On modelling metabolism-based biomarkers of exposure: a comparative analysis of nonlinear models with few repeated measurements.

Establishing and characterizing exposure-biomarker relationships is an important problem in molecular epidemiology. The problem is difficult due to several complicating features, namely, the biomarker response is a nonlinear function of exposure and unknown parameters; variation in exposure and biomarker levels occurs both within and between subjects; and errors tend to be heteroscedastic. To overcome some of the statistical challenges in analysing such data, it is common for the investigator to make several assumptions about the data structure. For example, it is common to assume that the natural logarithm of right-skewed, biomarker measurements lead to homoscedasicity and normality so the effect of outliers is minimized and Gauss-Markov theory is applicable. In this paper, we compare a lognormal maximum likelihood estimator (MLE) to generalized estimating equations (GEE) for drawing statistical inference in a nonlinear model of a benzene biomarker (benzene oxide-albumin adducts) as a function of benzene exposure. We explore the characteristic properties of the lognormal MLE under a certain type of model misspecification and compare its small sample performance to the estimating equation approach in simulation studies. We show that the multiplicative lognormal model can lead to severe biases for modest deviations from the true outcome (biomarker) distribution. Furthermore, the lognormal MLE can exhibit very poor small sample properties even under the true model. All methods are applied in a novel data analysis from a study of benzene-exposed workers in China.