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The formation history of binary black hole systems is imprinted on the distribution of their masses, spins, and eccentricity. While much has been learned studying these parameters in turn, recent studies have explored the joint distribution of binary black hole parameters in two or more dimensions. Most notably, it has recently been argued that binary black hole mass ratio and effective inspiral spin χeff are anticorrelated. We point out a previously overlooked subtlety in such 2D population studies: in order to conduct a controlled test for correlation, one ought to fix the two marginal distributions – lest the purported correlation be driven by improved fit in just one dimension. We address this subtlety using a tool from applied statistics: the copula density function. We use the previous work correlating mass ratio and χeff as a case study to demonstrate the power of copulas in gravitational-wave astronomy while scrutinizing their astrophysical inferences. Our findings, however, affirm their conclusions that binary black holes with unequal component masses exhibit larger χeff (98.7 per cent credibility). We conclude by discussing potential astrophysical implications of these findings as well as prospects for future studies using copulas. [ABSTRACT FROM AUTHOR]

In dose–response analysis, it is a challenge to choose appropriate linear or curvilinear shapes when considering multiple, differently scaled endpoints. It has been proposed to fit several marginal regression models that try sets of different transformations of the dose levels as explanatory variables for each endpoint. However, the multiple testing problem underlying this approach, involving correlated parameter estimates for the dose effect between and within endpoints, could only be adjusted heuristically. An asymptotic correction for multiple testing can be derived from the score functions of the marginal regression models. Based on a multivariate t‐distribution, the correction provides a one‐step adjustment of p‐values that accounts for the correlation between estimates from different marginal models. The advantages of the proposed methodology are demonstrated through three example datasets, involving generalized linear models with differently scaled endpoints, differing covariates, and a mixed effect model and through simulation results. The methodology is implemented in an R package. [ABSTRACT FROM AUTHOR]

Suppose HT ht . One may try to remove such ambiguity by restricting the minimum support of HT ht to be greater than I m i , but this essentially excludes the possibility that the primary event censors the mediating event. Therefore, the usual notion of having well-defined interventions for I A i and I M i for defining HT ht does not go through because HT ht may happen before I m i , and in that case, the role of I m i is ambiguous. Under a composition assumption, HT ht . [Extracted from the article]

We propose a new highly flexible and tractable Bayesian approach to undertake variable selection in non‐Gaussian regression models. It uses a copula decomposition for the joint distribution of observations on the dependent variable. This allows the marginal distribution of the dependent variable to be calibrated accurately using a nonparametric or other estimator. The family of copulas employed are "implicit copulas" that are constructed from existing hierarchical Bayesian models widely used for variable selection, and we establish some of their properties. Even though the copulas are high dimensional, they can be estimated efficiently and quickly using Markov chain Monte Carlo. A simulation study shows that when the responses are non‐Gaussian, the approach selects variables more accurately than contemporary benchmarks. A real data example in the Web Appendix illustrates that accounting for even mild deviations from normality can lead to a substantial increase in accuracy. To illustrate the full potential of our approach, we extend it to spatial variable selection for fMRI. Using real data, we show our method allows for voxel‐specific marginal calibration of the magnetic resonance signal at over 6000 voxels, leading to an increase in the quality of the activation maps. [ABSTRACT FROM AUTHOR]

Dynamic prediction uses patient information collected during follow-up to produce individualized survival predictions at given time points beyond treatment or diagnosis. This allows clinicians to obtain updated predictions of a patient's prognosis that can be used in making personalized treatment decisions. Two commonly used approaches for dynamic prediction are landmarking and joint modeling. Landmarking does not constitute a comprehensive probability model, and joint modeling often requires strong distributional assumptions and computationally intensive methods for estimation. We introduce an alternative approximate approach for dynamic prediction that aims to overcome the limitations of both methods while achieving good predictive performance. We separately specify the marker and failure time distributions conditional on surviving up to a prediction time of interest and use standard variable selection and goodness-of-fit techniques to identify the best-fitting models. Taking advantage of its analytic tractability and easy two-stage estimation, we use a Gaussian copula to link the marginal distributions smoothly at each prediction time with an association function. With simulation studies, we examine the proposed method's performance. We illustrate its use for dynamic prediction in an application to predicting death for heart valve transplant patients using longitudinal left ventricular mass index information. [ABSTRACT FROM AUTHOR]