arXiv Statistics @arxiv_stats@qoto.org

In biomedical and public health association studies, binary outcome variables may be subject to misclassification, resulting in substantial bias in effect estimates. The feasibility of addressing binary outcome misclassification in regression models is often hindered by model identifiability issues. In this paper, we characterize the identifiability problems in this class of models as a specific case of "label switching" and leverage a pattern in the resulting parameter estimates to solve the permutation invariance of the complete data log-likelihood. Our proposed algorithm in binary outcome misclassification models does not require gold standard labels and relies only on the assumption that outcomes are correctly classified at least 50% of the time. A label switching correction is applied within estimation methods to recover unbiased effect estimates and to estimate misclassification rates in cases with one or more sequential observed outcomes. Open source software is provided to implement the proposed methods for single- and two-stage models. We give a detailed simulation study for our proposed methodology and apply these methods to data for single-stage modeling of the Medical Expenditure Panel Survey (MEPS) from 2020 and two-stage modeling of data from the Virginia Department of Criminal Justice Services.

The recent explosion of genetic and high dimensional biobank and 'omic' data has provided researchers with the opportunity to investigate the shared genetic origin (pleiotropy) of hundreds to thousands of related phenotypes. However, existing methods for multi-phenotype genome-wide association studies (GWAS) do not model pleiotropy, are only applicable to a small number of phenotypes, or provide no way to perform inference. To add further complication, raw genetic and phenotype data are rarely observed, meaning analyses must be performed on GWAS summary statistics whose statistical properties in high dimensions are poorly understood. We therefore developed a novel model, theoretical framework, and set of methods to perform Bayesian inference in GWAS of high dimensional phenotypes using summary statistics that explicitly model pleiotropy, beget fast computation, and facilitate the use of biologically informed priors. We demonstrate the utility of our procedure by applying it to metabolite GWAS, where we develop new nonparametric priors for genetic effects on metabolite levels that use known metabolic pathway information and foster interpretable inference at the pathway level.

We consider the truncated multivariate normal distributions for which every component is one-sided truncated. We show that this family of distributions is an exponential family. We identify $\mathcal{D}$, the corresponding natural parameter space, and deduce that the family of distributions is not regular. We prove that the gradient of the cumulant-generating function of the family of distributions remains bounded near certain boundary points in $\mathcal{D}$, and therefore the family also is not steep. We also consider maximum likelihood estimation for $\boldsymbolμ$, the location vector parameter, and $\boldsymbolΣ$, the positive definite (symmetric) matrix dispersion parameter, of a truncated non-singular multivariate normal distribution. We prove that each solution to the score equations for $(\boldsymbolμ,\boldsymbolΣ)$ satisfies the method-of-moments equations, and we obtain a necessary condition for the existence of solutions to the score equations.

Let $X$ denote a random vector having a Bingham distribution on ${\mathcal{S}}^{d-1}$, the unit sphere centered at the origin in ${\mathbb{R}}^d$. With $Σ$ denoting the symmetric matrix parameter of the distribution, let $Ψ(Σ)$ be the corresponding normalizing constant of the distribution. We derive for $Ψ(Σ)$ and its first-order partial derivatives complete asymptotic expansions as $d \to \infty$. These expansions are obtained under the growth condition that $\|Σ\|$, the Frobenius norm of $Σ$, satisfies $\|Σ\| = O(d^{r/2})$, where $0 \le r < 1$. As a consequence, we obtain for the covariance matrix of $X$ an asymptotic expansion up to terms of arbitrary degree in $Σ$.

Generalised hyperbolic (GH) processes are a class of stochastic processes that are used to model the dynamics of a wide range of complex systems that exhibit heavy-tailed behavior, including systems in finance, economics, biology, and physics. In this paper, we present novel simulation methods based on subordination with a generalised inverse Gaussian (GIG) process and using a generalised shot-noise representation that involves random thinning of infinite series of decreasing jump sizes. Compared with our previous work on GIG processes, we provide tighter bounds for the construction of rejection sampling ratios, leading to improved acceptance probabilities in simulation. Furthermore, we derive methods for the adaptive determination of the number of points required in the associated random series using concentration inequalities. Residual small jumps are then approximated using an appropriately scaled Brownian motion term with drift. Finally the rejection sampling steps are made significantly more computationally efficient through the use of squeezing functions based on lower and upper bounds on the Lévy density. Experimental results are presented illustrating the strong performance under various parameter settings and comparing the marginal distribution of the GH paths with exact simulations of GH random variates. The new simulation methodology is made available to researchers through the publication of a Python code repository.

Recent developments in counter-adversarial system research have led to the development of inverse stochastic filters that are employed by a defender to infer the information its adversary may have learned. Prior works addressed this inverse cognition problem by proposing inverse Kalman filter (I-KF) and inverse extended KF (I-EKF), respectively, for linear and non-linear Gaussian state-space models. However, in practice, many counter-adversarial settings involve highly non-linear system models, wherein EKF's linearization often fails. In this paper, we consider the efficient numerical integration techniques to address such nonlinearities and, to this end, develop inverse cubature KF (I-CKF) and inverse quadrature KF (I-QKF). We derive the stochastic stability conditions for the proposed filters in the exponential-mean-squared-boundedness sense. Numerical experiments demonstrate the estimation accuracy of our I-CKF and I-QKF with the recursive Cramér-Rao lower bound as a benchmark.

We present neural frailty machine (NFM), a powerful and flexible neural modeling framework for survival regressions. The NFM framework utilizes the classical idea of multiplicative frailty in survival analysis to capture unobserved heterogeneity among individuals, at the same time being able to leverage the strong approximation power of neural architectures for handling nonlinear covariate dependence. Two concrete models are derived under the framework that extends neural proportional hazard models and nonparametric hazard regression models. Both models allow efficient training under the likelihood objective. Theoretically, for both proposed models, we establish statistical guarantees of neural function approximation with respect to nonparametric components via characterizing their rate of convergence. Empirically, we provide synthetic experiments that verify our theoretical statements. We also conduct experimental evaluations over $6$ benchmark datasets of different scales, showing that the proposed NFM models outperform state-of-the-art survival models in terms of predictive performance. Our code is publicly availabel at https://github.com/Rorschach1989/nfm

Technology adoption research aims to determine the reasons why and how individuals, corporations, and industries start using new technology. Furthermore, technology adoption itself is decomposed into underlying sub-processes which are characterized by a finite number of sequential states in order to capture its evolutionary nature. Building upon that, in this paper a technology adoption index is being constructed that allows for statistical testing. This new framework is flexible with respect to the number of underlying models, and accounts for nonlinearities within the evolution of technology adoption. It can be considered as novel because it gives opportunity to a quantitative analysis of technology adoption that has not existed before. Subsequently, this framework is applied for an integrated model of technology adoption.

Microbiome research is now moving beyond the compositional analysis of microbial taxa in a sample. Increasing evidence from large human microbiome studies suggests that functional consequences of changes in the intestinal microbiome may provide more power for studying their impact on inflammation and immune responses. Although 16S rRNA analysis is one of the most popular and a cost-effective method to profile the microbial compositions, marker-gene sequencing cannot provide direct information about the functional genes that are present in the genomes of community members. Bioinformatic tools have been developed to predict microbiome function with 16S rRNA gene data. Among them, PICRUSt2 has become one of the most popular functional profile prediction tools, which generates community-wide pathway abundances. However, no state-of-art inference tools are available to test the differences in pathway abundances between comparison groups. We have developed ggpicrust2, an R package, to do extensive differential abundance(DA) analyses and provide publishable visualization to highlight the signals.

Understanding the gradient variance of black-box variational inference (BBVI) is a crucial step for establishing its convergence and developing algorithmic improvements. However, existing studies have yet to show that the gradient variance of BBVI satisfies the conditions used to study the convergence of stochastic gradient descent (SGD), the workhorse of BBVI. In this work, we show that BBVI satisfies a matching bound corresponding to the $ABC$ condition used in the SGD literature when applied to smooth and quadratically-growing log-likelihoods. Our results generalize to nonlinear covariance parameterizations widely used in the practice of BBVI. Furthermore, we show that the variance of the mean-field parameterization has provably superior dimensional dependence.

This paper is concerned with sample size determination methodology for prediction models. We propose combining the individual calculations via a learning-type curve. We suggest two distinct ways of doing so, a deterministic skeleton of a learning curve and a Gaussian process centred upon its deterministic counterpart. We employ several learning algorithms for modelling the primary endpoint and distinct measures for trial efficacy. We find that the performance may vary with the sample size, but borrowing information across sample size universally improves the performance of such calculations. The Gaussian process-based learning curve appears more robust and statistically efficient, while computational efficiency is comparable. We suggest that anchoring against historical evidence when extrapolating sample sizes should be adopted when such data are available. The methods are illustrated on binary and survival endpoints.

The log-logistic regression model is one of the most commonly used accelerated failure time (AFT) models in survival analysis, for which statistical inference methods are mainly established under the frequentist framework. Recently, Bayesian inference for log-logistic AFT models using Markov chain Monte Carlo (MCMC) techniques has also been widely developed. In this work, we develop an alternative approach to MCMC methods and infer the parameters of the log-logistic AFT model via a mean-field variational Bayes (VB) algorithm. A piece-wise approximation technique is embedded in deriving the update equations in the VB algorithm to achieve conjugacy. The proposed VB algorithm is evaluated and compared with typical frequentist inferences using simulated data under various scenarios, and a publicly available dataset is employed for illustration. We demonstrate that the proposed VB algorithm can achieve good estimation accuracy and is not sensitive to sample sizes, censoring rates, and prior information.

Residual diagnostic methods play a critical role in assessing model assumptions and detecting outliers in statistical modelling. In the context of survival models with censored observations, Li et al. (2021) introduced the Z-residual, which follows an approximately normal distribution under the true model. This property makes it possible to use Z-residuals for diagnosing survival models in a way similar to how Pearson residuals are used in normal regression. However, computing residuals based on the full dataset can result in a conservative bias that reduces the power of detecting model mis-specification, as the same dataset is used for both model fitting and validation. Although cross-validation is a potential solution to this problem, it has not been commonly used in residual diagnostics due to computational challenges. In this paper, we propose a cross-validation approach for computing Z-residuals in the context of shared frailty models. Specifically, we develop a general function that calculates cross-validatory Z-residuals using the output from the \texttt{coxph} function in the \texttt{survival} package in R.Our simulation studies demonstrate that, for goodness-of-fit tests and outlier detection, cross-validatory Z-residuals are significantly more powerful and more discriminative than Z-residuals without cross-validation. We also compare the performance of Z-residuals with and without cross-validation in identifying outliers in a real application that models the recurrence time of kidney infection patients. Our findings suggest that cross-validatory Z-residuals can identify outliers that are missed by Z-residuals without cross-validation.

Motivated by applications in hydrodynamics and networks of thermostatically-control loads in buildings we study control of linear dynamical systems driven by additive and also multiplicative noise of a general position. Utilizing mathematical theory of stochastic multiplicative processes we present a universal way to estimate fat, algebraic tails of the state vector probability distributions. This motivates us to introduce and analyze Mean-$q$-Power stability criterion, generalizing the mean-square stability criterion, and then juxtapose these techniques to other, classic tools in control.

The presented methodology for testing the goodness-of-fit of an Autoregressive Hilbertian model (ARH(1) model) provides an infinite-dimensional formulation of the approach proposed in Koul and Stute (1999), based on empirical process marked by residuals. Applying a central and functional central limit result for Hilbert-valued martingale difference sequences, the asymptotic behavior of the formulated H-valued empirical process, also indexed by H, is obtained under the null hypothesis. The limiting process is H-valued generalized (i.e., indexed by H) Wiener process, leading to an asymptotically distribution free test. Consistency is also analyzed. The case of misspecified autocorrelation operator of the ARH(1) process is addressed as well. Beyond the Euclidean setting, this approach allows to implement goodness of fit testing in the context of manifold and spherical functional autoregressive processes.

The impacts of link recommendations on social networks are challenging to evaluate, and so far they have been studied in limited settings. Observational studies are restricted in the kinds of causal questions they can answer and naive A/B tests often lead to biased evaluations due to unaccounted network interference. Furthermore, evaluations in simulation settings are often limited to static network models that do not take into account the potential feedback loops between link recommendation and organic network evolution. To this end, we study the impacts of recommendations on social networks in dynamic settings. Adopting a simulation-based approach, we consider an explicit dynamic formation model -- an extension of the celebrated Jackson-Rogers model -- and investigate how link recommendations affect network evolution over time. Empirically, we find that link recommendations have surprising delayed and indirect effects on the structural properties of networks. Specifically, we find that link recommendations can exhibit considerably different impacts in the immediate term and in the long term. For instance, we observe that friend-of-friend recommendations can have an immediate effect in decreasing degree inequality, but in the long term, they can make the degree distribution substantially more unequal. Moreover, we show that the effects of recommendations can persist in networks, in part due to their indirect impacts on natural dynamics even after recommendations are turned off. We show that, in counterfactual simulations, removing the indirect effects of link recommendations can make the network trend faster toward what it would have been under natural growth dynamics.

Previously, we proposed a probabilistic data generation model represented by an unobservable tree and a sequential updating method to calculate a posterior distribution over a set of trees. The set is called a meta-tree. In this paper, we propose a more efficient batch updating method.

We propose the so-called jackknife empirical likelihood approach for the survey data of general unequal probability sampling designs, and analyze parameters defined according to U-statistics. We prove theoretically that jackknife pseudo-empirical likelihood ratio statistic is asymptotically distributed as a chi-square random variable, and can be used to construct confidence intervals for complex survey samples. In the process of research, we consider with or without auxiliary information, utilizing design weights or calibration weights. Simulation studies are included to examine that in terms of coverage probability and tail error rates, the jackknife pseudo-empirical likelihood ratio confidence intervals are superior to those based on the normal approximation.

Selection of covariates is crucial in the estimation of average treatment effects given observational data with high or even ultra-high dimensional pretreatment variables. Existing methods for this problem typically assume sparse linear models for both outcome and univariate treatment, and cannot handle situations with ultra-high dimensional covariates. In this paper, we propose a new covariate selection strategy called double screening prior adaptive lasso (DSPAL) to select confounders and predictors of the outcome for multivariate treatments, which combines the adaptive lasso method with the marginal conditional (in)dependence prior information to select target covariates, in order to eliminate confounding bias and improve statistical efficiency. The distinctive features of our proposal are that it can be applied to high-dimensional or even ultra-high dimensional covariates for multivariate treatments, and can deal with the cases of both parametric and nonparametric outcome models, which makes it more robust compared to other methods. Our theoretical analyses show that the proposed procedure enjoys the sure screening property, the ranking consistency property and the variable selection consistency. Through a simulation study, we demonstrate that the proposed approach selects all confounders and predictors consistently and estimates the multivariate treatment effects with smaller bias and mean squared error compared to several alternatives under various scenarios. In real data analysis, the method is applied to estimate the causal effect of a three-dimensional continuous environmental treatment on cholesterol level and enlightening results are obtained.

To what extent can the patient's length of stay in a hospital be predicted using only an X-ray image? We answer this question by comparing the performance of machine learning survival models on a novel multi-modal dataset created from 1235 images with textual radiology reports annotated by humans. Although black-box models predict better on average than interpretable ones, like Cox proportional hazards, they are not inherently understandable. To overcome this trust issue, we introduce time-dependent model explanations into the human-AI decision making process. Explaining models built on both: human-annotated and algorithm-extracted radiomics features provides valuable insights for physicians working in a hospital. We believe the presented approach to be general and widely applicable to other time-to-event medical use cases. For reproducibility, we open-source code and the TLOS dataset at https://github.com/mi2datalab/xlungs-trustworthy-los-prediction.