The effect of mis-adjusting instrumental variables on the estimation of causal effect in Logistic regression analysis model
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摘要:
目的 通过统计模拟和实例数据分析，探索当存在不可观测的混杂因素时，Logistic回归分析模型中调整工具变量(instrumental variable, Ⅳ)对估计因果效应的影响。 方法 设定变量均服从二项分布，在Logistic回归分析模型中依次使用不同的参数进行统计模拟，以因果效应估计值的偏倚和标准误作为评价指标；实例数据分析是基于山东省多家医院健康体检中心的体检随访数据，以高血压为目标结局，构建纵向观察队列，筛选单核苷酸多态性(single nucleotide polymorphism, SNP)位点rs12149832作为Ⅳ，在Logistic回归分析模型中，采用不同策略(纳入/不纳入rs12149832协变量)来分析BMI与患高血压风险之间的关系。 结果 统计模拟结果显示在以Logistic回归分析模型估计暴露与结局间的效应时，协变量集中纳入Ⅳ会增大效应估计的偏倚和标准误，但增大程度较小；实例分析中，高血压队列共纳入1 240名女性，基线年龄为(37.7±10.5)岁，BMI为(22.1±3.1)kg/m2。纳入Ⅳ的模型所得的效应估计值为0.225(P＜0.001)，略小于不包含Ⅳ的回归模型所得的效应估计值(0.228, P＜0.001)，基本验证了关于纳入Ⅳ进行调整的统计模拟结果。 结论 观察性流行病学研究中，Logistic回归分析模型误纳入Ⅳ对效应估计值的偏倚和标准误均有影响。 -
关键词:
- 工具变量 /
- 因果推断 /
- 混杂因素 /
- Logistic回归分析模型
Abstract:Objective To explore the effects of adjusting for instrumental variables (Ⅳs) in a Logistic regression model through statistical simulation and real data analysis while there were unmeasured confounding factors. Methods Simulations were carried out by traversing the value of parameters in the Logistic regression model, and variables were all binomial distribution. Bias and standard error were used to evaluate the performance of estimators. As for the real data analysis, a longitudinal hypertension cohort was constructed based on the multi-center health management cohort of Shandong Province, and single nucleotide polymorphism (SNP) rs12149832 was selected as the Ⅳ. Logistic regression models with and without adjusting Ⅳ(rs12149832) were used to estimate the effect of body mass index (BMI) on hypertension. Results The statistical simulation results showed that adjusting for Ⅳs in a Logistic regression model would increase the confounding bias and the standard error of effect estimation, but these increases were generally small. As for the real data analysis, a total of 1 240 women were included in the Hypertension cohort. The baseline age was (37.7±10.5) years and the BMI was (22.1±3.1) kg/m2. The estimated value with adjusting for Ⅳ (0.225, P < 0.001) was slightly less than the estimated value without adjusting for the Ⅳ (0.228, P < 0.001), which basically verified the statistical simulation results about adjusting Ⅳs. Conclusion In observational epidemiological studies, the mistaken inclusion of Ⅳs in the Logistic regression model has an impact on both the bias and standard error of the effect estimates. -
Key words:
- Instrumental variable /
- Causal inference /
- Confounding factor /
- Logistic regression model
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图 3 变化变量间OR值、Z生成概率及样本量时估计值的偏倚和标准误
Figure 3. Bias and standard error of the estimators with traversing the OR value of parameters, the generation probability of Z and the sample size
表 1 SNP位点与BMI的关联性
Table 1. The association between SNP and BMI
SNP位点 β值 sx值 t值 P值 rs12149832 0.433 0.196 2.208 0.027 
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表 2 三种策略下BMI对高血压的效应估计
Table 2. Estimation of the effect of BMI on hypertension under three strategies
模型 方法/自变量 估计值 sx值 OR(95% CI)值 Z值 P值 MR TSLS 1.066 0.433 2.904(1.212~6.656) 2.462 0.013 Logistic模型1 BMI 0.228 0.029 1.256(1.186~1.331) 7.764 ＜0.001 Logistic模型2 BMI+rs12149832 0.225 0.029 1.252(1.183~1.327) 7.653 ＜0.001
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