Copula-Based Estimation Methods for a Common Mean Vector for Bivariate Meta-Analyses

Scrutiny of a More Flexible Counterpart of Huang–Kotz FGM’s Distributions in the Perspective of Some Information Measures

In this work, we reveal some distributional traits of concomitants of order statistics (COSs) arising from the extended Farlie–Gumbel–Morgenstern (FGM) bivariate distribution, which was developed and studied in recent work. The joint distribution and product moments of COSs for this family are discussed. Moreover, some useful recurrence relations between single and product moments of concomitants are obtained. In addition, the asymptotic behavior of the concomitant’s rank for order statistics (OSs) is studied. The information measures, differential entropy, Kullback–Leibler (KL) distance, Fisher information number (FIN), and cumulative past inaccuracy (CPI) are theoretically and numerically studied.

Sensitivity Analysis for Survival Prognostic Prediction with Gene Selection: A Copula Method for Dependent Censoring

Prognostic analysis for patient survival often employs gene expressions obtained from high-throughput screening for tumor tissues from patients. When dealing with survival data, a dependent censoring phenomenon arises, and thus the traditional Cox model may not correctly identify the effect of each gene. A copula-based gene selection model can effectively adjust for dependent censoring, yielding a multi-gene predictor for survival prognosis. However, methods to assess the impact of various types of dependent censoring on the multi-gene predictor have not been developed. In this article, we propose a sensitivity analysis method using the copula-graphic estimator under dependent censoring, and implement relevant methods in the R package “compound.Cox”. The purpose of the proposed method is to investigate the sensitivity of the multi-gene predictor to a variety of dependent censoring mechanisms. In order to make the proposed sensitivity analysis practical, we develop a web application. We apply the proposed method and the web application to a lung cancer dataset. We provide a template file so that developers can modify the template to establish their own web applications.

Testing Equality of Multiple Population Means under Contaminated Normal Model Using the Density Power Divergence

This paper considers the problem of comparing several means under the one-way Analysis of Variance (ANOVA) setup. In ANOVA, outliers and heavy-tailed error distribution can seriously hinder the treatment effect, leading to false positive or false negative test results. We propose a robust test of ANOVA using an M-estimator based on the density power divergence. Compared with the existing robust and non-robust approaches, the proposed testing procedure is less affected by data contamination and improves the analysis. The asymptotic properties of the proposed test are derived under some regularity conditions. The finite-sample performance of the proposed test is examined via a series of Monte-Carlo experiments and two empirical data examples-bone marrow transplant dataset and glucose level dataset. The results produced by the proposed testing procedure are favorably compared with the classical ANOVA and robust tests based on Huber's M-estimator and Tukey's MM-estimator.

Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies

Survival and reliability analyses deal with incomplete failure time data, such as censored and truncated data. Recently, the classical left-truncation scheme was generalized to analyze “field data”, defined as samples collected within a fixed period. However, existing competing risks models dealing with left-truncated field data are not flexible enough. We propose copula-based competing risks models for latent failure times, permitting a flexible parametric form. We formulate maximum likelihood estimation methods under the Weibull, lognormal, and gamma distributions for the latent failure times. We conduct simulations to check the performance of the proposed methods. We finally give a real data example. We provide the R code to reproduce the simulations and data analysis results.