Statistics and its Interface

We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression coefficient tensor. Traditional tensor regression methods making use of the Tucker decomposition either assume the dimension of the core tensor to be known or estimate it via cross-validation or some model selection criteria. However, no existing method can simultaneously estimate the model dimension (the dimension of the core tensor) and other model parameters...

Heterogeneous survival data are commonly present in chronic disease studies. Delineating meaningful disease subtypes directly linked to a survival outcome can generate useful scientific implications. In this work, we develop a latent class proportional hazards (PH) regression framework to address such an interest. We propose mixture proportional hazards modeling, which flexibly accommodates class-specific covariate effects while allowing for the baseline hazard function to vary across latent classes. Adapting the strategy of nonparametric maximum likelihood estimation, we derive an Expectation-Maximization (E-M) algorithm to estimate the proposed model...

In this article, we propose a general framework to learn optimal treatment rules for type 2 diabetes (T2D) patients using electronic health records (EHRs). We first propose a joint modeling approach to characterize patient's pretreatment conditions using longitudinal markers from EHRs. The estimation accounts for informative measurement times using inverse-intensity weighting methods. The predicted latent processes in the joint model are used to divide patients into a finite of subgroups and, within each group, patients share similar health profiles in EHRs...

Evolving medical technologies have motivated the development of treatment decision rules (TDRs) that incorporate complex, costly data (e.g., imaging). In clinical practice, we aim for TDRs to be valuable by reducing unnecessary testing while still identifying the best possible treatment for a patient. Regardless of how well any TDR performs in the target population, there is an associated degree of uncertainty about its optimality for a specific patient. In this paper, we aim to quantify, via a confidence measure, the uncertainty in a TDR as patient data from sequential procedures accumulate in real-time...

This article presents a novel approach to clustering and feature selection for categorical time series via interpretable frequency-domain features. A distance measure is introduced based on the spectral envelope and optimal scalings, which parsimoniously characterize prominent cyclical patterns in categorical time series. Using this distance, partitional clustering algorithms are introduced for accurately clustering categorical time series. These adaptive procedures offer simultaneous feature selection for identifying important features that distinguish clusters and fuzzy membership when time series exhibit similarities to multiple clusters...

We compare two deletion-based methods for dealing with the problem of missing observations in linear regression analysis. One is the complete-case analysis (CC, or listwise deletion) that discards all incomplete observations and only uses common samples for ordinary least-squares estimation. The other is the available-case analysis (AC, or pairwise deletion) that utilizes all available data to estimate the covariance matrices and applies these matrices to construct the normal equation. We show that the estimates from both methods are asymptotically unbiased under missing completely at random (MCAR) and further compare their asymptotic variances in some typical situations...

A probability method is developed to decide when to initiate cancer screening for asymptomatic individuals. The probability of incidence is a function of screening sensitivity, time duration in the disease-free state and sojourn time in the preclinical state; and it is monotonically increasing as time increases, given a person's current age. So a unique solution of the first screening time can be found by limiting this probability to a small value, such as 10% or 20%. That is, with 90% or 80% probability, one will not be a clinical incident case before the first exam...

Estimation of the three key parameters: onset age of the preclinical state, sojourn time and screening sensitivity is critical in cancer screening, since all other terms are functions of the three. A novel link function to connect sensitivity with time in the preclinical state and the likelihood method were used in this project; since sensitivity depends on how long one has entered the preclinical state relative to the total sojourn time. Simulations using Markov Chain Monte Carlo and maximum likelihood estimate were carried out to estimate the key parameters for male and female heavy smokers separately in the low-dose computed tomography group of the National Lung Screening Trial...

In many scientific studies, it becomes increasingly important to delineate the pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate the pathway effects, commonly expressed as the product of coefficients. However, it becomes unstable and computationally challenging to fit such models with high-dimensional mediators. This paper proposes a sparse mediation model using a regularized SEM approach, where sparsity means that a small number of mediators have a nonzero mediation effect between a treatment and an outcome...

Electroencephalography (EEG) studies produce region-referenced functional data via EEG signals recorded across scalp electrodes. The high-dimensional data can be used to contrast neurodevelopmental trajectories between diagnostic groups, for example between typically developing (TD) children and children with autism spectrum disorder (ASD). Valid inference requires characterization of the complex EEG dependency structure as well as covariate-dependent heteroscedasticity, such as changes in variation over developmental age...

In controlled and observational studies, outcome measures are often observed longitudinally. Such data are difficult to compare among units directly because there is no natural ordering of curves. This is relevant not only in clinical trials, where typically the goal is to evaluate the relative efficacy of treatments on average, but also in the growing and increasingly important area of personalized medicine, where treatment decisions are optimized with respect to a relevant patient outcome. In personalized medicine, there are no methods for optimizing treatment decision rules using longitudinal outcomes, e...

Motivated by the self-thinning meta-data, a random-effects meta-analysis model with unknown precision parameters is proposed with a truncated Poisson regression model for missing sample sizes. The random effects are assumed to follow a heavy-tailed distribution to accommodate outlying aggregate values in the response variable. The logarithm of the pseudo-marginal likelihood (LPML) is used for model comparison. In addition, in order to determine which self-thinning law is more supported by the meta-data, a measure called "Plausibility Index (PI)" is developed...

Shotgun assays are widely used in biotechnologies to characterize large molecules, which are hard to be measured as a whole directly. For instance, in Liquid Chromatography - Mass Spectrometry (LC-MS) shotgun experiments, proteins in biological samples are digested into peptides, and then peptides are separated and measured. However, in proteomics study, investigators are usually interested in the performance of the whole proteins instead of those peptide fragments. In light of meta-analysis, we propose an adaptive thresholding method to select informative peptides, and combine peptide-level models to protein-level analysis...

Meta-analysis, the statistical procedure for combining results from multiple independent studies, has been widely used in medical research to evaluate intervention efficacy and drug safety. In many practical situations, treatment effects vary notably among the collected studies, and the variation, often modeled by the between-study variance parameter τ 2 , can greatly affect the inference of the overall effect size. In the past, comparative studies have been conducted for both point and interval estimation of τ 2 ...

Effect size can differ as a function of the elapsed time since treatment or as a function of other key covariates, such as sex or age. In evidence synthesis, a better understanding of the precise conditions under which treatment does work or does not work well has been highly valued. With increasingly accessible individual patient or participant data (IPD), more precise and informative inference can be within our reach. However, simultaneously combining multiple related parameters across heterogeneous studies is challenging because each parameter from each study has a specific interpretation within the context of the study and other covariates in the model...

A flexible class of multivariate meta-regression models are proposed for Individual Patient Data (IPD). The methodology is well motivated from 26 pivotal Merck clinical trials that compare statins (cholesterol lowering drugs) in combination with ezetimibe and statins alone on treatment-naïve patients and those continuing on statins at baseline. The research goal is to jointly analyze the multivariate outcomes, Low Density Lipoprotein Cholesterol (LDL-C), High Density Lipoprotein Cholesterol (HDL-C), and Triglycerides (TG)...

As an extension of pairwise meta-analysis of two treatments, network meta-analysis has recently attracted many researchers in evidence-based medicine because it simultaneously synthesizes both direct and indirect evidence from multiple treatments and thus facilitates better decision making. The Bayesian hierarchical model is a popular method to implement network meta-analysis, and it is generally considered more powerful than conventional pairwise meta-analysis, leading to more precise effect estimates with narrower credible intervals...

Tissue microarray (TMA) images have been used increasingly often in cancer studies and the validation of biomarkers. TACOMA-a cutting-edge automatic scoring algorithm for TMA images-is comparable to pathologists in terms of accuracy and repeatability. Here we consider how this algorithm may be further improved. Inspired by the recent success of deep learning, we propose to incorporate representations learnable through computation. We explore representations of a group nature through unsupervised learning, e...

Restricted Boltzmann machines (RBMs) have become a popular tool of feature coding or extraction for unsupervised learning in recent years. However, there still lacks an efficient algorithm for training the RBM due to that its likelihood function contains an intractable normalizing constant. The existing algorithms, such as contrastive divergence and its variants, approximate the gradient of the likelihood function using Markov chain Monte Carlo. However, the approximation is time consuming and, moreover, the approximation error often impedes the convergence of the training algorithm...

In many econometrics applications, the dataset under investigation spans heterogeneous regimes that are more appropriately modeled using piece-wise components for each of the data segments separated by change-points. We consider using Bayesian high-dimensional shrinkage priors in a change point setting to understand segment-specific relationship between the response and the covariates. Covariate selection before and after each change point can identify possibly different sets of relevant covariates, while the fully Bayesian approach ensures posterior inference for the change points is also available...