Spike-and-Slab Group Lassos for Grouped Regression and Sparse Generalized Additive Models

MIDAS-2: an enhanced Bayesian platform design for immunotherapy combinations with subgroup efficacy exploration

Although immunotherapy combinations have revolutionised cancer treatment, the rapid screening of effective and optimal therapies from large numbers of candidate combinations, as well as exploring subgroup efficacy, remains challenging. This necessitates innovative, integrated, and efficient trial designs. In this study, we extend the MIDAS design to include subgroup exploration and propose an enhanced Bayesian information borrowing platform design called MIDAS-2. MIDAS-2 enables quick and continuous screening of promising combination strategies and exploration of their subgroup effects within a unified platform design framework. We use a regression model to characterize the efficacy pattern in subgroups. Information borrowing is applied through Bayesian hierarchical modelling to improve trial efficiency considering the limited sample size in subgroups. Time trend calibration is also employed to avoid potential baseline drifts. Simulation results demonstrate that MIDAS-2 yields high probabilities for identifying the effective drug combinations as well as promising subgroups, facilitating appropriate selection of the best treatments for each subgroup. The proposed design is robust against small time trend drifts, and the type I error is successfully controlled after calibration when a large drift is expected. Overall, MIDAS-2 provides an adaptive drug screening and subgroup exploring framework to accelerate immunotherapy development in an efficient, accurate, and integrated fashion.

Methodological Challenges in Spatial and Contextual Exposome-Health Studies

The concept of the exposome encompasses the totality of exposures from a variety of external and internal sources across an individual's life course. The wealth of existing spatial and contextual data makes it appealing to characterize individuals' external exposome to advance our understanding of environmental determinants of health. However, the spatial and contextual exposome is very different from other exposome factors measured at the individual-level as spatial and contextual exposome data are more heterogenous with unique correlation structures and various spatiotemporal scales. These distinctive characteristics lead to multiple unique methodological challenges across different stages of a study. This article provides a review of the existing resources, methods, and tools in the new and developing field for spatial and contextual exposome-health studies focusing on four areas: (1) data engineering, (2) spatiotemporal data linkage, (3) statistical methods for exposome-health association studies, and (4) machine- and deep-learning methods to use spatial and contextual exposome data for disease prediction. A critical analysis of the methodological challenges involved in each of these areas is performed to identify knowledge gaps and address future research needs.

Spike-and-slab least absolute shrinkage and selection operator generalized additive models and scalable algorithms for high-dimensional data analysis

There are proposals that extend the classical generalized additive models (GAMs) to accommodate high-dimensional data ( p ≫ n $$ p\gg n $$ ) using group sparse regularization. However, the sparse regularization may induce excess shrinkage when estimating smooth functions, damaging predictive performance. Moreover, most of these GAMs consider an "all-in-all-out" approach for functional selection, rendering them difficult to answer if nonlinear effects are necessary. While some Bayesian models can address these shortcomings, using Markov chain Monte Carlo algorithms for model fitting creates a new challenge, scalability. Hence, we propose Bayesian hierarchical generalized additive models as a solution: we consider the smoothing penalty for proper shrinkage of curve interpolation via reparameterization. A novel two-part spike-and-slab LASSO prior for smooth functions is developed to address the sparsity of signals while providing extra flexibility to select the linear or nonlinear components of smooth functions. A scalable and deterministic algorithm, EM-Coordinate Descent, is implemented in an open-source R package BHAM. Simulation studies and metabolomics data analyses demonstrate improved predictive and computational performance against state-of-the-art models. Functional selection performance suggests trade-offs exist regarding the effect hierarchy assumption.

Posterior contraction in sparse generalized linear models

We study posterior contraction rates in sparse high-dimensional generalized linear models using priors incorporating sparsity. A mixture of a point mass at zero and a continuous distribution is used as the prior distribution on regression coefficients. In addition to the usual posterior, the fractional posterior, which is obtained by applying Bayes theorem with a fractional power of the likelihood, is also considered. The latter allows uniformity in posterior contraction over a larger subset of the parameter space. In our set-up, the link function of the generalized linear model need not be canonical. We show that Bayesian methods achieve convergence properties analogous to lasso-type procedures. Our results can be used to derive posterior contraction rates in many generalized linear models including logistic, Poisson regression and others.