Study of Zero-Inflated Regression Models in a Large-Scale Population Survey of Sub-Health Status and Its Influencing Factors<sup>△</sup>

Xu Tao; Zhu Guangjin; Han Shaomei

doi:10.24920/J1001-9294.2017.054

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Study of Zero-Inflated Regression Models in a Large-Scale Population Survey of Sub-Health Status and Its Influencing Factors^△

Chinese Medical Sciences Journal Vol. 32, Issue 4, Pages: 218-225(2017)

ORIGINAL ARTICLE | Updated：2024-04-10

- Study of Zero-Inflated Regression Models in a Large-Scale Population Survey of Sub-Health Status and Its Influencing Factors^△
- Affiliations：
  
  1. 1Department of Epidemiology and Statistics, Institute of Basic Medical Sciences, Chinese Academy of Medical Sciences & School of Basic Medicine, Peking Union Medical College, Beijing 100005, China;
  2. 2Department of physiopathology, Institute of Basic Medical Sciences, Chinese Academy of Medical Sciences & School of Basic Medicine, Peking Union Medical College, Beijing 100005, China;
- Author bio：
  
  *Corresponding author Tel: 86-10-69156408, E-mail: hansm1@vip.sina.com
- Funds：
- DOI：10.24920/J1001-9294.2017.054
  CLC：
- Received：30 March 2017，
  
  Published Online：30 December 2017，
  
  Published：2017-12
- Accepted：
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Xu Tao, Zhu Guangjin, Han Shaomei. Study of Zero-Inflated Regression Models in a Large-Scale Population Survey of Sub-Health Status and Its Influencing Factors^△[J]. Chinese medical sciences journal, 2017, 32(4): 218-225.
DOI：

Xu Tao, Zhu Guangjin, Han Shaomei. Study of Zero-Inflated Regression Models in a Large-Scale Population Survey of Sub-Health Status and Its Influencing Factors^△[J]. Chinese medical sciences journal, 2017, 32(4): 218-225. DOI： 10.24920/J1001-9294.2017.054.

摘要

目的

亚健康近年来引起了越来越多的医务人员和普通公众的注意。把亚健康症状数作为计数资料进行处理能够获得更完整和准确的分析结果。本研究旨在探讨计数资料模型的拟合优度以确定最佳的亚健康研究模型。

方法

研究样本来源于一项2007年到2014年在中国四省两自治区进行的一项关于生理和心理的大规模人群调查研究。用SAS软件拟合四个计数资料模型：Poisson回归、负二项回归(NB)、零频数过多的Poisson回归(ZIP)和零频数过多的Poisson回归负二项回归模型(ZINB)。亚健康症状数是主要结局变量。用α系数和

检验验证是否过度离散

用Vuong检验验证零频数是否过多。用预测概率曲线和似然比检验评价模型的拟合优度。

结果

在78

307名受试者中

38.53%的受试者没有任何亚健康症状。亚健康症状数的平均水平为2.98±3.72。

检验统计量为720.995 (P

0.001)。α系数为0.618 (95% 可信区间: 0.600-0.636)。Vuong检验的统计量

=45.487。ZINB模型有最大的似然比(-167519)、最小的赤池信息准则系数(335112) 和贝叶斯信息准则系数 (335455)。ZINB模型对大多数症状数的预测概率都优于其他模型。ZINB模型的logit部分显示年龄、性别、职业、吸烟、饮酒、民族、肥胖是发生亚健康症状的危险因素。负二项部分显示性别、职业、吸烟、饮酒、民族、婚姻状况和肥胖对于亚健康的程度有影响。

结论

各种拟合优度检验和预测概率曲线的综合结果表明ZINB模型是探索亚健康症状数的影响因素的最佳模型。

Abstract

Objective

Sub-health status has progressively gained more attention from both medical professionals and the publics. Treating the number of sub-health symptoms as count data rather than dichotomous data helps to completely and accurately analyze findings in sub-healthy population. This study aims to compare the goodness of fit for count outcome models to identify the optimum model for sub-health study.

Methods

The sample of the study derived from a large-scale population survey on physiological and psychological constants from 2007 to 2011 in 4 provinces and 2 autonomous regions in China. We constructed four count outcome models using SAS: Poisson model

negative binomial (NB) model

zero-inflated Poisson (ZIP) model and zero-inflated negative binomial (ZINB) model. The number of sub-health symptoms was used as the main outcome measure. The alpha dispersion parameter and

test were used to identify over-dispersed data

and Vuong test was used to evaluate the excessive zero count. The goodness of fit of regression models were determined by predictive probability curves and statistics of likelihood ratio test.

Results

Of all 78 307 respondents

38.53% reported no sub-health symptoms. The mean number of sub-health symptoms was 2.98

and the standard deviation was 3.72. The statistic

in over-dispersion test was 720.995 (

0.001); the estimated alpha was 0.618 (95%

: 0.600-0.636) comparing ZINB model and ZIP model; Vuong test statistic Z was 45.487. These results indicated over-dispersion of the data and excessive zero counts in this sub-health study. ZINB model had the largest log likelihood (-167 519)

the smallest Akaike’s Information Criterion coefficient (335 112) and the smallest Bayesian information criterion coefficient (335455)

indicating its best goodness of fit. The predictive probabilities for most counts in ZINB model fitted the observed counts best. The logit section of ZINB model analysis showed that age

sex

occupation

smoking

alcohol drinking

ethnicity and obesity were determinants for presence of sub-health symptoms; the binomial negative section of ZINB model analysis showed that sex

occupation

smoking

alcohol drinking

ethnicity

marital status and obesity had significant effect on the severity of sub-health.

Conclusions

All tests for goodness of fit and the predictive probability curve produced the same finding that ZINB model was the optimum model for exploring the influencing factors of sub-health symptoms.

关键词

Keywords

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