Generalisation of the Fractional Polynomial procedure for semi-continuous variables in epidemiology and clinical research

在流行病学和临床研究中，一个共同的目标是通过使用适当的回归模型来定量地估计协变量对结果的影响。这些协变量通常有一定比例的个体零接触，而接触人群的分布是连续的(变量的所谓峰值为零)，例如吸烟、哺乳时间或饮酒。然后，可以使用申请人开发的方法对剂量-反应函数进行建模，该方法是分数多项式方法的扩展。该项目的目的是开发新的改进的半连续变量研究的分析方法，并将其应用于研究分析，并提供软件工具来传播该方法。结果：到目前为止，我们已经开发并发布了最近发表的处理变量尖峰为零的变量的改进版本。我们通过调查特定的分配类别，为这一过程发展了理论上的理由。在对一个尖峰变量的模拟研究中，我们可以显示出与前一种方法相比，这种新方法的性能有所改善。对于两个尖峰变量，我们已经提出了几种方法来扩展该过程。实例表明，处理两个尖峰变量的方法强烈依赖于变量的双变量分布和相关结构。这些方法将在模拟研究的项目过程中得到进一步评价。对于三个或更多的尖峰变量，我们提出了一种策略。为了实际应用，我们从几项流行病学和临床研究中获得了数据，并准备好用我们的方法进行分析。在第一个资助期已经开始对这些数据应用该方法，并将一直持续到项目结束。工作计划：首先，在模拟研究中，我们将调查对于删失的生存数据，Logistic模型的结果是否会转移到Cox模型。然后，我们将在一个大型模拟研究中对两个尖峰变量的不同方法进行评估。必须确定适当的标准来评估物业和比较不同的提案。在一个有三个尖峰变量的例子中，我们将调查所提出的策略是否合适，或者是否需要进一步扩展。最近一种研究治疗和连续变量之间相互作用的方法将扩展到零变量时的峰值。我们将以激素受体的作用和激素治疗乳腺癌患者为例。对于吸烟，最近提出了几种剂量测量方法(如综合吸烟指数)。使用我们的方法，我们将得出新的剂量度量，并将其与文献中的建议进行比较。

In epidemiology and in clinical research, a common goal is to estimate the effect of covariables on an outcome quantitatively by using appropriate regression models. These covariates often have a proportion of individuals with zero exposure, while the distribution of the population exposed is continuous (variables with so-called spike at zero), e.g. smoking, duration of breastfeeding, or alcohol consumption. Modelling of the dose-response function is then possible with a method developed by the applicants which is an extension of the fractional polynomial approach. The aim of the project is to develop new improved methods for analysis of studies with semi-continuous variables, to apply them for the analysis of studies and to provide software tools to disseminate the methods.Results until now: We have developed and published an improved version of the recently published procedure to handle variables with a spike at zero. We have developed theoretical justifications for the procedure by investigating specific distribution classes. In a simulation study for one spike variable we could show improved properties of this new procedure in comparison to the former. For two spike variables we have proposed several approaches for an extension of the procedure. Examples have shown that methods of handling two spike variables are strongly dependent upon the bivariate distribution and the correlation structure of the variables. The approaches will be further evaluated in the course of the project in simulation studies. For three or more spike variables we have proposed a strategy. For practical applications, we have obtained data from several epidemiological and clinical studies and made these ready for analyses with our methods. Application of the method to these data has already started in the first funding period and will last until the end of the project. Work plan: First, in a simulation study we will investigate whether results from the logistic model transfer to the Cox model for censored survival data. Then we are going to evaluate the different approaches for two spike variables in a large simulation study. Suitable criteria to assess properties and to compare the different proposals have to be defined. In an example with three spike variables we will investigate whether the proposed strategy is suitable or whether further extensions are required. A recent approach to investigate for interactions between treatment and a continuous variable will be extended for spike at zero variables. We will use the role of hormonal receptors and treatment of breast cancer patients with hormonal therapy as an example. For smoking several dose metrics (e.g. comprehensive smoking index) have been proposed recently. Using our approaches we will derive new dose metrics and compare these with proposals from the literature.