Advances in Dose-Response Estimation and Calibration
The dose-response design is frequently used when it is necessary to measure a biological response at varying levels of an experimental factor. As might be expected, this type of problem is common in agricultural research involving the application of pesticides, but can also occur in other agricultural disciplines such as plant, animal, and environmental sciences. A typical goal of dose-response analyses is to estimate the specific dosages which will induce predetermined levels of the response. Such measures, commonly percentiles referred to as LD50, EC10, etc., are the standard means for the comparison and assessment of relative efficacy and safety of various treatments. Hence, appropriate statistical estimation and inference on the dose-response curve and its dose-related percentiles are of great importance. Additionally, the dose-response
curve can be used to determine an unknown dosage. This type of calibration problem forms the basis for bioassay analysis and is useful when observed responses are available, but their associated dosages are unknown. This situation could arise when, for example, pesticides drift or inadvertently contaminate agricultural areas. In such cases, it is necessary to determine if a specified pesticide is present and, if so, at what levels. While direct chemical assessments can often provide these answers, the tests involved are typically prohibitively expensive. Bioassays, on the other hand, can provide the same information at a reduced cost. Bioassay methods are a cost effective means of researching pesticide persistence and carry over effects. Past statistical approaches to estimation of dose-response percentiles and the bioassay problem in general have relied on inverted solutions and
approximations. Restrictive assumptions on response distributions and dose-response models have limited the scope and accuracy of the solutions. While theoretical improvements on these techniques have been long known, the means and methods to practically implement the required computations have been prohibitive. Recent advances in computer hardware and software, however, have brought these improvements within reach of agricultural researchers. Development and application of these newer methods will provide a wider range of options and better solution accuracy to the dose-response problem. This work proposes to develop advanced techniques in estimation and calibration of dose-response functions and implementation in a fashion readily available to the agricultural research community.