A problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment than others. A mixture model has traditionally been proposed to describe the distribution of responses in treatment groups for such experiments. Using a mixture dose-response model, we derive an upper confidence limit on additional risk, defined as the excess risk over the background risk due to an added dose. Our focus will be on experiments with continuous responses for which risk is the probability of an adverse effect defined as an event that is extremely rare in controls. The asymptotic distribution of the likelihood ratio statistic is used to obtain the upper confidence limit on additional risk. The method can also be used to derive a benchmark dose corresponding to a specified level of increased risk. The EM algorithm is utilized to find the maximum likelihood estimates of model parameters and an extension of the algorithm is proposed to derive the estimates when the model is subject to a specified level of added risk. An example is used to demonstrate the results, and it is shown that by using the mixture model a more accurate measure of added risk is obtained.
The aim of this study was to determine the heavy metal contents of dietary supplements manufactured from medicinal plants and assess the potential daily burden on their consumers. The study consisted of 41 dietary supplements produced from terrestrial plants or microalgae. The analysis of cadmium, lead, and mercury content was performed using analytical methods. The content of Cd and Pb was determined by flame atomic absorption spectrometry (FAAS). The mercury content was determined using atomic absorption spectrometry with the generation of cold mercury vapor (CVAAS). The presence of at least one of the three analyzed heavy metals was found in 79.2% samples of supplements produced from terrestrial plants and in 88.2% supplement samples produced from microalgae. Hazard quotient was used to calculate noncarcinogenic risk for humans by ingestion of dietary supplements containing heavy metals. From among all supplements, 68.3% of samples were contaminated with Cd and Pb (this does not always apply to the same samples) and 29.3% of samples were contaminated with Hg. The health risk assessment of consumers of dietary supplements showed, in an extreme case, that taking this supplement for only one week poses a health risk associated with exposure to Pb. The health risk associated with the intake of dietary supplements primarily depends on the duration of consumption.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.