Zou Yuhan, Peng Zuoxiang, Cornell Jerry, Ye Peng, He Hua
School of Mathematics and Statistics, Southwest University, Chongqing, China.
Department of Biostatistics and Data Science, Tulane University School of Public Health and Tropical Medicine, New Orleans, Louisiana, USA.
Stat Med. 2021 Feb 10;40(3):779-798. doi: 10.1002/sim.8802. Epub 2020 Nov 6.
Biomarkers of interest in urine, serum, or other biological matrices often have an assay limit of detection. When concentration levels of the biomarkers for some subjects fall below the limit, the measures for those subjects are censored. Censored data due to detection limits are very common in public health and medical research. If censored data from a single exposure group follow a normal distribution or follow a normal distribution after some transformations, Tobit regression models can be applied. Given a Tobit regression model and a detection limit, the proportion of censored data can be determined. However, in practice, it is common that the data can exhibit excessive censored observations beyond what would be expected under a Tobit regression model. One common cause is heterogeneity of the study population, that is, there exists a subpopulation who lack such biomarkers and their values are always under the detection limit, and hence are censored. In this article, we develop a new test for testing such latent class under a Tobit regression model by directly comparing the amount of observed censored data with what would be expected under the Tobit regression model. A closed form of the test statistic as well as its asymptotic properties are derived based on estimating equations. Simulation studies are conducted to investigate the performance of the new test and compare the new one with the existing ones including the Wald test, likelihood ratio test, and score test. Two real data examples are also included for illustrative purpose.
尿液、血清或其他生物基质中感兴趣的生物标志物通常有检测限。当某些受试者的生物标志物浓度水平低于该限时，这些受试者的测量值将被截尾。由于检测限导致的截尾数据在公共卫生和医学研究中非常常见。如果来自单个暴露组的截尾数据服从正态分布或经过某些变换后服从正态分布，则可以应用Tobit回归模型。给定一个Tobit回归模型和一个检测限，可以确定截尾数据的比例。然而，在实际中，数据常常会出现超出Tobit回归模型预期的过多截尾观测值。一个常见的原因是研究人群的异质性，即存在一个亚人群，他们缺乏此类生物标志物，其值总是低于检测限，因此被截尾。在本文中，我们通过直接比较观察到的截尾数据量与Tobit回归模型下预期的数据量，开发了一种新的检验方法来检验Tobit回归模型下的这种潜在类别。基于估计方程推导了检验统计量的封闭形式及其渐近性质。进行了模拟研究以考察新检验的性能，并将其与包括Wald检验、似然比检验和得分检验在内的现有检验进行比较。还包括两个真实数据示例以作说明。
