A two-level copula joint model for joint analysis of longitudinal and competing risks data.

In this article, we propose a two-level copula joint model to analyze clinical data with multiple disparate continuous longitudinal outcomes and multiple event-times in the presence of competing risks. At the first level, we use a copula to model the dependence between competing latent event-times, in the process constructing the submodel for the observed event-time, and employ the Gaussian copula to construct the submodel for the longitudinal outcomes that accounts for their conditional dependence; these submodels are glued together at the second level via the Gaussian copula to construct a joint model that incorporates conditional dependence between the observed event-time and the longitudinal outcomes. To have the flexibility to accommodate skewed data and examine possibly different covariate effects on quantiles of a non-Gaussian outcome, we propose linear quantile mixed models for the continuous longitudinal data. We adopt a Bayesian framework for model estimation and inference via Markov Chain Monte Carlo sampling. We examine the performance of the copula joint model through a simulation study and show that our proposed method outperforms the conventional approach assuming conditional independence with smaller biases and better coverage probabilities of the Bayesian credible intervals. Finally, we carry out an analysis of clinical data on renal transplantation for illustration.

The Risk Contagion between Chinese and Mature Stock Markets: Evidence from a Markov-Switching Mixed-Clayton Copula Model.

Exploring the risk spillover between Chinese and mature stock markets is a promising topic. In this study, we propose a Markov-switching mixed-Clayton (Ms-M-Clayton) copula model that combines a state transition mechanism with a weighted mixed-Clayton copula. It is applied to investigate the dynamic risk dependence between Chinese and mature stock markets in the Americas, Europe, and Asia-Oceania regions. Additionally, the conditional value at risk (CoVaR) is applied to analyze the risk spillovers between these markets. The empirical results demonstrate that there is mainly a time-varying but stable positive risk dependence structure between Chinese and mature stock markets, where the upside and downside risk correlations are asymmetric. Moreover, the risk contagion primarily spills over from mature stock markets to the Chinese stock market, and the downside effect is stronger. Finally, the risk contagion from Asia-Oceania to China is weaker than that from Europe and the Americas. The study provides insights into the risk association between emerging markets, represented by China, and mature stock markets in major regions. It is significant for investors and risk managers, enabling them to avoid investment risks and prevent risk contagion.

A New Family of Continuous Probability Distributions.

In this paper, a new parametric compound G family of continuous probability distributions called the Poisson generalized exponential G (PGEG) family is derived and studied. Relevant mathematical properties are derived. Some new bivariate G families using the theorems of "Farlie-Gumbel-Morgenstern copula", "the modified Farlie-Gumbel-Morgenstern copula", "the Clayton copula", and "the Renyi's entropy copula" are presented. Many special members are derived, and a special attention is devoted to the exponential and the one parameter Pareto type II model. The maximum likelihood method is used to estimate the model parameters. A graphical simulation is performed to assess the finite sample behavior of the estimators of the maximum likelihood method. Two real-life data applications are proposed to illustrate the importance of the new family.

Cost-offsets of prescription drug expenditures: data analysis via a copula-based bivariate dynamic hurdle model.

In this paper, we estimate a copula-based bivariate dynamic hurdle model of prescription drug and nondrug expenditures to test the cost-offset hypothesis, which posits that increased expenditures on prescription drugs are offset by reductions in other nondrug expenditures. We apply the proposed methodology to data from the Medical Expenditure Panel Survey, which have the following features: (i) the observed bivariate outcomes are a mixture of zeros and continuously measured positives; (ii) both the zero and positive outcomes show state dependence and inter-temporal interdependence; and (iii) the zeros and the positives display contemporaneous association. The point mass at zero is accommodated using a hurdle or a two-part approach. The copula-based approach to generating joint distributions is appealing because the contemporaneous association involves asymmetric dependence. The paper studies samples categorized by four health conditions: arthritis, diabetes, heart disease, and mental illness. There is evidence of greater than dollar-for-dollar cost-offsets of expenditures on prescribed drugs for relatively low levels of spending on drugs and less than dollar-for-dollar cost-offsets at higher levels of drug expenditures.

Application of the Joint Frailty Copula Model for Analyzing Time to Relapse and Time to Death of Women with Cervical Cancer.

Background: Worldwide, there were 12.7 million new cervical cancer cases, of which 5.6 million took place in industrialized nations and 7.1 million in underdeveloped nations. In eastern, western, middle, and southern Africa, it is the main cancer-related cause of death in female patients. In Ethiopia, cancer was responsible for roughly 5.8% of all fatalities. This study makes use of sophisticated statistical models that take into account population heterogeneity in terms of frailty and dependence between two endpoints in terms of copulas. Methods: Based on hospital registry data, this retrospective study intends to examine the time to relapse and time to death of cervical cancer. This study analyzes 907 cervical cancer-positive women from various parts of Ethiopia. The copula model was used to link time to relapse and time to death of women with cervical cancer. Shared frailty model was used to incorporate unexplained heterogeneity for women with cervical cancer patients. Results: Of the 907 cervical cancer patients, 275 (30.32%) experienced a relapse, 353 (38.92%) died, and 554 (61.08%) were censored. Age, smoking status, family planning, HIV status, family history, abortion, and stage are the most reliable predictors of both time to relapse and time to death of cervical cancer patients. The estimate of the copula parameter (θ = 1.476, 95% CI: 1.082, 1.870) shows moderate amount of dependence between time to relapse and time to death (Kendall's rank correlation (τ) = 0.425). The estimate of the variability (heterogeneity) parameter in the population of clusters (region) is η = 0.495, 95% CI: 0.101, 0.889. Conclusion: Age, smoking status, family planning, HIV status, family history, abortion, and more advanced stage significantly increase the risk of relapse and death of female cervical patients. There was a significant association between the time to relapse and the time to die for women with cervical cancer. There was a significant heterogeneity effect in the Tikur Anbessa Specialized Hospital.