a b s t r a c tInhaled aerosol dose models play critical roles in medicine, the regulation of air pollutants and basic research. The models fall into several categories: traditional, computational fluid dynamical (CFD), physiologically based pharmacokinetic (PBPK), empirical, semi-empirical, and "reference". Each type of model has its strengths and weaknesses, so multiple models are commonly used for practical applications. Aerosol dose models combine information on aerosol behavior and the anatomy and physiology of exposed human and laboratory animal subjects. Similar models are used for in-vitro studies. Several notable advances have been made in aerosol dose modeling in the past 80 years. The pioneers include Walter Findeisen, who in 1935 published the first traditional model and established the structure of modern models. His model combined aerosol behavior with simplified respiratory tract structures. Ewald Weibel established morphometric techniques for the lung in 1963 that are still used to develop data for modeling today. Advances in scanning techniques have similarly contributed to the knowledge of respiratory tract structure and its use in aerosol dose modeling. Several scientists and research groups have developed and advanced traditional, CFD, and PBPK models. Current issues under study include understanding individual and species differences; examining localized particle deposition; modeling non-ideal aerosols and nanoparticle behavior; linking the regions of the respiratory tract airways from nasal-oral to alveolar; and developing sophisticated supporting software. Although a complete history of inhaled aerosol dose modeling is far too extensive to cover here, selected highlights are described in this paper.

Statistical tests of carcinogenicity are shown to have varying degrees of robustness to the effects of mortality. Mortality induced by two different mechanisms is studied--mortality due to the tumor of interest, and mortality due to treatment independent of the tumor. The two most commonly used tests, the life-table test and the Cochran-Armitage linear trend test, are seen to be highly sensitive to increases in treatment lethality using small-sample simulations. Increases in tumor lethality are seen to affect the performance of commonly used prevalence tests such as logistic regression. A simple survival-adjusted quantal response test appears to be the most robust of all the procedures considered.

Experimenters in toxicology often compare the concentration-response relationship between two distinct populations using the median lethal concentration (LC50). This comparison is sometimes done by calculating the 95% confidence interval for the LC50 for each population, concluding that no significant difference exists if the two confidence intervals overlap. A more appropriate test compares the ratio of the LC50s to 1 or the log(LC50 ratio) to 0. In this ratio test, we conclude that no difference exists in LC50s if the confidence interval for the ratio of the LC50s contains 1 or the confidence interval for the log(LC50 ratio) contains 0. A Monte Carlo simulation study was conducted to compare the confidence interval overlap test to the ratio test. The confidence interval overlap test performs substantially below the nominal alpha = 0.05 level, closer to p = 0.005; therefore, it has considerably less power for detecting true differences compared to the ratio test. The ratio-based method exhibited better type I error rates and superior power properties in comparison to the confidence interval overlap test. Thus, a ratio-based statistical procedure is preferred to using simple overlap of two independently derived confidence intervals.

The area under a curve (AUC) of metabolite concentration or drug concentration over time has biological meaning in many situations, and the test of AUC equality among a set of different dosing regimens is often of interest. For the situation where the experimental unit must be sacrificed in order to obtain an estimate of the metabolite or drug concentration, it is noted that linear combinations of mean concentrations at time points for a particular dosing regimen can be used to estimate the AUC for that regimen. Contrasts among AUC estimates are readily constructed and tested within this derivation.