Tightrope Walking: Using Predictors of 25(OH)D Concentration Based on Multivariable Linear Regression to Infer Associations with Health Risks

The debate on the causal association between vitamin D status, measured as serum concentration of 25-hydroxyvitamin D (25[OH]D), and various health outcomes warrants investigation in large-scale health surveys. Measuring the 25(OH)D concentration for each participant is not always feasible, because of the logistics of blood collection and the costs of vitamin D testing. To address this problem, past research has used predicted 25(OH)D concentration, based on multivariable linear regression, as a proxy for unmeasured vitamin D status. We restate this approach in a mathematical framework, to deduce its possible pitfalls. Monte Carlo simulation and real data from the National Health and Nutrition Examination Survey 2005–06 are used to confirm the deductions. The results indicate that variables that are used in the prediction model (for 25[OH]D concentration) but not in the model for the health outcome (called instrumental variables), play an essential role in the identification of an effect. Such variables should be unrelated to the health outcome other than through vitamin D; otherwise the estimate of interest will be biased. The approach of predicted 25(OH)D concentration derived from multivariable linear regression may be valid. However, careful verification that the instrumental variables are unrelated to the health outcome is required.针对以血清25-羟维生素D（25-hydroxyvitamin D, 25[OH]D）浓度为衡量标准的维生素D状态与多种健康结局之间的因果关联的学术讨论，亟需在大规模健康调查中开展相关研究。由于血液采集的流程规范与维生素D检测的成本限制，为每位参与者实测25(OH)D浓度并非始终可行。为解决这一难题，既往研究采用基于多变量线性回归的预测25(OH)D浓度，作为未实测维生素D状态的替代指标。我们在数学框架下重新阐释了该方法，以推导其潜在的局限性。本研究采用蒙特卡洛模拟（Monte Carlo simulation）以及2005-2006年国家健康与营养检查调查（National Health and Nutrition Examination Survey）的真实数据，对上述推导结果进行验证。研究结果显示，在25(OH)D浓度预测模型中纳入但未被纳入健康结局模型的变量（即工具变量（instrumental variables）），在效应识别环节发挥着至关重要的作用。此类变量除通过维生素D介导的通路外，应与健康结局无关联；否则目标效应估计值将出现偏倚。基于多变量线性回归得到的预测25(OH)D浓度方法具备一定有效性，但仍需仔细验证工具变量与健康结局不存在除维生素D介导之外的其他关联。