Fontaine Charles, Daurès Jean-Pierre, Landais Paul
UPRES EA2415-Institut Universitaire de Recherche Clinique, Université de Montpellier, 641, Av. du doyen G.-Giraud, Montpellier, France.
BMC Med Res Methodol. 2017 Feb 15;17(1):27. doi: 10.1186/s12874-017-0305-9.
Information and theory beyond copula concepts are essential to understand the dependence relationship between several marginal covariates distributions. In a therapeutic trial data scheme, most of the time, censoring occurs. That could lead to a biased interpretation of the dependence relationship between marginal distributions. Furthermore, it could result in a biased inference of the joint probability distribution function. A particular case is the cost-effectiveness analysis (CEA), which has shown its utility in many medico-economic studies and where censoring often occurs.
This paper discusses a copula-based modeling of the joint density and an estimation method of the costs, and quality adjusted life years (QALY) in a cost-effectiveness analysis in case of censoring. This method is not based on any linearity assumption on the inferred variables, but on a punctual estimation obtained from the marginal distributions together with their dependence link.
Our results show that the proposed methodology keeps only the bias resulting statistical inference and don't have anymore a bias based on a unverified linearity assumption. An acupuncture study for chronic headache in primary care was used to show the applicability of the method and the obtained ICER keeps in the confidence interval of the standard regression methodology.
For the cost-effectiveness literature, such a technique without any linearity assumption is a progress since it does not need the specification of a global linear regression model. Hence, the estimation of the a marginal distributions for each therapeutic arm, the concordance measures between these populations and the right copulas families is now sufficient to process to the whole CEA.
除了Copula概念之外的信息和理论对于理解多个边缘协变量分布之间的依赖关系至关重要。在治疗试验数据方案中，大多数情况下会出现删失。这可能导致对边缘分布之间依赖关系的解释产生偏差。此外，这可能会导致对联合概率分布函数的推断出现偏差。一个特殊的情况是成本效益分析（CEA），它在许多医学经济研究中显示出了效用，并且经常会出现删失。
本文讨论了在存在删失的情况下，成本效益分析中基于Copula的联合密度建模以及成本和质量调整生命年（QALY）的估计方法。该方法不是基于对推断变量的任何线性假设，而是基于从边缘分布及其依赖关系中获得的逐点估计。
我们的结果表明，所提出的方法仅保留了统计推断产生的偏差，并且不再具有基于未经验证的线性假设的偏差。一项针对初级保健中慢性头痛的针灸研究被用来展示该方法的适用性，并且所获得的增量成本效果比（ICER）保持在标准回归方法的置信区间内。
对于成本效益文献而言，这样一种没有任何线性假设的技术是一种进步，因为它不需要指定全局线性回归模型。因此，现在对每个治疗组的边缘分布进行估计、这些总体之间的一致性度量以及正确的Copula族就足以进行整个成本效益分析。
