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In this paper, we present a method for generating a copula by composing two arbitrary n-dimensional copulas via a vector of bivariate functions, where the resulting copula is named as the multivariate composite copula. A necessary and sufficient condition on the vector guaranteeing the composite function to be a copula is given, and a general approach to construct the vector satisfying this necessary and sufficient condition via bivariate copulas is provided. The multivariate composite copula proposes a new framework for the construction of flexible multivariate copula from existing ones, and it also includes some known classes of copulas. It is shown that the multivariate composite copula has a clear probability structure, and it satisfies the characteristic of uniform convergence as well as the reproduction property for its component copulas. Some properties of multivariate composite copulas are discussed. Finally, numerical illustrations and an empirical example on financial data are provided to show the advantages of the multivariate composite copula, especially in capturing the tail dependence.
We aimed to evaluate the association between coffee and/or tea consumption and breast cancer (BC) risk among premenopausal and postmenopausal women and to conduct a network meta-analysis.
Systematic review and network meta-analysis.
We conducted a systematic review of electronic publications in the last 30 years to identify case–control studies or prospective cohort studies that evaluated the effects of coffee and tea intake.
Forty-five studies that included more than 3 323 288 participants were eligible for analysis. Network meta-analysis was performed to determine the effects of coffee and/or tea consumption on reducing BC risk in a dose-dependent manner and differences in coffee/tea type, menopause status, hormone receptor and the BMI in subgroup and meta-regression analyses. According to the first pairwise meta-analysis, low-dose coffee intake and high-dose tea intake may exhibit efficacy in preventing ER(estrogen receptor)− BC, particularly in postmenopausal women. Then, we performed another pairwise and network meta-analysis and determined that the recommended daily doses were 2–3 cups/d of coffee or ≥5 cups/d of tea, which contained a high concentration of caffeine, particularly in postmenopausal women.
Coffee and tea consumption is not associated with a reduction in the overall BC risk in postmenopausal women and is associated with a potentially lower risk of ER− BC. And the highest recommended dose is 2–3 cups of coffee/d or ≥5 cups of tea/d. They are potentially useful dietary protectants for preventing BC.
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