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是用统计模型计算的，自变量没有误差。在基于个体数据的研究中，当自变量误差不小时，用通常的统计模型得到的参数含有自变量与因变量之间零关系的偏差，即估计不足。在自变量误差不大且误差大小已知的情况下，给出了修正参数估计不足的方法。为了减少自变量误差的影响，有时会进行基于自变量和因变量分组的生态学研究。然而，人们指出，在进行生态学研究时，有时没有充分考虑混杂因素，在流行病学研究中，根据大米中镉浓度(Cd-R)计算的镉(Cd-R)摄入量与肾功能不全之间的剂量-反应关系的流行病学研究中，剂量的误差很大。因此，用通常的统计模型对表示自变量和因变量之间关系强弱的参数进行修正是不可能的，因为通常的统计模型是基于个体数据的自变量没有误差。在流行病学研究区，可以开展Cd污染区和对照区Cd-R均值与肾功能障碍患病率之间关系的生态学研究。流行病学研究没有适当考虑混杂变量，混杂变量代表CD-R以外的其他环境因素。因此，利用CD-R进行流行病学研究得出的Cd的环境安全水平是不够的。

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.