Testing for Gene–Environment and Gene–Gene Interactions Under Monotonicity Constraints
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Recent genome-wide association studies (GWASs) designed to detect the main effects of genetic markers have had considerable success with many findings validated by replication studies. However, relatively few findings of gene–gene or gene–environment interactions have been successfully reproduced. Besides the main issues associated with insufficient sample size in current studies, a complication is that interactions that rank high based on p-values often correspond to extreme forms of joint effects that are biologically less plausible. To reduce false positives and to increase power, we develop various gene–environment/gene–gene tests based on biologically more plausible constraints using bivariate isotonic regressions for case–control data. We extend our method to exploit gene–environment or gene–gene independence information, integrating the approach proposed by Chatterjee and Carroll. We propose appropriate nonparametric and parametric permutation procedures for evaluating the significance of the tests. Simulations show that our method gains power over traditional unconstrained methods by reducing the sizes of alternative parameter spaces. We apply our method to several real-data examples, including an analysis of bladder cancer data to detect interactions between the NAT2 gene and smoking. We also show that the proposed method is computationally feasible for large-scale problems by applying it to the National Cancer Institute (NCI) lung cancer GWAS data.
We develop a semiparametric continuous time inferential framework for testing cumulative treatment effects, including both immediate and carryover effects. The latent state process is modeled by an ordinary differential equation (ODE) whose drift depends on state and treatment, while the observed data are noisy measurements of this latent state at irregular, multi resolution time points. We define the average treatment effect (ATE) as the difference of expected cumulative…
We study inference for continuous linear functionals of solutions to ill-posed inverse problems, including Euclidean parameters arising in nonparametric instrumental variables, proximal causal inference, and shadow-variable models. Although pointwise root-$n$ inference is possible under standard conditions, we show that this need not translate into locally reliable inference. Under a model imposing only minimal regularity conditions, the target is Hellinger discontinuous…
Motivation: Mediation analysis is an important tool for elucidating causal mechanisms in biomedical research and has recently gained increasing attention in microbiome studies. Motivated by a microbiome study of acute myeloid leukemia (AML) patients, we investigate whether the effect of induction chemotherapy intensity on infection status is mediated through gut microbial taxa. This problem poses substantial methodological challenges due to the high dimensionality, zero…
This article introduces a framework for evaluating statistical decisions under both prior ambiguity and likelihood misspecification. We begin with an ambiguity set - a frequentist model that pairs a possibly misspecified likelihood with every possible prior - and uniformly expand it by a Kullback-Leibler radius to accommodate likelihood misspecification. We show that optimal decisions under this framework are equivalent to minimax decisions with an exponentially tilted loss…
RBF 核高斯过程最大似然估计的精确渐近理论
Gaussian processes (GPs) are widely used across machine learning, spatial statistics, time-series analysis, optimization, Bayesian statistics, and scientific applications. A central component of a GP model is its kernel, which is typically specified through a parametric family. Among the most widely used choices is the radial basis function (RBF), also known as the squared exponential or Gaussian kernel, owing to its simple form, smoothness, and flexibility. In practice, the…
PICPIs:预测区间条件预测区间
A classical question in statistics is which observable quantities to condition on when drawing inferences about unobservable targets. For conformal prediction in nonparametric uncertainty quantification, standard marginal validity offers limited resolution at the prediction values on which decisions are based, and fully conditional guarantees with respect to the covariates are provably unattainable. We address this gap by introducing a prediction-based conditioning framework…