Wildlife monitoring for open populations can be performed using a number of different survey methods. Each survey method gives rise to a type of data and, in the last five decades, a large number of associated statistical models have been developed for analyzing these data. Although these models have been parameterized and fitted using different approaches, they have all been designed to either model the pattern with which individuals enter and/or exit the population, or to estimate the population size by accounting for the corresponding observation process, or both. However, existing approaches rely on a predefined model structure and complexity, either by assuming that parameters linked to the entry and exit pattern (EEP) are specific to sampling occasions, or by employing parametric curves to describe the EEP. Instead, we propose a novel Bayesian nonparametric framework for modeling EEPs based on the Polya tree (PT) prior for densities. Our Bayesian nonparametric approach avoids overfitting when inferring EEPs, while simultaneously allowing more flexibility than is possible using parametric curves. Finally, we introduce the replicate PT prior for defining classes of models for these data allowing us to impose constraints on the EEPs, when required. We demonstrate our new approach using capture-recapture, count, and ring-recovery data for two different case studies.

Functional data analysis has emerged as a powerful tool in response to the ever-increasing resources and efforts devoted to collecting information about response curves or anything that varies over a continuum. However, limited progress has been made with regard to linking the covariance structures of response curves to external covariates, as most functional models assume a common covariance structure. We propose a new functional regression model with covariate-dependent mean and covariance structures. Particularly, by allowing variances of random scores to be covariate-dependent, we identify eigenfunctions for each individual from the set of eigenfunctions that govern the variation patterns across all individuals, resulting in high interpretability and prediction power. We further propose a new penalized quasi-likelihood procedure that combines regularization and B-spline smoothing for model selection and estimation and establish the convergence rate and asymptotic normality of the proposed estimators. The utility of the developed method is demonstrated via simulations, as well as an analysis of the Avon Longitudinal Study of Parents and Children concerning parental effects on the growth curves of their offspring, which yields biologically interesting results.

The receptive field (RF) of a visual neuron is the region of the space that elicits neuronal responses. It can be mapped using different techniques that allow inferring its spatial and temporal properties. Raw RF maps (RFmaps) are usually noisy, making it difficult to obtain and study important features of the RF. A possible solution is to smooth them using P-splines. Yet, raw RFmaps are characterized by sharp transitions in both space and time. Their analysis thus asks for spatiotemporal adaptive P-spline models, where smoothness can be locally adapted to the data. However, the literature lacks proposals for adaptive P-splines in more than two dimensions. Furthermore, the extra flexibility afforded by adaptive P-spline models is obtained at the cost of a high computational burden, especially in a multidimensional setting. To fill these gaps, this work presents a novel anisotropic locally adaptive P-spline model in two (e.g., space) and three (space and time) dimensions. Estimation is based on the recently proposed SOP (Separation of Overlapping Precision matrices) method, which provides the speed we look for. Besides the spatiotemporal analysis of the neuronal activity data that motivated this work, the practical performance of the proposal is evaluated through simulations, and comparisons with alternative methods are reported.

A dynamic treatment regime (DTR) is a sequence of decision rules that provide guidance on how to treat individuals based on their static and time-varying status. Existing observational data are often used to generate hypotheses about effective DTRs. A common challenge with observational data, however, is the need for analysts to consider "restrictions" on the treatment sequences. Such restrictions may be necessary for settings where (1) one or more treatment sequences that were offered to individuals when the data were collected are no longer considered viable in practice, (2) specific treatment sequences are no longer available, or (3) the scientific focus of the analysis concerns a specific type of treatment sequences (eg, "stepped-up" treatments). To address this challenge, we propose a restricted tree-based reinforcement learning (RT-RL) method that searches for an interpretable DTR with the maximum expected outcome, given a (set of) user-specified restriction(s), which specifies treatment options (at each stage) that ought not to be considered as part of the estimated tree-based DTR. In simulations, we evaluate the performance of RT-RL versus the standard approach of ignoring the partial data for individuals not following the (set of) restriction(s). The method is illustrated using an observational data set to estimate a two-stage stepped-up DTR for guiding the level of care placement for adolescents with substance use disorder.

In the COVID-19 pandemic, workplace transmission plays an important role. For this type of transmission, the longitudinal 14-day incidence curve of SARS-CoV-2 infections per economic sector is a proxy. In Belgium, a census of confirmed 14-day incidences per NACE-BEL sector level three is available from September 2020 until June 2021, encompassing two waves of infections. However, these high-dimensional data, with a relatively small number of NACE-BEL sectors, are challenging to analyze. We propose a nonlinear Gaussian-Gaussian model that combines parametric and semi-parametric elements to describe the incidence curves with a small set of meaningful parameters. These parameters are further analyzed with conventional statistical methods, such as CCA and linear models, to provide insight into predictive characteristics of the first wave for the second wave. Those nonlinear models classify economic sectors into three groups: sectors with two regular waves of infections, sectors with only a first wave and sectors with a more irregular profile, which may indicate a clear effect of COVID-19 vaccination. The Gaussian-Gaussian model thus allows for analyzing and comparing incidence curves and to bring out key characteristics of such curves. Finally, we consider in which other settings the proposed approach could be applied, together with possible pitfalls.

High-throughput biological experiments are essential tools for identifying biologically interesting candidates in large-scale omics studies. The results of a high-throughput biological experiment rely heavily on the operational factors chosen in its experimental and data-analytic procedures. Understanding how these operational factors influence the reproducibility of the experimental outcome is critical for selecting the optimal parameter settings and designing reliable high-throughput workflows. However, the influence of an operational factor may differ between strong and weak candidates in a high-throughput experiment, complicating the selection of parameter settings. To address this issue, we propose a novel segmented regression model, called segmented correspondence curve regression, to assess the influence of operational factors on the reproducibility of high-throughput experiments. Our model dissects the heterogeneous effects of operational factors on strong and weak candidates, providing a principled way to select operational parameters. Based on this framework, we also develop a sup-likelihood ratio test for the existence of heterogeneity. Simulation studies show that our estimation and testing procedures yield well-calibrated type I errors and are substantially more powerful in detecting and locating the differences in reproducibility across workflows than the existing method. Using this model, we investigated an important design question for ChIP-seq experiments: How many reads should one sequence to obtain reliable results in a cost-effective way? Our results reveal new insights into the impact of sequencing depth on the binding-site identification reproducibility, helping biologists determine the most cost-effective sequencing depth to achieve sufficient reproducibility for their study goals.

Capturing complex dependence structures between outcome variables (e.g., study endpoints) is of high relevance in contemporary biomedical data problems and medical research. Distributional copula regression provides a flexible tool to model the joint distribution of multiple outcome variables by disentangling the marginal response distributions and their dependence structure. In a regression setup, each parameter of the copula model, that is, the marginal distribution parameters and the copula dependence parameters, can be related to covariates via structured additive predictors. We propose a framework to fit distributional copula regression via model-based boosting, which is a modern estimation technique that incorporates useful features like an intrinsic variable selection mechanism, parameter shrinkage and the capability to fit regression models in high-dimensional data setting, that is, situations with more covariates than observations. Thus, model-based boosting does not only complement existing Bayesian and maximum-likelihood based estimation frameworks for this model class but rather enables unique intrinsic mechanisms that can be helpful in many applied problems. The performance of our boosting algorithm for copula regression models with continuous margins is evaluated in simulation studies that cover low- and high-dimensional data settings and situations with and without dependence between the responses. Moreover, distributional copula boosting is used to jointly analyze and predict the length and the weight of newborns conditional on sonographic measurements of the fetus before delivery together with other clinical variables.

Detecting and characterizing subgroups with differential effects of a binary treatment has been widely studied and led to improvements in patient outcomes and population risk management. Under the setting of a continuous treatment, however, such investigations remain scarce. We propose a semiparametric change-plane model and consequently a doubly robust test statistic for assessing the existence of two subgroups with differential treatment effects under a continuous treatment. The proposed testing procedure is valid when either the baseline function for the covariate effects or the generalized propensity score function for the continuous treatment is correctly specified. The asymptotic distributions of the test statistic under the null and local alternative hypotheses are established. When the null hypothesis of no subgroup is rejected, the change-plane parameters that define the subgroups can be estimated. This paper provides a unified framework of the change-plane method to handle various types of outcomes, including the exponential family of distributions and time-to-event outcomes. Additional extensions with nonparametric estimation approaches are also provided. We evaluate the performance of our proposed methods through extensive simulation studies under various scenarios. An application to the Health Effects of Arsenic Longitudinal Study with a continuous environmental exposure of arsenic is presented.

We propose a unified framework for likelihood-based regression modeling when the response variable has finite support. Our work is motivated by the fact that, in practice, observed data are discrete and bounded. The proposed methods assume a model which includes models previously considered for interval-censored variables with log-concave distributions as special cases. The resulting log-likelihood is concave, which we use to establish asymptotic normality of its maximizer as the number of observations n tends to infinity with the number of parameters d fixed, and rates of convergence of L1 -regularized estimators when the true parameter vector is sparse and d and n both tend to infinity with log(d)/n → 0 . We consider an inexact proximal Newton algorithm for computing estimates and give theoretical guarantees for its convergence. The range of possible applications is wide, including but not limited to survival analysis in discrete time, the modeling of outcomes on scored surveys and questionnaires, and, more generally, interval-censored regression. The applicability and usefulness of the proposed methods are illustrated in simulations and data examples.

The additive hazards model specifies the effect of covariates on the hazard in an additive way, in contrast to the popular Cox model, in which it is multiplicative. As the non-parametric model, additive hazards offer a very flexible way of modeling time-varying covariate effects. It is most commonly estimated by ordinary least squares. In this paper, we consider the case where covariates are bounded, and derive the maximum likelihood estimator under the constraint that the hazard is non-negative for all covariate values in their domain. We show that the maximum likelihood estimator may be obtained by separately maximizing the log-likelihood contribution of each event time point, and we show that the maximizing problem is equivalent to fitting a series of Poisson regression models with an identity link under non-negativity constraints. We derive an analytic solution to the maximum likelihood estimator. We contrast the maximum likelihood estimator with the ordinary least-squares estimator in a simulation study and show that the maximum likelihood estimator has smaller mean squared error than the ordinary least-squares estimator. An illustration with data on patients with carcinoma of the oropharynx is provided.

Semi-competing risks refer to the time-to-event analysis setting, where the occurrence of a non-terminal event is subject to whether a terminal event has occurred, but not vice versa. Semi-competing risks arise in a broad range of clinical contexts, including studies of preeclampsia, a condition that may arise during pregnancy and for which delivery is a terminal event. Models that acknowledge semi-competing risks enable investigation of relationships between covariates and the joint timing of the outcomes, but methods for model selection and prediction of semi-competing risks in high dimensions are lacking. Moreover, in such settings researchers commonly analyze only a single or composite outcome, losing valuable information and limiting clinical utility-in the obstetric setting, this means ignoring valuable insight into timing of delivery after preeclampsia has onset. To address this gap, we propose a novel penalized estimation framework for frailty-based illness-death multi-state modeling of semi-competing risks. Our approach combines non-convex and structured fusion penalization, inducing global sparsity as well as parsimony across submodels. We perform estimation and model selection via a pathwise routine for non-convex optimization, and prove statistical error rate results in this setting. We present a simulation study investigating estimation error and model selection performance, and a comprehensive application of the method to joint risk modeling of preeclampsia and timing of delivery using pregnancy data from an electronic health record.

Discussion on "A formal causal interpretation of the case-crossover design" by Zach Shahn, Miguel A. Hernan, and James M. Robins.

Shahn, Hernan, and Robins give conditions under which estimates from a case-crossover analysis converge to the desired causal relative risk times a bias factor, and they discuss conditions needed to have small bias. To simplify the problem, we discuss only two exposure times and rely on randomized exposure assignments, thereby avoiding the need for potential outcome notation. We identify many, but not all, of the conditions discussed by Shahn et al. in this simple analysis.

It has always been clear that the case-crossover design works, for some definition of "works," but some of the details have been surprisingly elusive, and it is good to see more of them nailed down by Shahn et al. My interest in case-crossover analyses has mostly been in the context of air pollution epidemiology mentioned at the end of the paper. The air pollution setting is distinctive for several reasons: as the exposure variable is plausibly exogenous, it is possible to use control times after the case time, the effects of interest are quite small, and the same measured exposure series is shared over many-perhaps all-of the cohort.

This paper introduces a flexible and adaptive nonparametric method for estimating the association between multiple covariates and power spectra of multiple time series. The proposed approach uses a Bayesian sum of trees model to capture complex dependencies and interactions between covariates and the power spectrum, which are often observed in studies of biomedical time series. Local power spectra corresponding to terminal nodes within trees are estimated nonparametrically using Bayesian penalized linear splines. The trees are considered to be random and fit using a Bayesian backfitting Markov chain Monte Carlo (MCMC) algorithm that sequentially considers tree modifications via reversible-jump MCMC techniques. For high-dimensional covariates, a sparsity-inducing Dirichlet hyperprior on tree splitting proportions is considered, which provides sparse estimation of covariate effects and efficient variable selection. By averaging over the posterior distribution of trees, the proposed method can recover both smooth and abrupt changes in the power spectrum across multiple covariates. Empirical performance is evaluated via simulations to demonstrate the proposed method's ability to accurately recover complex relationships and interactions. The proposed methodology is used to study gait maturation in young children by evaluating age-related changes in power spectra of stride interval time series in the presence of other covariates.

Advances in information technologies have made network data increasingly frequent in a spectrum of big data applications, which is often explored by probabilistic graphical models. To precisely estimate the precision matrix, we propose an optimal model averaging estimator for Gaussian graphs. We prove that the proposed estimator is asymptotically optimal when candidate models are misspecified. The consistency and the asymptotic distribution of model averaging estimator, and the weight convergence are also studied when at least one correct model is included in the candidate set. Furthermore, numerical simulations and a real data analysis on yeast genetic data are conducted to illustrate that the proposed method is promising.