Liu Chaofeng, Xie Jun, Zhang Ying
Novartis Pharmaceuticals Company, One Health Plaza, East Hanover, NJ 07936-1080, USA.
Stat Med. 2007 Dec 20;26(29):5303-19. doi: 10.1002/sim.2914.
Hierarchical models have a variety of applications, including multi-center clinical trials, local estimation of disease rates, longitudinal studies, risk assessment, and meta-analysis. In a hierarchical model, observations are sampled conditional on individual unit-specific parameters and these parameters are sampled from a mixing distribution. In observational studies or nonrandomized clinical trails, observations may be biased samples from a population and heterogeneous with respect to some confounding factors. Without controlling the heterogeneity in the sample, the standard estimation of the mixing distribution may lead to inaccurate statistical inferences. In this article, we propose a weighted nonparametric maximum likelihood estimate (NPMLE) of the mixing distribution and its smoothed version via weighted smoothing by roughening. The proposed estimator reduces bias by assigning a weight to each subject in the sample. The weighted NPMLE is shown to be weighted self-consistent and therefore can be easily calculated through a recursive approach. Simulation studies were conducted to evaluate the performance of the proposed estimator. We applied this method to clinical trial data evaluating a new treatment for stress urinary incontinence.
分层模型有多种应用，包括多中心临床试验、疾病发病率的局部估计、纵向研究、风险评估和荟萃分析。在分层模型中，观测值是在个体特定参数的条件下进行抽样的，并且这些参数是从混合分布中抽样得到的。在观察性研究或非随机临床试验中，观测值可能是来自总体的有偏样本，并且在某些混杂因素方面存在异质性。如果不控制样本中的异质性，混合分布的标准估计可能会导致不准确的统计推断。在本文中，我们提出了混合分布的加权非参数最大似然估计（NPMLE）及其通过粗糙加权平滑得到的平滑版本。所提出的估计器通过为样本中的每个个体分配权重来减少偏差。加权NPMLE被证明是加权自洽的，因此可以通过递归方法轻松计算。进行了模拟研究以评估所提出估计器的性能。我们将此方法应用于评估压力性尿失禁新疗法的临床试验数据。
