Methodological Problems Arising from the Choice of an Independent Variable in Linear Regression, with Application to an Air Pollution Epidemiological Study

摘要

In epidemiological studies using linear regression, it is often necessary for reasons of economy or unavailability of data to use as the independent variable not the variable ideally demanded by the hypothesis under study but some convenient practical approximation to it. If the correlation coefficient between the ''practical'' and ''ideal'' variables can be obtained, then a range of uncertainty can be obtained within which the desired regression coefficient of dependent on ideal variable may lie. This range can be quite wide, even if the practical and ideal variables are fairly well correlated, expecially if the regression of dependent on practical variable explains only a small part of the variance in the dependent variable. These points are illustrated with data and observed regression coefficients from an air pollution epidemiological study, in which pollution measured at one station in a large metropolitan area (containing 40 aerometric stations) was used as the practical approximation to the city-wide average pollution. The uncertainties in the regression coefficients were found to exceed the regression coefficients themselves by factors of 15 to 150. (ERA citation 03:037960)