Development of Regression Models with Below‐Detection Data

Abstract

When a model is used to fit data containing dependent variables some of which are known only to be below some limit, special techniques must be employed. The present paper shows that ordinary regression, omitting those observations lacking measured values, results in biased estimation of the parameters in a model. The use of maximum-likelihood estimation, frequently employed in the field of life testing, is found to yield estimates of less bias and greater precision for such data. The maximum-likelihood estimation technique is also found to be at least as robust to deviations from normality as ordinary regression. Application of this technique is illustrated with reference to the problem of developing relationships for a non-THM disinfection [trichloroacetic acid (TCAA)] by-product of water chlorination. Diagnostic tests for goodness of fit of the resulting model are also shown. Finished water TCAA concentrations are shown to be described by a function including chloroform concentration, pH, and type of water-treatment process (straight chlorination, chlorammoniation, etc.).