We present PPI++: a computationally lightweight methodology for estimation and inference based on a small labeled dataset and a typically much larger dataset of machine-learning predictions. The methods automatically adapt to the quality of available predictions, yielding easy-to-compute confidence sets -- for parameters of any dimensionality -- that always improve on classical intervals using only the labeled data. PPI++ builds on prediction-powered inference (PPI), which targets the same problem setting, improving its computational and statistical efficiency. Real and synthetic experiments demonstrate the benefits of the proposed adaptations.
An understanding of the body size of individuals and the relationships between different dimensions is critical for monitoring the status and the health of a wildlife population. Morphometric data have traditionally been collected by physically handling and measuring individual animals, but recent technological advancements allow researchers to deploy sophisticated but affordable instruments, like drones and camera traps, to take photos of individual animals from which morphometric measurements are extracted. However, morphometric data obtained from photographs can be less accurate than those from direct measurement. In this paper we propose a new linear mixed-effects model approach, involving multivariate normal distributions, to describe the latent true measurements and to accommodate measurement error. Our method can be used to estimate relationships between dimensions, to predict the measurement of any one dimension from any subset of other dimensions, and to make inference on allometry, including testing for allometric growth. We demonstrate the use of our method with an application to morphometric data of the reef manta ray Mobula alfredi collected by drones.
Genetic interactions are essential for understanding the risk and progression of complex diseases. However, signals from individual genes and their pairwise interactions are often weak; most phenotypes are driven by alterations in a limited number of pathways and interactions between them. Identifying such pathways and their interactions is critical in biomedical research. Although traditional analyses have extended beyond main effects to include gene-gene interactions, most existing methods remain at the gene level and fail to capture higher-level pathway interactions. In this paper we propose a novel group-level model that jointly identifies key pathways and their interactions associated with clinical outcomes such as disease status or survival. The model involves estimating a high-dimensional binary matrix, which presents significant computational challenges. To overcome this, we reformulate the problem as a standard high-dimensional estimation task with hierarchical and exclusivity constraints and develop a two-stage estimation procedure. Theoretical analysis, simulation studies, and applications to TCGA breast cancer and Michigan lung cancer datasets demonstrate the superior performance of our method. In particular, our approach yields biologically meaningful insights, reveals novel gene-pathway mechanisms, and achieves substantially improved prediction accuracy and sensitivity, with comparable specificity to competing methods, including those modeling gene-gene interactions or employing two-step procedures that separately estimate pathways and their interactions.
Given the complex interactions between the microbiome, the host, and external factors, causal mediation analysis is essential for unraveling how dysbiosis or microbial imbalance mediates the effects of interventions or environmental exposures on health outcomes. However, zero inflation in microbiome count data complicates high-dimensional mediation analysis, as frequently employed zero-inflated models often struggle to distinguish true zero inflation from the underlying count distribution. To address this, we employ a zero-inflated negative binomial distribution for each mediator within a Bayesian framework, incorporating spike-and-slab priors to enable sparsity in estimating natural indirect effects (NIE) and an informative prior based on nonzero counts to improve dispersion estimation and account for zero sources. Recognizing the distinct biological mechanisms underlying microbial presence vs. abundance, we developed a dual mediation model, ZIMMA, to separate the NIE into pathways for mediator abundance and prevalence. Extensive simulations demonstrate ZIMMA’s superior performance in capturing distinct mediation mechanisms for both rare and abundant species compared to existing methods. Its application to human microbiome studies examining the effects of dietary intake and metabolic syndrome underscores its efficacy in identifying key microbial mediators, offering valuable insights and biological interpretation into the role of the microbiome in disease physiology and health sciences.
Somatic mutations, which accumulate in cells after conception, drive cancer development. Their characteristic patterns, namely mutational signatures, reflect the underlying mutational processes and have provided valuable insights into cancer etiology, evolution and therapeutic strategies. While non-negative matrix factorization (NMF) is commonly used to infer de novo mutational signatures and their activities, it requires large datasets for reliable estimation. When the sample size is limited, signature refitting is typically used, which estimates the signature activities using a set of reference signatures derived from external studies. However, current signature refitting methods often use the full list of reference signatures, leading to overfitting and compromised interpretability and accuracy. Despite its importance, the problem of selecting an appropriate subset of reference signatures received little attention. We proposed BayesSigRefitting, a Bayesian model selection framework to select an optimal subset of reference signatures for accurate refitting. Our approach employs a Bayesian hierarchical model with a sparsity-inducing Laplace prior, and the Shotgun Stochastic Search (SSS) algorithm to efficiently explore possible signature subsets and identify the optimal one. We established the model selection consistency of BayesSigRefitting and demonstrated, through simulation and real data studies across seven cancer types, that it outperformed existing methods in both signature selection and signature activity estimation. These findings highlight the potential of BayesSigRefitting to enhance the accuracy and reliability of mutational signature analysis, especially in settings with limited sample sizes.
