零膨胀对数正态分布左删失的过敏原的最大似然估计

Maximum likelihood inference of zero-inflated log-normal distribution for left-censored allergen data

目的探讨最大似然法处理左删失过敏原数据的效果。方法运用实例与模拟试验比较最大似然法与常用的LOD/2替代法和删除法在分析左删失蟑螂过敏原与哮喘病发作与否的关系的优劣。最大似然法分别选择对数正态分布和零膨胀对数正态分布作为左删失蟑螂过敏原的分布,并以Logistic回归来模拟过敏原与哮喘病发作的关系。结果总体上,最大似然法构建的零膨胀对数正态分布左删失模型是处理左删失蟑螂过敏原数据较合理及稳定的方法。LOD/2替代法则可导致相反及错误的过敏原与哮喘病关系。结论对于左删失过敏原的处理,建议先构建零膨胀对数正态分布左删失模型,据此再采用最大似然法进行参数估计和假设检验。

Objective To apply maximum likelihood （ML） inference to left-censored allergen data. Methods Using both case study and simulated data,we compared ML method with substitution （using LOD/2） and deletion of left-censored values in analyzing the relationship between left-censored Bla g roach allergen and asthma. A log-normal distribution and a zero-inflated log-normal distribution were chosen as the distribution of left-censored Bla g roach allergen for the ML method, and I.ogistic regression was used to model the relationship between Bla g allergen and asthma. Results In general,the ML methods with the zero inflated log-normal distribution for left-censored data produced more reasonable and stable results in treating left-censored allergen data. The common method of substitution using LOD/2, however, resulted in an erroneous and opposite Bla g allergen and asthma association. Conclusions When dealing with the left-censored allergen data, we suggest using a zero- inflated log-normal distribution to model left-censored data and apply ML for parameter estimation and hypothesis testing.