Tue, 08 Aug 2023
1.A Dual Cox Model Theory And Its Applications In Oncology
Authors:Powei Chen, Siying Hu, Dr. Haojin Zhou
Abstract: Given the prominence of targeted therapy and immunotherapy in cancer treatment, it becomes imperative to consider heterogeneity in patients' responses to treatments, which contributes greatly to the widely used proportional hazard assumption invalidated as in several clinical trials. To address the challenge, we develop a Dual Cox model theory including a Dual Cox model and a fitting algorithm. As one of the finite mixture models, the proposed Dual Cox model consists of two independent Cox models based on patients' responses to one designated treatment (usually the experimental one) in the clinical trial. Responses of patients in the designated treatment arm can be observed and hence those patients are known responders or non-responders. From the perspective of subgroup classification, such a phenomenon renders the proposed model as a semi-supervised problem, compared to the typical finite mixture model where the subgroup classification is usually unsupervised. A specialized expectation-maximization algorithm is utilized for model fitting, where the initial parameter values are estimated from the patients in the designated treatment arm and then the iteratively reweighted least squares (IRLS) is applied. Under mild assumptions, the consistency and asymptotic normality of its estimators of effect parameters in each Cox model are established. In addition to strong theoretical properties, simulations demonstrate that our theory can provide a good approximation to a wide variety of survival models, is relatively robust to the change of censoring rate and response rate, and has a high prediction accuracy and stability in subgroup classification while it has a fast convergence rate. Finally, we apply our theory to two clinical trials with cross-overed KM plots and identify the subgroups where the subjects benefit from the treatment or not.
2.A Spatial Autoregressive Graphical Model with Applications in Intercropping
Authors:Sjoerd Hermes, Joost van Heerwaarden, Pariya Behrouzi
Abstract: Within the statistical literature, there is a lack of methods that allow for asymmetric multivariate spatial effects to model relations underlying complex spatial phenomena. Intercropping is one such phenomenon. In this ancient agricultural practice multiple crop species or varieties are cultivated together in close proximity and are subject to mutual competition. To properly analyse such a system, it is necessary to account for both within- and between-plot effects, where between-plot effects are asymmetric. Building on the multivariate spatial autoregressive model and the Gaussian graphical model, the proposed method takes asymmetric spatial relations into account, thereby removing some of the limiting factors of spatial analyses and giving researchers a better indication of the existence and extend of spatial relationships. Using a Bayesian-estimation framework, the model shows promising results in the simulation study. The model is applied on intercropping data consisting of Belgian endive and beetroot, illustrating the usage of the proposed methodology. An R package containing the proposed methodology can be found on https:// CRAN.R-project.org/package=SAGM.
3.Multiple Testing of Local Extrema for Detection of Structural Breaks in Piecewise Linear Models
Authors:Zhibing He, Dan Cheng, Yunpeng Zhao
Abstract: In this paper, we propose a new generic method for detecting the number and locations of structural breaks or change points in piecewise linear models under stationary Gaussian noise. Our method transforms the change point detection problem into identifying local extrema (local maxima and local minima) through kernel smoothing and differentiation of the data sequence. By computing p-values for all local extrema based on peak height distributions of smooth Gaussian processes, we utilize the Benjamini-Hochberg procedure to identify significant local extrema as the detected change points. Our method can distinguish between two types of change points: continuous breaks (Type I) and jumps (Type II). We study three scenarios of piecewise linear signals, namely pure Type I, pure Type II and a mixture of Type I and Type II change points. The results demonstrate that our proposed method ensures asymptotic control of the False Discover Rate (FDR) and power consistency, as sequence length, slope changes, and jump size increase. Furthermore, compared to traditional change point detection methods based on recursive segmentation, our approach only requires a single test for all candidate local extrema, thereby achieving the smallest computational complexity proportionate to the data sequence length. Additionally, numerical studies illustrate that our method maintains FDR control and power consistency, even in non-asymptotic cases when the size of slope changes or jumps is not large. We have implemented our method in the R package "dSTEM" (available from https://cran.r-project.org/web/packages/dSTEM).
4.Are Information criteria good enough to choose the right the number of regimes in Hidden Markov Models?
Authors:Bouchra R Nasri, Bruno N Rémillard, Mamadou Y Thioub
Abstract: Selecting the number of regimes in Hidden Markov models is an important problem. There are many criteria that are used to select this number, such as Akaike information criterion (AIC), Bayesian information criterion (BIC), integrated completed likelihood (ICL), deviance information criterion (DIC), and Watanabe-Akaike information criterion (WAIC), to name a few. In this article, we introduced goodness-of-fit tests for general Hidden Markov models with covariates, where the distribution of the observations is arbitrary, i.e., continuous, discrete, or a mixture of both. Then, a selection procedure is proposed based on this goodness-of-fit test. The main aim of this article is to compare the classical information criterion with the new criterion, when the outcome is either continuous, discrete or zero-inflated. Numerical experiments assess the finite sample performance of the goodness-of-fit tests, and comparisons between the different criteria are made.
5.Contour Location for Reliability in Airfoil Simulation Experiments using Deep Gaussian Processes
Authors:Annie S. Booth, S. Ashwin Renganathan, Robert B. Gramacy
Abstract: Bayesian deep Gaussian processes (DGPs) outperform ordinary GPs as surrogate models of complex computer experiments when response surface dynamics are non-stationary, which is especially prevalent in aerospace simulations. Yet DGP surrogates have not been deployed for the canonical downstream task in that setting: reliability analysis through contour location (CL). Level sets separating passable vs. failable operating conditions are best learned through strategic sequential design. There are two limitations to modern CL methodology which hinder DGP integration in this setting. First, derivative-based optimization underlying acquisition functions is thwarted by sampling-based Bayesian (i.e., MCMC) inference, which is essential for DGP posterior integration. Second, canonical acquisition criteria, such as entropy, are famously myopic to the extent that optimization may even be undesirable. Here we tackle both of these limitations at once, proposing a hybrid criteria that explores along the Pareto front of entropy and (predictive) uncertainty, requiring evaluation only at strategically located "triangulation" candidates. We showcase DGP CL performance in several synthetic benchmark exercises and on a real-world RAE-2822 transonic airfoil simulation.