A Bayesian adaptive biomarker stratified phase II randomized clinical trial design for radiotherapies with competing risk survival outcomes.

In recent decades, many phase II clinical trials have used survival outcomes as the primary endpoints. If radiotherapy is involved, the competing risk issue often arises because the time to disease progression can be censored by the time to normal tissue complications, and vice versa. Besides, many existing research has examined that patients receiving the same radiotherapy dose may yield distinct responses due to their heterogeneous radiation susceptibility statuses. Therefore, the "one-size-fits-all" strategy often fails, and it is more relevant to evaluate the subgroup-specific treatment effect with the subgroup defined by the radiation susceptibility status. In this paper, we propose a Bayesian adaptive biomarker stratified phase II trial design evaluating the subgroup-specific treatment effects of radiotherapy. We use the cause-specific hazard approach to model the competing risk survival outcomes. We propose restricting the candidate radiation doses based on each patient's radiation susceptibility status. Only the clinically feasible personalized dose will be considered, which enhances the benefit for the patients in the trial. In addition, we propose a stratified Bayesian adaptive randomization scheme such that more patients will be randomized to the dose reporting more favorable survival outcomes. Numerical studies and an illustrative trial example have shown that the proposed design performed well and outperformed the conventional design ignoring the competing risk issue.

How Social Networks Influence Human Behavior: An Integrated Latent Space Approach for Differential Social Influence.

How social networks influence human behavior has been an interesting topic in applied research. Existing methods often utilized scale-level behavioral data (e.g., total number of positive responses) to estimate the influence of a social network on human behavior. This study proposes a novel approach to studying social influence that utilizes item-level behavioral measures. Under the latent space modeling framework, we integrate the two latent spaces for respondents' social network data and item-level behavior measures into a single space we call 'interaction map'. The interaction map visualizes the association between the latent homophily among respondents and their item-level behaviors, revealing differential social influence effects across item-level behaviors. We also measure overall social influence by assessing the impact of the interaction map. We evaluate the properties of the proposed approach via extensive simulation studies and demonstrate the proposed approach with a real data in the context of studying how students' friendship network influences their participation in school activities.

Application of a joint latent space item response model to clustering stressful life events and the Beck Depression Inventory-II: results from Korean epidemiological survey data.

OBJECTIVES: According to previous findings, stressful life events (SLEs) and their subtypes are associated with depressive symptoms. However, few studies have explored potential models for these events and incidental symptoms of depression. METHODS: Participants (3,966 men; 5,709 women) were recruited from the Cardiovascular and Metabolic Diseases Etiology Research Center cohort. SLEs were measured using a 47-item Life Experiences Survey (LES) with a standardized protocol. Depressive symptoms were assessed using the Beck Depression Inventory-II (BDI-II). Joint latent space item response models were applied by gender and age group (<50 vs. ≥50 years old). RESULTS: Among the LES items, death or illness of close relatives, legal problems, sexual difficulties, family relationships, and social relationships shared latent positions with major depressive symptoms regardless of gender or age. We also observed a gender-specific domain: occupational and family-related items. CONCLUSIONS: By projecting LES and BDI-II data onto the same interaction map for each subgroup, we could specify the associations between specific LES items and depressive symptoms.

Analyzing differences between parent- and self-report measures with a latent space approach.

We explore potential cross-informant discrepancies between child- and parent-report measures with an example of the Child Behavior Checklist (CBCL) and the Youth Self Report (YSR), parent- and self-report measures on children's behavioral and emotional problems. We propose a new way of examining the parent- and child-report differences with an interaction map estimated using a Latent Space Item Response Model (LSIRM). The interaction map enables the investigation of the dependency between items, between respondents, and between items and respondents, which is not possible with the conventional approach. The LSIRM captures the differential positions of items and respondents in the latent spaces for CBCL and YSR and identifies the relationships between each respondent and item according to their dependent structures. The results suggest that the analysis of item response in the latent space using the LSIRM is beneficial in uncovering the differential structures embedded in the response data obtained from different perspectives in children and their parents. This study also argues that the differential hidden structures of children and parents' responses should be taken together to evaluate children's behavioral problems.

Mapping Unobserved Item-Respondent Interactions: A Latent Space Item Response Model with Interaction Map.

Classic item response models assume that all items with the same difficulty have the same response probability among all respondents with the same ability. These assumptions, however, may very well be violated in practice, and it is not straightforward to assess whether these assumptions are violated, because neither the abilities of respondents nor the difficulties of items are observed. An example is an educational assessment where unobserved heterogeneity is present, arising from unobserved variables such as cultural background and upbringing of students, the quality of mentorship and other forms of emotional and professional support received by students, and other unobserved variables that may affect response probabilities. To address such violations of assumptions, we introduce a novel latent space model which assumes that both items and respondents are embedded in an unobserved metric space, with the probability of a correct response decreasing as a function of the distance between the respondent's and the item's position in the latent space. The resulting latent space approach provides an interaction map that represents interactions of respondents and items, and helps derive insightful diagnostic information on items as well as respondents. In practice, such interaction maps enable teachers to detect students from underrepresented groups who need more support than other students. We provide empirical evidence to demonstrate the usefulness of the proposed latent space approach, along with simulation results.

Social Network Mediation Analysis: A Latent Space Approach.

A social network comprises both actors and the social connections among them. Such connections reflect the dependence among social actors, which is essential for individuals' mental health and social development. In this article, we propose a mediation model with a social network as a mediator to investigate the potential mediation role of a social network. In the model, the dependence among actors is accounted for by a few mutually orthogonal latent dimensions which form a social space. The individuals' positions in such a latent social space are directly involved in the mediation process between an independent and dependent variable. After showing that all the latent dimensions are equivalent in terms of their relationship to the social network and the meaning of each dimension is arbitrary, we propose to measure the whole mediation effect of a network. Although individuals' positions in the latent space are not unique, we rigorously articulate that the proposed network mediation effect is still well defined. We use a Bayesian estimation method to estimate the model and evaluate its performance through an extensive simulation study under representative conditions. The usefulness of the network mediation model is demonstrated through an application to a college friendship network.

A Bayesian adaptive phase I/II clinical trial design with late-onset competing risk outcomes.

Early-phase dose-finding clinical trials are often subject to the issue of late-onset outcomes. In phase I/II clinical trials, the issue becomes more intractable because toxicity and efficacy can be competing risk outcomes such that the occurrence of the first outcome will terminate the other one. In this paper, we propose a novel Bayesian adaptive phase I/II clinical trial design to address the issue of late-onset competing risk outcomes. We use the continuation-ratio model to characterize the trinomial response outcomes and the cause-specific hazard rate method to model the competing-risk survival outcomes. We treat the late-onset outcomes as missing data and develop a Bayesian data augmentation method to impute the missing data from the observations. We also propose an adaptive dose-finding algorithm to allocate patients and identify the optimal biological dose during the trial. Simulation studies show that the proposed design yields desirable operating characteristics.

hubViz: A Novel Tool for Hub-centric Visualization.

Visualization algorithms have been widely used for intuitive interrogation of genomic data and popularly used tools include MDS, t-SNE, and UMAP. However, these algorithms are not tuned for the visualization of binary data and none of them consider the hubness of observations for the visualization. In order to address these limitations, here we propose hubViz, a novel tool for hub-centric visualization of binary data. We evaluated the performance of hubViz with its application to the gene expression data measured in multiple brain regions of rats exposed to cocaine, the single-cell RNA-seq data of peripheral blood mononuclear cells treated with interferon beta, and the literature mining data to investigate relationships among diseases. We further evaluated the performance of hubViz using simulation studies. We showed that hubViz provides effective visual inspection by locating the hub in the center and the contrasting elements in the opposite sides around the center. We believe that hubViz and its software can be powerful tools that can improve visualizations of various genomic data. The hubViz is implemented as an R package hubviz, which is publicly available at https://dongjunchung.github.io/hubviz/.

A Doubly Latent Space Joint Model for Local Item and Person Dependence in the Analysis of Item Response Data.

Item response theory (IRT) is one of the most widely utilized tools for item response analysis; however, local item and person independence, which is a critical assumption for IRT, is often violated in real testing situations. In this article, we propose a new type of analytical approach for item response data that does not require standard local independence assumptions. By adapting a latent space joint modeling approach, our proposed model can estimate pairwise distances to represent the item and person dependence structures, from which item and person clusters in latent spaces can be identified. We provide an empirical data analysis to illustrate an application of the proposed method. A simulation study is provided to evaluate the performance of the proposed method in comparison with existing methods.

Structural Equation Modeling of Social Networks: Specification, Estimation, and Application.

Psychologists are interested in whether friends and couples share similar personalities or not. However, no statistical models are readily available to test the association between personalities and social relations in the literature. In this study, we develop a statistical model for analyzing social network data with the latent personality traits as covariates. Because the model contains a measurement model for the latent traits and a structural model for the relationship between the network and latent traits, we discuss it under the general framework of structural equation modeling (SEM). In our model, the structural relation between the latent variable(s) and the outcome variable is no longer linear or generalized linear. To obtain model parameter estimates, we propose to use a two-stage maximum likelihood (ML) procedure. This modeling framework is evaluated through a simulation study under representative conditions that would be found in social network data. Its usefulness is then demonstrated through an empirical application to a college friendship network.

A BAYESIAN HIERARCHICAL SPATIAL MODEL FOR DENTAL CARIES ASSESSMENT USING NON-GAUSSIAN MARKOV RANDOM FIELDS.

Research in dental caries generates data with two levels of hierarchy: that of a tooth overall and that of the different surfaces of the tooth. The outcomes often exhibit spatial referencing among neighboring teeth and surfaces, i.e., the disease status of a tooth or surface might be influenced by the status of a set of proximal teeth/surfaces. Assessments of dental caries (tooth decay) at the tooth level yield binary outcomes indicating the presence/absence of teeth, and trinary outcomes at the surface level indicating healthy, decayed, or filled surfaces. The presence of these mixed discrete responses complicates the data analysis under a unified framework. To mitigate complications, we develop a Bayesian two-level hierarchical model under suitable (spatial) Markov random field assumptions that accommodates the natural hierarchy within the mixed responses. At the first level, we utilize an autologistic model to accommodate the spatial dependence for the tooth-level binary outcomes. For the second level and conditioned on a tooth being non-missing, we utilize a Potts model to accommodate the spatial referencing for the surface-level trinary outcomes. The regression models at both levels were controlled for plausible covariates (risk factors) of caries, and remain connected through shared parameters. To tackle the computational challenges in our Bayesian estimation scheme caused due to the doubly-intractable normalizing constant, we employ a double Metropolis-Hastings sampler. We compare and contrast our model performances to the standard non-spatial (naive) model using a small simulation study, and illustrate via an application to a clinical dataset on dental caries.

Phase I trial design for drug combinations with Bayesian model averaging.

Various statistical models have been proposed for two-dimensional dose finding in drug-combination trials. However, it is often a dilemma to decide which model to use when conducting a particular drug-combination trial. We make a comprehensive comparison of four dose-finding methods, and for fairness, we apply the same dose-finding algorithm under the four model structures. Through extensive simulation studies, we compare the operating characteristics of these methods in various practical scenarios. The results show that different models may lead to different design properties and that no single model performs uniformly better in all scenarios. As a result, we propose using Bayesian model averaging to overcome the arbitrariness of the model specification and enhance the robustness of the design. We assign a discrete probability mass to each model as the prior model probability and then estimate the toxicity probabilities of combined doses in the Bayesian model averaging framework. During the trial, we adaptively allocated each new cohort of patients to the most appropriate dose combination by comparing the posterior estimates of the toxicity probabilities with the prespecified toxicity target. The simulation results demonstrate that the Bayesian model averaging approach is robust under various scenarios.

Using Data Augmentation to Facilitate Conduct of Phase I-II Clinical Trials with Delayed Outcomes.

A practical impediment in adaptive clinical trials is that outcomes must be observed soon enough to apply decision rules to choose treatments for new patients. For example, if outcomes take up to six weeks to evaluate and the accrual rate is one patient per week, on average three new patients will be accrued while waiting to evaluate the outcomes of the previous three patients. The question is how to treat the new patients. This logistical problem persists throughout the trial. Various ad hoc practical solutions are used, none entirely satisfactory. We focus on this problem in phase I-II clinical trials that use binary toxicity and efficacy, defined in terms of event times, to choose doses adaptively for successive cohorts. We propose a general approach to this problem that treats late-onset outcomes as missing data, uses data augmentation to impute missing outcomes from posterior predictive distributions computed from partial follow-up times and complete outcome data, and applies the design's decision rules using the completed data. We illustrate the method with two cancer trials conducted using a phase I-II design based on efficacy-toxicity trade-offs, including a computer stimulation study.

A Monte Carlo Metropolis-Hastings algorithm for sampling from distributions with intractable normalizing constants.

Simulating from distributions with intractable normalizing constants has been a long-standing problem in machine learning. In this letter, we propose a new algorithm, the Monte Carlo Metropolis-Hastings (MCMH) algorithm, for tackling this problem. The MCMH algorithm is a Monte Carlo version of the Metropolis-Hastings algorithm. It replaces the unknown normalizing constant ratio by a Monte Carlo estimate in simulations, while still converges, as shown in the letter, to the desired target distribution under mild conditions. The MCMH algorithm is illustrated with spatial autologistic models and exponential random graph models. Unlike other auxiliary variable Markov chain Monte Carlo (MCMC) algorithms, such as the Møller and exchange algorithms, the MCMH algorithm avoids the requirement for perfect sampling, and thus can be applied to many statistical models for which perfect sampling is not available or very expensive. The MCMH algorithm can also be applied to Bayesian inference for random effect models and missing data problems that involve simulations from a distribution with intractable integrals.

Bayesian Analysis for Exponential Random Graph Models Using the Adaptive Exchange Sampler.

Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the intractable normalizing constant and model degeneracy. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the intractable normalizing constant and model degeneracy issues encountered in Markov chain Monte Carlo (MCMC) simulations. The adaptive exchange sampler can be viewed as a MCMC extension of the exchange algorithm, and it generates auxiliary networks via an importance sampling procedure from an auxiliary Markov chain running in parallel. The convergence of this algorithm is established under mild conditions. The adaptive exchange sampler is illustrated using a few social networks, including the Florentine business network, molecule synthetic network, and dolphins network. The results indicate that the adaptive exchange algorithm can produce more accurate estimates than approximate exchange algorithms, while maintaining the same computational efficiency.