RAS Student Paper Competition Award Section

We develop a nonparametric Bayesian modeling framework for clustered ordinal responses in developmental toxicity studies, which typically exhibit extensive heterogeneity. The primary focus of these studies is to examine the dose-response relationship, which is depicted by the (conditional) probability of an endpoint across the dose (toxin) levels. Standard parametric approaches, limited in terms of the response distribution and/or the dose-response relationship, hinder reliable uncertainty quantification in this context. We propose nonparametric mixture models that are built from dose-dependent stick-breaking process priors, leveraging the continuation-ratio logits representation of the multinomial distribution to formulate the mixture kernel. We further elaborate the modeling approach, amplifying the mixture models with an overdispersed kernel which offers enhanced control of variability. We conduct a simulation study to demonstrate the benefits of both the discrete nonparametric mixing structure and the overdispersed kernel in delivering coherent uncertainty quantification. Further illustration is provided with different forms of risk assessment, using data from a toxicity experiment on the effects of ethylene glycol. 

In clinical practice, there is significant interest in integrating novel biomarkers with existing clinical data to construct interpretable and robust decision rules. Motivated by the need to improve decision-making for early disease detection, we propose a framework for developing an optimal biomarker-based clinical decision rule that is both clinically meaningful and practically feasible. Specifically, our procedure constructs a linear decision rule designed to achieve optimal performance among class of linear rules by maximizing the true positive rate while adhering to a pre-specified positive predictive value constraint. Additionally, our method can adaptively incorporate individual risk information from external source to enhance performance when such information is beneficial. We establish the asymptotic properties of our propose estimator and compare to the standard approach used in practice through extensive simulation studies. Results indicate that our approach demonstrates strong finite-sample performance. Finally, we apply the proposed methods to develop biomarker-based screening rules for pancreatic ductal adenocarcinoma (PDAC) among new-onset diabetes (NOD) patients. 

Joint modeling of longitudinal data and survival data has been extended to accommodate multilevel data structures. In dental studies, data often exhibit a multilevel hierarchy: each patient has multiple teeth, and one or more biomarkers are measured repeatedly over time for each tooth. In addition to biomarker measurements, the time to tooth loss may vary differently between patients as some people are more susceptible to tooth loss, conditional on other risk factors. In this work, we account for intra-patient and intra-tooth correlations in the longitudinal measurement of a continuous biomarkers, probing pocket depth (PPD), and a binary biomarker, mobility. We also account for the correlation in time to tooth loss between teeth within the same patient. We jointly model the two biomarker measurements and the risk of tooth loss using a Bayesian estimation approach. Our simulation study shows that the proposed joint model produced more desirable estimates with better coverage compared to the standard bivariate joint model that ignores the multilevel data structure. We applied our model to electronic periodontal data obtained from the Canadian Armed Forces (CAF). The results of both the simulation and the real data application suggest that our model accurately estimates the parameters and standard errors, whereas the standard joint model tends to underestimate the standard errors. 

Transient data analysis, which evaluates the impact of ordinal time-dependent covariates on survival, poses unique challenges. In a motivating study investigating increasing mixed chimerism (IMC) as a biomarker for disease relapse for post-transplant leukemia patients, existing approaches prove inadequate for a fallacious abrupt decline to zero in IMC2 stage, coupled with inflated type I error control in risk comparisons. To address these limitations, we propose a novel non-parametric approach to enhancing estimation and hypothesis testing for transient data. By conceptualizing state transitions as pseudo-competing events, we reformulate the analysis as a competing events problem, which enables enlarged risk sets of later transient states, facilitating robust analysis and intuitive interpretation. Moreover, the estimation of survival probabilities is calibrated to mitigate systematic bias from the pseudo-competing transition risks. A non-parametric bootstrap approach is introduced for uncertainty quantification and statistical testing. Simulation studies demonstrate robust estimation, outperforming competing approaches. An application to the motivating data improves statistical testing, highlighting the method's broad applicability to transient data.