Spatio-Network Generalised Linear Mixed Models for Areal Unit and Network Data

Implements a class of univariate and multivariate spatio-network generalised linear mixed models for areal unit and network data, with inference in a Bayesian setting using Markov chain Monte Carlo (MCMC) simulation. The response variable can be binomial, Gaussian, or Poisson. Spatial autocorrelation is modelled by a set of random effects that are assigned a conditional autoregressive (CAR) prior distribution following the Leroux model (Leroux et al. (2000) ). Network structures are modelled by a set of random effects that reflect a multiple membership structure (Browne et al. (2001) ).

Leveraging eQTLs to Identify Individual-Level Tissue of Interest for a Complex Trait

Genetic predisposition for complex traits is often manifested through multiple tissues of interest at different time points in the development. As an example, the genetic predisposition for obesity could be manifested through inherited variants that control metabolism through regulation of genes expressed in the brain and/or through the control of fat storage in the adipose tissue by dysregulation of genes expressed in adipose tissue. We present a method eGST (eQTL-based genetic subtyper) that integrates tissue-specific eQTLs with GWAS data for a complex trait to probabilistically assign a tissue of interest to the phenotype of each individual in the study. eGST estimates the posterior probability that an individual's phenotype can be assigned to a tissue based on individual-level genotype data of tissue-specific eQTLs and marginal phenotype data in a genome-wide association study (GWAS) cohort. Under a Bayesian framework of mixture model, eGST employs a maximum a posteriori (MAP) expectation-maximization (EM) algorithm to estimate the tissue-specific posterior probability across individuals. Methodology is available from: A Majumdar, C Giambartolomei, N Cai, MK Freund, T Haldar, T Schwarz, J Flint, B Pasaniuc (2019) .

Bayesian Multivariate Analysis of Summary Statistics

Multivariate tool for analyzing genome-wide association study results in the form of univariate summary statistics. The goal of 'bmass' is to comprehensively test all possible multivariate models given the phenotypes and datasets provided. Multivariate models are determined by assigning each phenotype to being either Unassociated (U), Directly associated (D) or Indirectly associated (I) with the genetic variant of interest. Test results for each model are presented in the form of Bayes factors, thereby allowing direct comparisons between models. The underlying framework implemented here is based on the modeling developed in "A Unified Framework for Association Analysis with Multiple Related Phenotypes", M. Stephens (2013) .

Partitioning of Individual Autozygosity into Multiple Homozygous-by-Descent Classes

Functions to identify Homozygous-by-Descent (HBD) segments associated with runs of homozygosity (ROH) and to estimate individual autozygosity (or inbreeding coefficient). HBD segments and autozygosity are assigned to multiple HBD classes with a model-based approach relying on a mixture of exponential distributions. The rate of the exponential distribution is distinct for each HBD class and defines the expected length of the HBD segments. These HBD classes are therefore related to the age of the segments (longer segments and smaller rates for recent autozygosity / recent common ancestor). The functions allow to estimate the parameters of the model (rates of the exponential distributions, mixing proportions), to estimate global and local autozygosity probabilities and to identify HBD segments with the Viterbi decoding. The method is fully described in Druet and Gautier (2017) and Druet and Gautier (2022) .

Functions to Simplify the Use of 'glmnet' for Machine Learning

Provides several functions to simplify using the 'glmnet' package: converting data frames into matrices ready for 'glmnet'; b) imputing missing variables multiple times; c) fitting and applying prediction models straightforwardly; d) assigning observations to folds in a balanced way; e) cross-validate the models; f) selecting the most representative model across imputations and folds; and g) getting the relevance of the model regressors; as described in several publications: Solanes et al. (2022) , Palau et al. (2023) , Salazar de Pablo et al. (2025) .

Programmatic Utilities for Manipulating Formulas, Expressions, Calls, Assignments and Other R Objects

These utilities facilitate the programmatic manipulations of formulas, expressions, calls, assignments and other R language objects. These objects all share the same structure: a left-hand side, operator and right-hand side. This packages provides methods for accessing and modifying this structures as well as extracting and replacing names and symbols from these objects.

Spatial Generalised Linear Mixed Models for Areal Unit Data

Implements a class of univariate and multivariate spatial generalised linear mixed models for areal unit data, with inference in a Bayesian setting using Markov chain Monte Carlo (MCMC) simulation using a single or multiple Markov chains. The response variable can be binomial, Gaussian, multinomial, Poisson or zero-inflated Poisson (ZIP), and spatial autocorrelation is modelled by a set of random effects that are assigned a conditional autoregressive (CAR) prior distribution. A number of different models are available for univariate spatial data, including models with no random effects as well as random effects modelled by different types of CAR prior, including the BYM model (Besag et al., 1991, ) and Leroux model (Leroux et al., 2000, ). Additionally, a multivariate CAR (MCAR) model for multivariate spatial data is available, as is a two-level hierarchical model for modelling data relating to individuals within areas. Full details are given in the vignette accompanying this package. The initial creation of this package was supported by the Economic and Social Research Council (ESRC) grant RES-000-22-4256, and on-going development has been supported by the Engineering and Physical Science Research Council (EPSRC) grant EP/J017442/1, ESRC grant ES/K006460/1, Innovate UK / Natural Environment Research Council (NERC) grant NE/N007352/1 and the TB Alliance.

Phase I/II CRM Based Drug Combination Design

Implements the adaptive designs for integrated phase I/II trials of drug combinations via continual reassessment method (CRM) to evaluate toxicity and efficacy simultaneously for each enrolled patient cohort based on Bayesian inference. It supports patients assignment guidance in a single trial using current enrolled data, as well as conducting extensive simulation studies to evaluate operating characteristics before the trial starts. It includes various link functions such as empiric, one-parameter logistic, two-parameter logistic, and hyperbolic tangent, as well as considering multiple prior distributions of the parameters like normal distribution, gamma distribution and exponential distribution to accommodate diverse clinical scenarios. Method using Bayesian framework with empiric link function is described in: Wages and Conaway (2014) .

Mixed GAM Computation Vehicle with Automatic Smoothness Estimation

Generalized additive (mixed) models, some of their extensions and other generalized ridge regression with multiple smoothing parameter estimation by (Restricted) Marginal Likelihood, Cross Validation and similar, or using iterated nested Laplace approximation for fully Bayesian inference. See Wood (2025) for an overview. Includes a gam() function, a wide variety of smoothers, 'JAGS' support and distributions beyond the exponential family.

Graph/Network Visualization

Build graph/network structures using functions for stepwise addition and deletion of nodes and edges. Work with data available in tables for bulk addition of nodes, edges, and associated metadata. Use graph selections and traversals to apply changes to specific nodes or edges. A wide selection of graph algorithms allow for the analysis of graphs. Visualize the graphs and take advantage of any aesthetic properties assigned to nodes and edges.