Section for Clinical Biometrics, Center for Medical Statistics, Informatics, and Intelligent Systems, Medical University of Vienna, Vienna, Austria.
Stat Med. 2019 Oct 15;38(23):4733-4748. doi: 10.1002/sim.8331. Epub 2019 Aug 6.
We suggest measures to quantify the degrees of necessity and of sufficiency of prognostic factors for dichotomous and for survival outcomes. A cause, represented by certain values of prognostic factors, is considered necessary for an event if, without the cause, the event cannot develop. It is considered sufficient for an event if the event is unavoidable in the presence of the cause. Necessity and sufficiency can be seen as the two faces of causation, and this symmetry and equal relevance are reflected by the suggested measures. The measures provide an approximate, in some cases an exact, multiplicative decomposition of explained variation as defined by Schemper and Henderson for censored survival and for dichotomous outcomes. The measures, ranging from zero to one, are simple, intuitive functions of unconditional and conditional probabilities of an event such as disease or death. These probabilities often will be derived from logistic or Cox regression models; the measures, however, do not require any particular model. The measures of the degree of necessity implicitly generalize the established attributable fraction or risk for dichotomous prognostic factors and dichotomous outcomes to continuous prognostic factors and to survival outcomes. In a setting with multiple prognostic factors, they provide marginal and partial results akin to marginal and partial odds and hazard ratios from multiple logistic and Cox regression. Properties of the measures are explored by an extensive simulation study. Their application is demonstrated by three typical real data examples.
我们建议了一些措施来量化二分类和生存结局预后因素的必要性和充分性程度。如果没有某个预后因素的特定值，就不会发生某个事件，那么这个预后因素就被认为是该事件发生的必要原因。如果在存在该原因的情况下，事件不可避免地发生，则该原因被认为是该事件的充分原因。必要性和充分性可以被视为因果关系的两个方面，这种对称性和同等重要性反映在我们提出的措施中。这些措施提供了一种近似的、在某些情况下是精确的、乘法分解，用于解释由 Schemper 和 Henderson 为删失生存和二分类结局所定义的变异。这些措施的取值范围从 0 到 1，是疾病或死亡等事件的无条件和条件概率的简单、直观的函数。这些概率通常可以从逻辑斯蒂回归或 Cox 回归模型中得出；但是，这些措施不需要任何特定的模型。必要性程度的度量方法隐含地将已建立的归因分数或风险推广到二分类预后因素和生存结局的连续预后因素。在具有多个预后因素的情况下，它们提供了类似于多个逻辑斯蒂回归和 Cox 回归的边际和部分比值比和危险比的边缘和部分结果。通过广泛的模拟研究探讨了这些措施的性质。通过三个典型的真实数据示例展示了它们的应用。
