Teoria da regressão isotônica e delineamentos sequenciais aplicados a ensaios de dose-resposta

Abstract

The goal of many analysis methods for sensibility data, obtained in doseresponse designs, is to estimate the dose-target that will produce a predefined result on 􀀀 percent of the population. Initially the usual was 􀀀 = 0:5 corresponding to the so called 50% lethal dose, LD50. Methods like probit, logit and Up and Down estimate efficiently such dose and, among them, the Up and Down method, based on the theory of sequential designs, has the advantage of reduced sample size. When dealing with estimation of quantile of the tolerance curve, as in Phase I clinical essays or acute toxicity tests, some Up and Down based design, like the biased coin design and the modified Narayana design, has shown to be efficient. As the dose-response is usually a increasing curve, the appropriate statistical method for estimation is the isotonic regression. One of the objectives of this work is to propose new estimators, based on the theory of isotonic regression, to be used when dealing with sequential designs as well as estimators applied to probit and logit theory. It is also proposed a sequential isotonic Bayesian design. To evaluate the accomplishment of the estimator we used Monte Carlo Method to evaluate MSE and bias for different sample sizes. Results has shown feasibility for practical use of the new estimators and the proposed design.