When there is a predictive biomarker, enrichment can focus the clinical trial on a benefiting subpopulation. We describe a two-stage enrichment design, in which the first stage is designed to efficiently estimate a threshold and the second stage is a “phase III-like” trial on the enriched population. The goal of this paper is to explore design issues: sample size in Stages 1 and 2, and re-estimation of the Stage 2 sample size following Stage 1. By treating these as separate trials, we can gain insight into how the predictive nature of the biomarker specifically impacts the sample size. We also show that failure to adequately estimate the threshold can have disastrous consequences in the second stage. While any bivariate model could be used, we assume a continuous outcome and continuous biomarker, described by a bivariate normal model. The correlation coefficient between the outcome and biomarker is the key to understanding the behavior of the design, both for predictive and prognostic biomarkers. Through a series of simulations we illustrate the impact of model misspecification, consequences of poor threshold estimation, and requisite sample sizes that depend on the predictive nature of the biomarker. Such insight should be helpful in understanding and designing enrichment trials. 相似文献
Based on imperfect data and theory, agencies such as the United States Environmental Protection Agency (USEPA) currently derive “reference doses” (RfDs) to guide risk managers charged with ensuring that human exposures to chemicals are below population thresholds. The RfD for a chemical is typically reported as a single number, even though it is widely acknowledged that there are significant uncertainties inherent in the derivation of this number.
In this article, the authors propose a probabilistic alternative to the EPA's method that expresses the human population threshold as a probability distribution of values (rather than a single RfD value), taking into account the major sources of scientific uncertainty in such estimates. The approach is illustrated using much of the same data that USEPA uses to justify their current RfD procedure.
Like the EPA's approach, our approach recognizes the four key extrapolations that are necessary to define the human population threshold based on animal data: animal to human, human heterogeneity, LOAEL to NOAEL, and subchronic to chronic. Rather than using available data to define point estimates of “uncertainty factors” for these extrapolations, the proposed approach uses available data to define a probability distribution of adjustment factors. These initial characterizations of uncertainty can then be refined when more robust or specific data become available for a particular chemical or class of chemicals.
Quantitative characterization of uncertainty in noncancer risk assessment will be useful to risk managers who face complex trade-offs between control costs and protection of public health. The new approach can help decision-makers understand how much extra control cost must be expended to achieve a specified increase in confidence that the human population threshold is not being exceeded. 相似文献
Paralysis caused by feeding female Ixodes rubicundus ticks is a major problem in large areas of South Africa. As the life cycle of the tick extends over a period of 2 years, it was hypothesized that strategic treatment of sheep with an acaricide over a 2 year period, timed to kill most engorging females, should markedly lower the biotic potential of the tick. Two flocks of sheep grazing in separate paddocks known to be infested with I. rubicundus were treated either strategically or on a threshold basis (i.e. only when tick challenge exceeded a predetermined critical level in terms of paralysis) for a 2 year period. The tick burdens of untreated control sheep running with the two flocks were monitored over a 4 year period and their seasonal dynamics determined. The times at which peak infestations occurred were similar for both flocks of sheep, but significant differences in mean tick burdens between the two flocks were recorded. Tick numbers on sheep in the strategically treated flock did not decrease during the third and fourth years of the trial as was expected. Possible reasons for this were low stocking densities, especially during times of peak abundance of adults and the presence of wild hosts which maintained tick populations. 相似文献
A model of single-species growth in the chemostat on two non-reproducing, growth-limiting, noninhibitory, perfectly substitutable resources is considered. The medium in the growth vessel is enriched by increasing the input concentration of one of the resources. Analytical methods are used to determine the effects of enrichment on the asymptotic behaviour of the model for different dilution rates. It is shown that there exists a threshold value for the dilution rate which depends on the maximal growth rate of the species on each of the resources. Provided the dilution rate is below the threshold, enrichment is beneficial in the sense that the carrying capacity of the environment is increased, regardless of which resource is used to enrich the environment. When the dilution rate is increased beyond the threshold, it becomes important to consider which resource is used for enrichment. For one of the resources it is shown that, while moderate enrichment can be beneficial, sufficient enrichment leads to the extinction of the microbial population. For the other resource, enrichment leads from washout or initial condition dependent outcomes to survival, and is thus beneficial. There are important implications of these results to the management of natural aquatic ecosystems. For example, while enrichment may be beneficial to the microbial species during the summer months, it can lead to their decimation during spring run-off, when the natural dilution rate is higher.Research partially supported by an Ontario Graduate Scholarship. This author's contribution was motivated by results in her Ph.D. thesis at McMaster UniversityResearch supported by the National Sciences and Engineering Research Council of Canada. 相似文献