Conditional copula models for correlated survival endpoints: Individual patient data meta-analysis of randomized controlled trials

Correlations among survival endpoints are important for exploring surrogate endpoints of the true endpoint. With a valid surrogate endpoint tightly correlated with the true endpoint, the efficacy of a new drug/treatment can be measurable on it. However, the existing methods for measuring correlation between two endpoints impose an invalid assumption: correlation structure is constant across different treatment arms. In this article, we reconsider the definition of Kendall's concordance measure (tau) in the context of individual patient data meta-analyses of randomized controlled trials. According to our new definition of Kendall's tau, its value depends on the treatment arms. We then suggest extending the existing copula (and frailty) models so that their Kendall's tau can vary across treatment arms. Our newly proposed model, a joint frailty-conditional copula model, is the implementation of the new definition of Kendall's tau in meta-analyses. In order to facilitate our approach, we develop an original R function condCox.reg(.) and make it available in the R package joint.Cox ( https://CRAN.R-project.org/package=joint.Cox ). We apply the proposed method to a gastric cancer dataset (3288 patients in 14 randomized trials from the GASTRIC group). This data analysis concludes that Kendall's tau has different values between the surgical treatment arm and the adjuvant chemotherapy arm ( p-value<0.001), whereas disease-free survival remains a valid surrogate at individual level for overall survival in these trials.

Tail Dependence between Crude Oil Volatility Index and WTI Oil Price Movements during the COVID-19 Pandemic

This study investigates the dependence between extreme returns of West Texas Intermediate (WTI) crude oil prices and the Crude Oil Volatility Index (OVX) changes as well as the predictive power of OVX to generate accurate Value at Risk (VaR) forecasts for crude oil. We focus on the COVID-19 pandemic period as the most violate in the history of the oil market. The static and dynamic conditional copula methodology is used to measure the tail dependence coefficient (TDC) between the variables. We found a strong relationship in the tail dependence between negative returns on crude oil and OVX changes and the tail independence for positive returns. The time-varying copula discloses the strongest tail dependence of negative oil price shocks and the index changes during the COVID-19 health crisis. The findings indicate the ability of the OVX index to be a fear gauge with respect to the oil market. However, we cannot confirm the ability of OVX to improve one day-ahead forecasts of the Value at Risk. The impact of investors’ expectations embedded in OVX on VaR forecasts seems to be negligible.

Reflection of government performance from foreign exchange market through engineered mechanism using conditional copula model

This paper investigates governments’ performance in the country. We achieved this objective differently. We employed an inverse method of assessment, with the utilization of factor copula modeling technique, to study the dependence relationship of exchange rates returns as auxiliary variables, the performance of political and army government tenures in the country in the last two decades are evaluated. Through factor analysis, common factors for the exchange rate are obtained. The analysis shows that conditioned on the common factors, the dependence amongst the elected currencies are strongly asymmetric in most of the tenures except the term of Pakistan Muslim League-Nawaz, and condition on common factor Clayton copula demonstrating hypothesis is more suitable. However, we perceive high left tail reliance among foreign currency returns during Pakistan Muslim League-Nawaz tenure, and the condition on common factor Gumbel copula molding assumption is more appropriate. We are signifying the foulest government performance in the country among all occupancies under consideration.

Estimation of the Value at Risk Using the Stochastic Approach of Taylor Formula

The aim of this paper is to provide an approximation of the value-at-risk of the multivariate copula associated with financial loss and profit function. A higher dimensional extension of the Taylor–Young formula is used for this estimation in a Euclidean space. Moreover, a time-varying and conditional copula is used for the modeling of the VaR.

Multi-Objective Interval Prediction of Load Based on the Conditional Copula Function

Compared with the point prediction, the interval prediction of the load could more effectively guarantee the safe operation of the power system. In view of the problem that the correlation between adjacent load data is not fully utilized so that the prediction accuracy is reduced, this paper proposes the conditional copula function interval prediction method, which could make full use of the correlation relationship between adjacent load data so as to obtain the interval prediction result. At the same time, there are the different prediction results of the method under different parameters, and the evaluation results of the two accuracy evaluation indicators containing PICP (prediction interval coverage probability) and the PIAW (prediction interval average width) are inconsistent, the above result that the optimal parameters and prediction results cannot be obtained, therefore, the NSGA-II (Non-dominated Sorting Genetic Algorithm-II) multi-objective optimization algorithm is proposed to seek out the optimal solution set, and by evaluating the solution set, obtain the optimal prediction model parameters and the corresponding prediction results. Finally, the proposed method is applied to the three regions of Shaanxi Province, China to conduct ultra-short-term load prediction, and compare it with the commonly used load interval prediction method such as Gaussian process regression (GPR) algorithm, artificial neural network (ANN), extreme learning machine (ELM) and others, and the results show that the proposed method always has better prediction accuracy when applying it to different regions.