Electronic health records (EHRs) offer unprecedented opportunities to answer epidemiologic questions. However, unlike in ordinary cohort studies or randomized trials, EHR data are collected somewhat idiosyncratically. In particular, patients who have more contact with the medical system have more opportunities to receive diagnoses, which are then recorded in their EHRs. The goal of this article is to shed light on the nature and scope of this phenomenon, known as informative presence, which can bias estimates of associations. We show how this can be characterized as an instance of misclassification bias. As a consequence, we show that informative presence bias can occur in a broader range of settings than previously thought, and that simple adjustment for the number of visits as a confounder may not fully correct for bias. Additionally, where previous work has considered only underdiagnosis, investigators are often concerned about overdiagnosis; we show how this changes the settings in which bias manifests. We report on a comprehensive series of simulations to shed light on when to expect informative presence bias, how it can be mitigated in some cases, and cases in which new methods need to be developed.

Many physical models contain nuisance parameters that quantify unknown properties of an experiment that are not of primary relevance. Typically, these cannot be measured except by fitting the models to the data from the experiment, requiring simultaneous measurement of interesting parameters that are our target of inference and nuisance terms that are not directly of interest. A recent example of this is fitting Effective Field Theory (EFT) models to large-scale structure (LSS) data to make cosmological inferences. These models have a large number of nuisance parameters that are typically correlated with cosmological parameters in the posterior, leading to strong dependence on the nuisance parameter priors. We introduce a reparametrization method that leverages Generalized Additive Models (GAMs) to decorrelate nuisance parameters from the parameters of interest in the likelihood, even in the presence of non-linear relationships. This reparametrization forms a natural basis within which to define priors that are independent between nuisance and target parameters: the separation means that the marginal posterior for cosmological parameters does not depend on simple priors placed on nuisance terms. In application to EFT models using LSS data, we demonstrate that the proposed approach leads to robust cosmological inference.

A key goal of environmental health research is to assess the risk posed by mixtures of pollutants. As epidemiologic studies of mixtures can be expensive to conduct, it behooves researchers to incorporate prior knowledge about mixtures into their analyses. This work extends the Bayesian multiple index model (BMIM), which assumes the exposure‐response function is a nonparametric function of a set of linear combinations of pollutants formed with a set of exposure‐specific weights. The framework is attractive because it combines the flexibility of response‐surface methods with the interpretability of linear index models. We propose three strategies to incorporate prior toxicological knowledge into construction of indices in a BMIM: (a) imposing directional homogeneity constraints on the weights, (b) structuring index weights by exposure transformations, and (c) placing informative priors on the index weights. We propose a novel prior specification that combines spike‐and‐slab variable selection with an informative Dirichlet distribution based on relative potency factors often derived from previous toxicological studies. In simulations we show that the proposed priors improve inferences when prior information is correct and can protect against misspecification suffered by naïve toxicological models when prior information is incorrect. Moreover, different strategies may be mixed‐and‐matched for different indices to suit available information (or lack thereof). We demonstrate the proposed methods on an analysis of data from the National Health and Nutrition Examination Survey and incorporate prior information on relative chemical potencies obtained from toxic equivalency factors available in the literature.

We present a powerful and innovative statistical framework to address key cosmological questions about the universe's fundamental properties, performing Bayesian model averaging (BMA) and model selection. Utilizing this framework, we systematically explore extensions beyond the standard ΛCDM model, considering a varying curvature density parameter Ω_K, a spectral index n_s = 1 and a varying n _run, a constant dark energy equation of state (EOS) w ₀CDM and a time-dependent one w ₀ w _aCDM. We also assess cosmological data against a varying effective number of neutrino species N _eff. Our analysis incorporates data from various combinations of cosmic microwave background (CMB) data from the latest Planck PR4 analysis, CMB lensing from Planck 2018, baryonic acoustic oscillations (BAO), and the Bicep-KECK 2018 results. We reinforce the standard ΛCDM model statistical preference when combining CMB data with CMB lensing, BAO, and Bicep-KECK 2018 data against the K-ΛCDM model and dn_s /d ln k-ΛCDM with a probability > 80%. When evaluating the dark energy EOS, we find that this dataset does not exhibit a strong preference between the standard ΛCDM model and the constant dark energy EOS model w ₀CDM, with a model posterior probability distribution of approximately ≈ 40%:60% in favour of w ₀CDM, while the time-varying dark energy EOS model only holds below 1% probability. We find a similar result also when considering the N _eff-ΛCDM model, with a split probability almost 50%-50% from both our datasets. Overall, our application of BMA reveals that including model uncertainty in these cases does not significantly impact the Hubble tension, showcasing BMA's robustness and utility in cosmological model evaluation.