Dose-response Study Based On Trend

The process of getting a new drug to market must experience many period, such as laboratory experiment, animal experiment, human experiment. Clinical trial is basically an experiment designed to evaluate the beneficial and adverse effects of a new medical treatment or intervention, where are many questions relating to dose response. In study of dose response, the response pattern in multi-dose have some trend. For example, the toxicity curve and the efficacy curve both are non-decreasing. Genes with similar expression trend may func-tionally related or reveal much about the genes’ regulatory systems. In biological experiments, laboratory subjects may be different in their patterns of suscepti-bility to a treatment, that is, different subjects have different response trends.This paper emphasizes on the following questions relating to dose response based on trend. (1) The selection and clustering question of gene relate to time-dose-response. (2) The determination of different susceptibility patterns. Chapter two, three, four studies on the three questions respectively.Chapter two studies the method for selecting and clustering genes accord-ing to their time-course or dose-response profiles. Different genes usually have different expression profiles. Genes with similar expression patterns (coexpressed genes) contains some special information. For example, many functionally re-lated genes are coexpressed, or coexpression may reveal much about the genes’ regulatory systems. Hence, grouping with similar expression levels can reveal the function of previously uncharacterized genes, and there is likely to be a re-lationship between coexpression and coregulation. So selecting and clustering coexpressed genes is very important. People usually utilize bootstrap sampling to obtain the sampling distribution under null hypothesis for hypothesis test because the true distributions of the observed genes are unknown in fact. In this work, we utilize likelihood ratio method to resolve the question of selecting and clustering, which necessitates the assumption of a constant variance through time or among dosages. This homoscedasticity assumption is, however, seldom satisfied in practice. Via the application of Shi’s (1994,1998) algorithms and a modified bootstrap procedure, we proposed a generalized order-restricted infer-ence methodology for the same task without the homoscedasticity restriction.Chapter three emphasizes on the classification of the susceptibility’s pat-terns. In some biological experiments, it is quite common that laboratory subjects differ in their patterns of susceptibility to a treatment. Finite mixture models are useful in those situations. In this chapter we model the number of components and the component parameters jointly, and base inference about these quantities on their posterior probabilities, making use of the reversible jump Markov chain Monte Carlo methods. In particular, we apply the methodology to the analysis of univariate normal mixtures with multidimensional parameters using a hierar-chical prior model that allows weak priors while avoiding improper priors in the mixture context.In the study of these questions, we used likelihood ratio test, Bootstrap sampling, Bayes method; reversible jump MCMC method, mixture model et al. Also we carried simulation studies, example analysis, and sensitivity analysis of all proposed method. Analysis results demonstrates all proposed methods are significant.