Problems of safety levels derived from epidemiologic studies using independent variable with measurement error

在毒性因子与生物反应或效应之间的剂量-反应或效应关系的流行病学或实验研究中，表示自变量和因变量之间关系强度的参数通常使用自变量无误差的统计模型来计算。在基于个体数据的研究中，当自变量误差较大时，通常使用统计模型得到的参数存在自变量与因变量零关系的偏差，即估计不足。在自变量误差不大且误差大小已知的情况下，提出了修正参数过低估计的方法。为了减少自变量误差的影响，有时采用自变量和因变量在群体中的均值进行生态学研究。然而，有人指出，生态学研究有时在进行时没有适当考虑混杂因素。在以大米中镉浓度（Cd- r）为剂量计算的肾脏功能障碍与镉摄入量的剂量-反应关系的流行病学研究中，剂量误差很大。因此，用通常的基于个体数据的自变量无误差统计模型来校正表示自变量与因变量之间关系强度的参数是不可能的。在流行病学研究领域，可以开展Cd- r手段与Cd污染和控制地区肾功能障碍患病率关系的生态学研究。流行病学研究没有适当考虑混杂变量，它代表Cd-R以外的其他环境因素。因此，使用Cd- r进行的流行病学研究得出的Cd环境安全水平并不充分。

In epidemiologic or experimental studies for dose-response or -effect relationship between toxic factors and biological responses or effects, parameters which express strength of relationship between independent and dependent variables are usually calculated using statistical models without errors in independent variable. When error in independent variable is not small in study based on individual data, obtained parameter using usual statistical model includes bias toward null relationship between independent and dependent variables i.e. under estimate. When the error in independent variable is not large and the magnitude of the error is known, the methods which correct the under estimate of the parameter were developed. Ecologic study based on means of independent and dependent variables in groups are sometimes conducted in order to decrease effect of error in independent variables. It is, however, pointed out that ecologic study is sometimes carried out without due consideration for confounding factors.In epidemiologic study for dose-response relationship between renal dysfunction as response and cadmium (Cd) intake calculated from Cd concentration in rice (Cd-R) as dose, error of the dose is very large. Therefore, it is impossible to correct the parameter, which express strength of relationship between independent and dependent variables, using usual statistical model without error in independent variable based on individual data. In the epidemiologic study area, ecologic studies for relationship between means of Cd-R and prevalences of renal dysfunction in Cd polluted and control areas can be carried out. The epidemiologic studies were conducted without due consideration for confounding variable which represents the other environmental factors than Cd-R. Therefore environmental safety level of Cd derived from the epidemiologic studies using Cd-R is not adequate.