data from a prostate cancer study. As a result, a prostate-specific antigen velocity greater than 2.0 ng/mL per year and higher biopsy Gleason scores are positively associated with a shorter time to death due to prostate cancer.

Bayesian adaptive lasso for additive hazard regression with current status data.

Variable selection is a crucial issue in model building and it has received considerable attention in the literature of survival analysis. However, available approaches in this direction have mainly focused on time-to-event data with right censoring. Moreover, a majority of existing variable selection procedures for survival models are developed in a frequentist framework. In this article, we consider additive hazards model in the presence of current status data. We propose a Bayesian adaptive least absolute shrinkage and selection operator procedure to conduct a simultaneous variable selection and parameter estimation. Efficient Markov chain Monte Carlo methods are developed to implement posterior sampling and inference. The empirical performance of the proposed method is demonstrated by simulation studies. An application to a study on the risk factors of heart failure disease for type 2 diabetes patients is presented.

Bayesian semiparametric failure time models for multivariate censored data with latent variables.

In this paper, we propose a semiparametric failure time model to analyze multivariate censored data with latent variables. The proposed model generalizes the conventional accelerated failure time model to accommodate latent risk factors that could be measured by multiple observed variables through a factor analysis and to incorporate additive nonparametric functions of observed and latent risk factors to examine their functional effects on multivariate failure times of interest. A Bayesian approach, along with Bayesian P-splines and Markov chain Monte Carlo techniques, is developed to estimate the unknown parameters and functions. The empirical performance of the proposed methodology is evaluated by a simulation study. An application to a study on the risk factors of two diabetes complications is presented.

Bayesian Diagnostics of Hidden Markov Structural Equation Models with Missing Data.

Cocaine is a type of drug that functions to increase the availability of the neurotransmitter dopamine in the brain. However, cocaine dependence or abuse is highly related to an increased risk of psychiatric disorders and deficits in cognitive performance, attention, and decision-making abilities. Given the chronic and persistent features of drug addiction, the progression of abstaining from cocaine often evolves across several states, such as addiction to, moderate dependence on, and swearing off cocaine. Hidden Markov models (HMMs) are well suited to the characterization of longitudinal data in terms of a set of unobservable states, and have increasingly been used to uncover the dynamic heterogeneity in progressive diseases or activities. However, the existence of outliers or influential points may misidentify the hidden states and distort the associated inference. In this study, we develop a Bayesian local influence procedure for HMMs with latent variables in the presence of missing data. The proposed model enables us to investigate the dynamic heterogeneity of multivariate longitudinal data, reveal how the interrelationships among latent variables change from one state to another, and simultaneously conduct statistical diagnosis for the given data, model assumptions, and prior inputs. We apply the proposed procedure to analyze a dataset collected by the UCLA center for advancing longitudinal drug abuse research. Several outliers or influential points that seriously influence estimation results are identified and removed. The proposed procedure also discovers the effects of treatment and individuals' psychological problems on cocaine use behavior and delineates their dynamic changes across the cocaine-addiction states.

Structure detection of semiparametric structural equation models with Bayesian adaptive group lasso.

Structural equation models (SEMs) are widely recognized as the most important statistical tool for assessing the interrelationships among latent variables. This study develops a Bayesian adaptive group least absolute shrinkage and selection operator procedure to perform simultaneous model selection and estimation for semiparametric SEMs, wherein the structural equation is formulated using the additive nonparametric functions of observed and latent variables. We propose the use of basis expansions to approximate the unknown functions. By introducing adaptive penalties to the groups of basis expansions, the nonlinear, linear, or non-existent effects of observed and latent variables in the structural equation can be automatically detected. A simulation study demonstrates that the proposed method performs satisfactorily. This paper presents an application of revealing the observed and latent risk factors of diabetic kidney disease.

Bayesian analysis for nonlinear mixed-effects models under heavy-tailed distributions.

A common assumption in nonlinear mixed-effects models is the normality of both random effects and within-subject errors. However, such assumptions make inferences vulnerable to the presence of outliers. More flexible distributions are therefore necessary for modeling both sources of variability in this class of models. In the present paper, I consider an extension of the nonlinear mixed-effects models in which random effects and within-subject errors are assumed to be distributed according to a rich class of parametric models that are often used for robust inference. The class of distributions I consider is the scale mixture of multivariate normal distributions that consist of a wide range of symmetric and continuous distributions. This class includes heavy-tailed multivariate distributions, such as the Student's t and slash and contaminated normal. With the scale mixture of multivariate normal distributions, robustification is achieved from the tail behavior of the different distributions. A Bayesian framework is adopted, and MCMC is used to carry out posterior analysis. Model comparison using different criteria was considered. The procedures are illustrated using a real dataset from a pharmacokinetic study. I contrast results from the normal and robust models and show how the implementation can be used to detect outliers.

Fully semiparametric Bayesian approach for modeling survival data with cure fraction.

In this paper, we consider a piecewise exponential model (PEM) with random time grid to develop a full semiparametric Bayesian cure rate model. An elegant mechanism enjoying several attractive features for modeling the randomness of the time grid of the PEM is assumed. To model the prior behavior of the failure rates of the PEM we assume a hierarchical modeling approach that allows us to control the degree of parametricity in the right tail of the survival curve. Properties of the proposed model are discussed in detail. In particular, we investigate the impact of assuming a random time grid for the PEM on the estimation of the cure fraction. We further develop an efficient collapsed Gibbs sampler algorithm for carrying out posterior computation. A Bayesian diagnostic method for assessing goodness of fit and performing model comparisons is briefly discussed. Finally, we illustrate the usefulness of the new methodology with the analysis of a melanoma clinical trial that has been discussed in the literature.

Extending exploratory diagnostic classification models: Inferring the effect of covariates.

Diagnostic models provide a statistical framework for designing formative assessments by classifying student knowledge profiles according to a collection of fine-grained attributes. The context and ecosystem in which students learn may play an important role in skill mastery, and it is therefore important to develop methods for incorporating student covariates into diagnostic models. Including covariates may provide researchers and practitioners with the ability to evaluate novel interventions or understand the role of background knowledge in attribute mastery. Existing research is designed to include covariates in confirmatory diagnostic models, which are also known as restricted latent class models. We propose new methods for including covariates in exploratory RLCMs that jointly infer the latent structure and evaluate the role of covariates on performance and skill mastery. We present a novel Bayesian formulation and report a Markov chain Monte Carlo algorithm using a Metropolis-within-Gibbs algorithm for approximating the model parameter posterior distribution. We report Monte Carlo simulation evidence regarding the accuracy of our new methods and present results from an application that examines the role of student background knowledge on the mastery of a probability data set.

Dynamic survival analysis for non-Markovian epidemic models.

We present a new method for analysing stochastic epidemic models under minimal assumptions. The method, dubbed dynamic survival analysis (DSA), is based on a simple yet powerful observation, namely that population-level mean-field trajectories described by a system of partial differential equations may also approximate individual-level times of infection and recovery. This idea gives rise to a certain non-Markovian agent-based model and provides an agent-level likelihood function for a random sample of infection and/or recovery times. Extensive numerical analyses on both synthetic and real epidemic data from foot-and-mouth disease in the UK (2001) and COVID-19 in India (2020) show good accuracy and confirm the method's versatility in likelihood-based parameter estimation. The accompanying software package gives prospective users a practical tool for modelling, analysing and interpreting epidemic data with the help of the DSA approach.

A Bayesian shared parameter model for joint modeling of longitudinal continuous and binary outcomes.

Joint modeling of associated mixed biomarkers in longitudinal studies leads to a better clinical decision by improving the efficiency of parameter estimates. In many clinical studies, the observed time for two biomarkers may not be equivalent and one of the longitudinal responses may have recorded in a longer time than the other one. In addition, the response variables may have different missing patterns. In this paper, we propose a new joint model of associated continuous and binary responses by accounting different missing patterns for two longitudinal outcomes. A conditional model for joint modeling of the two responses is used and two shared random effects models are considered for intermittent missingness of two responses. A Bayesian approach using Markov Chain Monte Carlo (MCMC) is adopted for parameter estimation and model implementation. The validation and performance of the proposed model are investigated using some simulation studies. The proposed model is also applied for analyzing a real data set of bariatric surgery.

A Bayesian analysis for pseudo-compositional data with spatial structure.

We proposed a Bayesian analysis of pseudo-compositional data in presence of a latent factor, assuming a spatial structure. This development was motivated by a dataset containing information on the number of newborns of primiparous mothers living in each of the microregions of the state of Sao Paulo, Brazil, in the year of 2015, stratified by the age of the mothers (15-18, 19-29 and 30 years or more). Considering that data on newborns are not stochastically distributed among the three age groups, but they are explained in relation to women's population structure, we adopted the expression "pseudo-compositional data" to refer to this data structure. The hypothesis of interest establishes that the age of the first pregnancy is associated with the economic conditions of the geographic area where the mother lives. The incidence of poverty was included as an independent variable. Additive log-ratio (alr) and isometric log-ratio (ilr) transformations were considered, as is usually done in the analysis of compositional data. The model included a random effect related to the spatial effect assumed to have a conditional autoregressive structure. A Bayesian Markov Chain Monte Carlo (MCMC) simulation procedure was used to get the posterior summaries of interest. The model based on the (ilr) transformation was well fitted to the data, showing that in the microregions with the highest incidence of poverty, there are higher proportions of women who have their first child in adolescence, while in the microregions with the lowest incidence of poverty, there are higher proportions of women who have their first child after the age of 30 years. From these results it is possible to conclude that this Bayesian approach was very useful in the estimation of the parameters of the proposed model. The proposed method should have a broad application to other problems involving pseudo-compositional data.

Multilevel Heterogeneous Factor Analysis and Application to Ecological Momentary Assessment.

Ansari et al. (Psychometrika 67:49-77, 2002) applied a multilevel heterogeneous model for confirmatory factor analysis to repeated measurements on individuals. While the mean and factor loadings in this model vary across individuals, its factor structure is invariant. Allowing the individual-level residuals to be correlated is an important means to alleviate the restriction imposed by configural invariance. We relax the diagonality assumption of residual covariance matrix and estimate it using a formal Bayesian Lasso method. The approach improves goodness of fit and avoids ad hoc one-at-a-time manipulation of entries in the covariance matrix via modification indexes. We illustrate the approach using simulation studies and real data from an ecological momentary assessment.

Uncertainty quantification in epidemiological models for the COVID-19 pandemic.

Mathematical modeling of epidemiological diseases using differential equations are of great importance in order to recognize the characteristics of the diseases and their outbreak. The procedure of modeling consists of two essential components: the first component is to solve the mathematical model numerically, the so-called forward modeling. The second component is to identify the unknown parameter values in the model, which is known as inverse modeling and leads to identifying the epidemiological model more precisely. The main goal of this paper is to develop the forward and inverse modeling of the coronavirus (COVID-19) pandemic using novel computational methodologies in order to accurately estimate and predict the pandemic. This leads to governmental decisions support in implementing effective protective measures and prevention of new outbreaks. To this end, we use the logistic equation and the SIR (susceptible-infected-removed) system of ordinary differential equations to model the spread of the COVID-19 pandemic. For the inverse modeling, we propose Bayesian inversion techniques, which are robust and reliable approaches, in order to estimate the unknown parameters of the epidemiological models. We deploy an adaptive Markov-chain Monte-Carlo (MCMC) algorithm for the estimation of a posteriori probability distribution and confidence intervals for the unknown model parameters as well as for the reproduction number. We perform our analyses on the publicly available data for Austria to estimate the main epidemiological model parameters and to study the effectiveness of the protective measures by the Austrian government. The estimated parameters and the analysis of fatalities provide useful information for decision-makers and makes it possible to perform more realistic forecasts of future outbreaks. According to our Bayesian analysis for the logistic model, the growth rate and the carrying capacity are estimated respectively as 0.28 and 14974. Moreover for the parameters of the SIR model, namely the transmission rate and recovery rate, we estimate 0.36 and 0.06, respectively. Additionally, we obtained an average infectious period of 17 days and a transmission period of 3 days for COVID-19 in Austria. We also estimate the reproduction number over time for Austria. This quantity is estimated around 3 on March 26, when the first recovery was reported. Then it decays to 1 at the beginning of April. Furthermore, we present a fatality analysis for COVID-19 in Austria, which is also of importance for governmental protective decision-making. According to our analysis, the case fatality rate (CFR) is estimated as 4% and a prediction of the number of fatalities for the coming 10 days is also presented. Additionally, the ICU bed usage in Austria indicates that around 2% of the active infected individuals are critical cases and require ICU beds. Therefore, if Austrian governmental protective measures would not have taken place and for instance if the number of active infected cases would have been around five times larger, the ICU bed capacity could have been exceeded.

Bayesian hidden Markov models for delineating the pathology of Alzheimer's disease.

Alzheimer's disease is a firmly incurable and progressive disease. The pathology of Alzheimer's disease usually evolves from cognitive normal, to mild cognitive impairment, to Alzheimer's disease. The aim of this paper is to develop a Bayesian hidden Markov model to characterize disease pathology, identify hidden states corresponding to the diagnosed stages of cognitive decline, and examine the dynamic changes of potential risk factors associated with the cognitive normal-mild cognitive impairment-Alzheimer's disease transition. The hidden Markov model framework consists of two major components. The first one is a state-dependent semiparametric regression for delineating the complex associations between clinical outcomes of interest and a set of prognostic biomarkers across neurodegenerative states. The second one is a parametric transition model, while accounting for potential covariate effects on the cross-state transition. The inter-individual and inter-process differences are taken into account via correlated random effects in both components. Based on the Alzheimer's Disease Neuroimaging Initiative data set, we are able to identify four states of Alzheimer's disease pathology, corresponding to common diagnosed cognitive decline stages, including cognitive normal, early mild cognitive impairment, late mild cognitive impairment, and Alzheimer's disease and examine the effects of hippocampus, age, gender, and APOE- ε4 on degeneration of cognitive function across the four cognitive states.