Point and interval estimation of exposure effects and interaction between the exposures based on logistic model for observational studies

Xiaoqin Wang; Weimin Ye; Li Yin

Home/Archive/arXiv

arXiv · 1501.05121

Point and interval estimation of exposure effects and interaction between the exposures based on logistic model for observational studies

Xiaoqin Wang·Weimin Ye·Li Yin

View original source ↗Read source document ↗Export metadata ↓

Abstract

In observational studies with dichotomous outcome of a population, researchers need to present the effects of exposures and interaction between the exposures jointly in order to learn the relationship between the exposure effects and the interaction. In this article we study point and interval estimation of exposure effects and the interaction based on logistic model, where the exposure effects are measured by risk differences while the interaction is measured by difference between risk differences. Using approximate normal distribution of the maximum-likelihood (ML) estimate of the model parameters, we obtain approximate non-normal distribution of the ML estimate of the exposure effects and the interaction. Using the obtained distribution, we obtain point estimate and confidence region of (exposure effect, interaction) as well as point estimate and confidence interval of the interaction when the ML estimate of an exposure effect falls into specified range. Our maximum-likelihood-based approach provides a simple but reliable method of interval estimation of exposure effects and the interaction.

Explore related subjects

stat.ME

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Xiaoqin Wang, Weimin Ye, Li Yin. 2015-01-21. Point and interval estimation of exposure effects and interaction between the exposures based on logistic model for observational studies. https://arxiv.org/abs/1501.05121

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Bayesian Framework for Multivariate Differential Analysis

Differential analysis is a routine procedure in the statistical analysis toolbox across many applied fields, including quantitative proteomics, the main illustration of the present paper. The state-of-the-art limma approach uses a hierarchical formulation with moderated-variance estimators for each analyte directly injected into the t-statistic. While standard hypothesis testing strategies are recognised for their low computational cost, allowing for quick extraction of the most differential among thousands of elements, they generally overlook key aspects such as handling missing values, inter-element correlations, and uncertainty quantification. The present paper proposes a fully Bayesian framework for differential analysis, leveraging a conjugate hierarchical formulation for both the mean and the variance. Inference is performed by computing the posterior distribution of compared experimental conditions and sampling from the distribution of differences. This approach provides well-calibrated uncertainty quantification at a similar computational cost as hypothesis testing by leveraging closed-form equations. Furthermore, a natural extension enables multivariate differential analysis that accounts for possible inter-element correlations. We also demonstrate that, in this Bayesian treatment, missing data should generally be ignored in univariate settings, and further derive a tailored approximation that handles multiple imputation for the multivariate setting. We argue that probabilistic statements in terms of effect size and associated uncertainty are better suited to practical decision-making. Therefore, we finally propose simple and intuitive inference criteria, such as the overlap coefficient, which express group similarity as a probability rather than traditional, and often misleading, p-values.

stat.ME↗

arXiv2026

Interpretable Deep Neural Network for Modeling Functional Surrogates

Developing surrogates for computer models has become increasingly important for addressing complex problems in science and engineering. This article introduces an artificial intelligent (AI) surrogate, referred to as the DeepSurrogate, for analyzing functional outputs with vector-valued inputs. The relationship between the functional output and vector-valued input is modeled as an infinite sequence of unknown functions, each representing the relationship at a specific location within the functional domain. These spatially indexed functions are expressed through a combination of basis functions and their corresponding coefficient functions, both of which are modeled using deep neural networks (DNN). The proposed framework accounts for spatial dependencies across locations, while capturing the relationship between the functional output and scalar predictors. It also integrates a Monte Carlo (MC) dropout strategy to quantify prediction uncertainty, enhancing explainability in the deep neural network architecture. The proposed method enables efficient inference on datasets with approximately 50,000 spatial locations and 20 simulations, achieving results in under 10 minutes using standard hardware. The approach is validated on extensive synthetic datasets and a large-scale simulation from the Sea Lake and Overland Surge from Hurricanes (SLOSH) simulator. An open-source Python package implementing the method is made available.

stat.ME↗

arXiv2026

Bayesian inference for the learning rate in Generalised Bayesian inference

In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior. However, in some settings there exist unknown ``true'' hyperparameter-values about which it is meaningful to have prior belief. It is then possible to use Bayesian inference with held-out data to get hyperparameter-posteriors. We define two hyperparameter posteriors, one based on an Expected Log Pointwise Predictive Density (ELPPD)-utility and one aiming to cover the pseudo-true parameter. The new framework supports estimation and uncertainty quantification for multiple hyperparameters jointly. Experiments show that the resulting GBI-posteriors outperform Bayesian inference on simulated test data and select optimal or near-optimal hyperparameter values in a large real problem of text analysis. Generalised Bayesian inference is particularly useful for combining multiple data sets and most of our examples belong to that setting. We also give asymptotic results for some of the special ``multi-modular'' Generalised Bayes posteriors which we use in our examples.

stat.ME↗