Joint models of longitudinal and survival data have become an important tool for modeling associations between longitudinal biomarkers and event processes. The association between marker and log-hazard is assumed to be linear in existing shared random effects models, with this assumption usually remaining unchecked. We present an extended framework of flexible additive joint models that allows the estimation of nonlinear, covariate specific associations by making use of Bayesian P-splines. Our joint models are estimated in a Bayesian framework using structured additive predictors for all model components, allowing for great flexibility in the specification of smooth nonlinear, time-varying and random effects terms for longitudinal submodel, survival submodel and their association. The ability to capture truly linear and nonlinear associations is assessed in simulations and illustrated on the widely studied biomedical data on the rare fatal liver disease primary biliary cirrhosis. All methods are implemented in the R package bamlss to facilitate the application of this flexible joint model in practice.
As with the advancement of geographical information systems, non-Gaussian spatial data sets are getting larger and more diverse. This study develops a general framework for fast and flexible non-Gaussian regression, especially for spatial/spatiotemporal modeling. The developed model, termed the compositionally-warped additive mixed model (CAMM), combines an additive mixed model (AMM) and the compositionally-warped Gaussian process to model a wide variety of non-Gaussian continuous data including spatial and other effects. A specific advantage of the proposed CAMM is that it requires no explici…
Generalized additive models (GAMs) provide a way to blend parametric and non-parametric (function approximation) techniques together, making them flexible tools suitable for many modeling problems. For instance, GAMs can be used to introduce flexibility to standard linear regression models, to express "almost linear" behavior for a phenomenon. A need for GAMs often arises also in physical models, where the model given by theory is an approximation of reality, and one wishes to express the coefficients as functions instead of constants. In this paper, we discuss GAMs from the Bayesian perspecti…
We provide a flexible framework for selecting among a class of additive partial linear models that allows both linear and nonlinear additive components. In practice, it is challenging to determine which additive components should be excluded from the model while simultaneously determining whether nonzero additive components should be represented as linear or non-linear components in the final model. In this paper, we propose a Bayesian model selection method that is facilitated by a carefully specified class of models, including the choice of a prior distribution and the nonparametric model us…
Large scale study of primary school student performance relative to their LMS activity and socioeconomic demographics using a Bayesian Additive Regression Trees containing random effects
Background: Interpreting instrumental variable results often requires further assumptions in addition to the core assumptions of relevance, independence, and the exclusion restriction. Methods: We assess whether instrument-exposure additive homogeneity renders the Wald estimand equal to the average derivative effect (ADE) in the case of a binary instrument and a continuous exposure. Results: Instrument-exposure additive homogeneity is insufficient for ADE identification when the instrument is binary, the exposure is continuous and the effect of the exposure on the outcome is non-linear on the …
MPBART - Multinomial Probit Bayesian Additive Regression Trees
本文提出了多项式概率贝叶斯加性回归树（MPBART）作为BART-贝叶斯加性回归树的多项式概率扩展（Chipman et al（2010））。MPBART是灵活的，允许包括预测，描述观察单位以及可用的选择方案。通过两个模拟研究和四个真实数据的例子，我们表明，MPBART具有很好的预测性能相比，其他离散选择和多类分类方法。为了实现MPBART，我们开发了一个R包mpbart，可以从CRAN仓库免费获得。
Gaussian Process (GP) models are a class of flexible non-parametric models that have rich representational power. By using a Gaussian process with additive structure, complex responses can be modelled whilst retaining interpretability. Previous work showed that additive Gaussian process models require high-dimensional interaction terms. We propose the orthogonal additive kernel (OAK), which imposes an orthogonality constraint on the additive functions, enabling an identifiable, low-dimensional representation of the functional relationship. We connect the OAK kernel to functional ANOVA decompos…
Hypothesis Testing for Nonlinear and Interactive Effects Using Additive Gaussian Processes
Department of Biostatistics, University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校生物统计系）；Department of Environmental Sciences and Engineering, University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校环境科学与工程系）
Methods utilizing instrumental variables have been a fundamental statistical approach to estimation in the presence of unmeasured confounding, usually occurring in non-randomized observational data common to fields such as economics and public health. However, such methods usually make constricting linearity and additivity assumptions that are inapplicable to the complex modeling challenges of today. The growing body of observational data being collected will necessitate flexible regression modeling while also being able to control for confounding using instrumental variables. Therefore, this …
Hierarchical Additive Modeling of Nonlinear Association with Spatial Correlations-An Application to Relate Alcohol Outlet Density and Neighborhood Assault Rates
Hamilton Institute（汉密尔顿研究所）；Insight Centre for Data Analytics（洞察数据分析中心）；Maynooth University（梅努斯大学）
Bayesian Additive Regression Trees (BART) is a tree-based machine learning method that has been successfully applied to regression and classification problems. BART assumes regularisation priors on a set of trees that work as weak learners and is very flexible for predicting in the presence of non-linearity and high-order interactions. In this paper, we introduce an extension of BART, called Model Trees BART (MOTR-BART), that considers piecewise linear functions at node levels instead of piecewise constants. In MOTR-BART, rather than having a unique value at node level for the prediction, a li…
We develop a new family of marked point processes by focusing the characteristic properties of marked Hawkes processes exclusively to the space of marks, providing the freedom to specify a different model for the occurrence times. This is possible through the decomposition of the joint distribution of marks and times that allows to separately specify the conditional distribution of marks given the filtration of the process and the current time. We develop a Bayesian framework for the inference and prediction from this family of marked point processes that can naturally accommodate process and …
Cox proportional hazards model is one of the most popular models in biomedical data analysis. There have been continuing efforts to improve the flexibility of such models for complex signal detection, for example, via additive functions. Nevertheless, the task to extend Cox additive models to accommodate high-dimensional data is nontrivial. When estimating additive functions, commonly used group sparse regularization may introduce excess smoothing shrinkage on additive functions, damaging predictive performance. Moreover, an "all-in-all-out" approach makes functional selection challenging to a…
As the sequencing costs are decreasing, there is great incentive to perform large scale association studies to increase power of detecting new variants. Federated association testing among different institutions is a viable solution for increasing sample sizes by sharing the intermediate testing statistics that are aggregated by a central server. There are, however, standing challenges to performing federated association testing. Association tests are known to be confounded by numerous factors such as population stratification, which can be especially important in multiancestral studies and in…
Models for dependent data are distinguished by their targets of inference. Marginal models are useful when interest lies in quantifying associations averaged across a population of clusters. When the functional form of a covariate-outcome association is unknown, flexible regression methods are needed to allow for potentially non-linear relationships. We propose a novel marginal additive model (MAM) for modelling cluster-correlated data with non-linear population-averaged associations. The proposed MAM is a unified framework for estimation and uncertainty quantification of a marginal mean model…
We develop a model-based boosting approach for multivariate distributional regression within the framework of generalized additive models for location, scale, and shape. Our approach enables the simultaneous modeling of all distribution parameters of an arbitrary parametric distribution of a multivariate response conditional on explanatory variables, while being applicable to potentially high-dimensional data. Moreover, the boosting algorithm incorporates data-driven variable selection, taking various different types of effects into account. As a special merit of our approach, it allows for mo…
University of Gothenburg（哥德堡大学）；Chalmers University of Technology（查尔姆斯理工大学）
Non-parametric, additive models are able to capture complex data dependencies in a flexible, yet interpretable way. However, choosing the format of the additive components often requires non-trivial data exploration. Here, as an alternative, we propose PrAda-net, a one-hidden-layer neural network, trained with proximal gradient descent and adaptive lasso. PrAda-net automatically adjusts the size and architecture of the neural network to reflect the complexity and structure of the data. The compact network obtained by PrAda-net can be translated to additive model components, making it suitable …
