Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem, 91905, Israel.
Stat Med. 2015 Nov 20;34(26):3415-23. doi: 10.1002/sim.6535. Epub 2015 May 13.
Repeated cross-sectional sampling results in multiple biased samples with possibly different weight functions. The standard non-parametric maximum likelihood estimator for the lifetime distribution of interest solves a set of nonlinear equations, and its variance has a very complicated form. We suggest a simple closed-form estimator for the case where entrances to the population of interest follow a Poisson model. The variance of the estimator and confidence intervals are easily calculated. Our motivating example concerns a series of cross-sectional surveys conducted in Israeli hospitals. We discuss the bias mechanism in our data and suggest a simple design plan that provides valid estimators even when the weight functions are unknown. The new method is applied to estimate the distribution of hospitalization time after bowel and hernia surgeries.
重复的横断面抽样会导致多个存在偏倚的样本，这些样本可能具有不同的权重函数。标准的非参数最大似然估计器可用于估计感兴趣的寿命分布，该估计器需要求解一组非线性方程，其方差具有非常复杂的形式。对于感兴趣人群的进入符合泊松模型的情况，我们提出了一个简单的闭式估计器。该估计器的方差和置信区间可以很容易地计算出来。我们的实例研究涉及在以色列医院进行的一系列横断面调查。我们讨论了数据中的偏差机制，并提出了一种简单的设计方案，即使在权重函数未知的情况下，该方案也可以提供有效的估计器。该新方法应用于估计肠和疝手术后住院时间的分布。
