Hierarchical correction of p-values via an ultrametric tree running Ornstein-Uhlenbeck process

Statistical testing is classically used as an exploratory tool to search for association between a phenotype and many possible explanatory variables. This approach often leads to multiple testing under dependence. We assume a hierarchical structure between tests via an Ornstein-Uhlenbeck process on a tree. The process correlation structure is used for smoothing the p-values. We design a penalized estimation of the mean of the Ornstein-Uhlenbeck process for p-value computation. The performances of the algorithm are assessed via simulations. Its ability to discover new associations is demonstrated on a metagenomic dataset. The corresponding R package is available from https://github.com/abichat/zazou.

A parallel algorithm for ridge-penalized estimation of the multivariate exponential family from data of mixed types

Computationally efficient evaluation of penalized estimators of multivariate exponential family distributions is sought. These distributions encompass among others Markov random fields with variates of mixed type (e.g., binary and continuous) as special case of interest. The model parameter is estimated by maximization of the pseudo-likelihood augmented with a convex penalty. The estimator is shown to be consistent. With a world of multi-core computers in mind, a computationally efficient parallel Newton–Raphson algorithm is presented for numerical evaluation of the estimator alongside conditions for its convergence. Parallelization comprises the division of the parameter vector into subvectors that are estimated simultaneously and subsequently aggregated to form an estimate of the original parameter. This approach may also enable efficient numerical evaluation of other high-dimensional estimators. The performance of the proposed estimator and algorithm are evaluated and compared in a simulation study. Finally, the presented methodology is applied to data of an integrative omics study.

Non-Convex Penalized Estimation of Count Data Responses via Generalized Linear Model (GLM)

This study provided a non-convex penalized estimation procedure via Smoothed Clipped Absolute Deviation (SCAD) and Minimax Concave Penalty (MCP) for count data responses to checkmate the problem of covariates exceeding the sample size . The Generalized Linear Model (GLM) approach was adopted in obtaining the penalized functions needed by the MCP and SCAD non-convex penalizations of Binomial, Poisson and Negative-Binomial related count responses regression. A case study of the colorectal cancer with six (6) covariates against sample size of five (5) was subjected to the non-convex penalized estimation of the three distributions. It was revealed that the non-convex penalization of Binomial regression via MCP and SCAD best explained four un-penalized covariates needed in determining whether surgical or therapy ideal for treating the turmoil.