Vergnes Jean-Noel, Boucher Jean-Philippe, Lelong Nathalie, Sixou Michel, Nabet Cathy
Dental Faculty, Paul Sabatier University, Department of Epidemiology and Public Health, CHU de Toulouse, Toulouse, France.
Caries Res. 2017;51(1):68-78. doi: 10.1159/000450891. Epub 2016 Dec 23.
Methods for analysing dental caries and associated risk indicators have evolved considerably in recent decades. The use of zero-inflated or hurdle models is increasing so as to take account of the decayed, missing, and filled teeth (DMFT) distribution, which is positively skewed and has a high proportion of zero scores. However, there is a need to develop new statistical models that involve pragmatic biological considerations on dental caries in epidemiological surveys. In this paper, we show that the zero-inflated and the hurdle models can both be expressed as a compound sum. Using the same compound sum, we then present the generalized negative binomial (GNB) distribution for dental caries count data, and provide a numerical application using the data of the EPIPAP study. The GNB model generates the best score functions while handling the lifetime dental caries disease process better. In conclusion, the GNB model suits the nature of some count data, in particular when structural zeros are unlikely to occur and when several latent spells can lead to new countable events. For these reasons, the use of the GNB distribution appears to be relevant for the modelling of dental caries count data.
近几十年来，分析龋齿及相关风险指标的方法有了很大发展。零膨胀或门槛模型的使用越来越多，以考虑到龋失补牙数（DMFT）的分布情况，该分布呈正偏态且零分比例很高。然而，有必要开发新的统计模型，在流行病学调查中纳入关于龋齿的实际生物学考量。在本文中，我们表明零膨胀模型和门槛模型都可以表示为复合和。然后，使用相同的复合和，我们给出了龋齿计数数据的广义负二项分布（GNB），并利用EPIPAP研究的数据进行了数值应用。GNB模型在更好地处理终生龋齿疾病过程的同时，产生了最佳得分函数。总之，GNB模型适合某些计数数据的性质，特别是当不太可能出现结构零，且多个潜在发作可导致新的可数事件时。出于这些原因，GNB分布的使用似乎与龋齿计数数据的建模相关。
