Martinussen T, Sørensen T I
Department of Biostatistics, University of Copenhagen, Denmark.
Biometrics. 1998 Sep;54(3):989-1001.
Epidemiologic studies of time to some failure often show a quadratic relation between the risk of failure and covariate(s). We study the nadir for a given covariate, i.e., the value of the covariate associated with the lowest risk (supposing a U-shape), within Aalen's additive risk model. This model was applied since the effect of the covariate(s) is allowed to vary over time and, as a consequence, a given nadir can vary over time. We propose a test for the null hypothesis that the nadir is time independent and, if this is the case, an estimate of the nadir. Large sample properties of the test statistic and estimator are derived. The methods are illustrated with data where time to death is related to body mass index.
对某种失效时间的流行病学研究常常表明，失效风险与协变量之间存在二次关系。我们在阿伦累加风险模型中研究给定协变量的最低点，即与最低风险相关联的协变量值（假设呈U形）。应用该模型是因为协变量的效应随时间变化，因此，给定的最低点也可能随时间变化。我们提出了一个针对最低点与时间无关这一零假设的检验，如果情况确实如此，还提出了最低点的估计方法。推导了检验统计量和估计量的大样本性质。通过将死亡时间与体重指数相关的数据对这些方法进行了说明。
