Statistical problems in estimating elimination rates by compartmental models

The rate of lead elimination in blood by occupationally exposed individuals has been studies using a compartment model with three exponential terms. The analysis of data by exponential regression leads to numerical problems. It is often a difficult task to decide how many measurements should be performed, the length of the observation period, and how the observations should be distributed to get high accuracy. In a simulation study, the sensitivity of the parameter estimates was investigated as a function of these three factors. The effects of missing observations in some interval was also studied. It is shown that a too short observation time leads to a relatively high frequency of outliers in the estimated values of all three half-times. It is also shown that missing values in one compartment affect the parameter estimates of that and faster compartments. The results obtained can be used as a help to decide what experimental accuracy is needed for a given accuracy of compartment model parameters for a variety of medical and biological problems.