A simulation study of methods for constructing confidence intervals for bioaccumulation factors

Toxicokinetics describe the time course of xenobiotics in an exposed organism. The steady state concentration of the xenobiotic is a characteristic of frequent concern, often summarized in terms of bioaccumulation factors (BAFs). Two experimental protocols are commonly used when estimating BAFs: a continuous exposure experiment and a start‐stop exposure experiment. Nonlinear regression is then used for estimating components of the BAF. A variety of methods are available for constructing confidence intervals (CI) for the BAF, including the delta method and Fieller's method. The properties of these CI methods are explored through a simulation study. In particular, the coverage properties of the two CI methods along with their interval widths are examined for a variety of time‐course patterns, error distributions, experimental protocols, and sampling designs. Fieller's method is observed to exceed nominal coverage probabilities for all conditions considered (the coverage probability being the probability that a confidence interval contains a parameter it estimates over repeated experiments). The delta method exhibited observed coverage probabilities lower than nominally specified for a number of conditions. For sampling designs in which more of the sampling times are prior to steady state or the stop exposure time, the delta method is observed to provide nominal coverage probabilities with interval widths much narrower than observed with the Fieller's method. Thus, the delta method is preferable when the above sampling time condition is met; however, in all other cases, Fieller's method should be used.