This thesis concerns optimal designs and estimation approaches for a class of nonlinear dose response models, namely multi-response Emax models. These models describe the relationship between the dose of a drug and two or more efficacy and/or safety variables. In order to obtain precise parameter estimates it is important to choose efficient estimation approaches and to use optimal designs to control the level of the doses administered to the patients in the study. We provide some optimal designs that are efficient for estimating the parameters, a subset of the parameters, and a function of the parameters in multi-response Emax models. The function of interest is an estimate of the best dose to administer to a group of patients. More specifically the dose that maximizes the Clinical Utility Index (CUI) which assesses the net benefit of a drug taking both effects and side-effects into account. The designs derived in this thesis are locally optimal, that is they depend upon the true parameter values. An important part of this thesis is to study how sensitive the optimal designs are to misspecification of prior parameter values. For multi-response Emax models it is possible to derive maximum likelihood (ML) estimates separately for the parameters in each dose response relation. However, ML estimation can also be carried out simultaneously for all response profiles by making use of dependencies between the profiles (system estimation). In this thesis we compare the performance of these two approaches by using a simulation study where a bivariate Emax model is fitted and by fitting a four dimensional Emax model to real dose response data. The results are that system estimation can substantially increase the precision of parameter estimates, especially when the correlation between response profiles is strong or when the study has not been designed in an efficient way. / <p>At the time of the doctoral defence the following papers were unpublished and had a status as follows: Paper 1: Manuscript; Paper 2: Manuscript; Paper 3: Manuscript; Paper 4: Manuscript.</p>

Italian ryegrass (Lolium perenne spp. multiflorum) is a common weed management problem in turfgrasses, cereals and non-crop areas in the United States. In Oregon, the number of populations with multiple-resistance continues to increase. To manage these resistant populations, the resistance patterns must be determined. In this study, five Italian ryegrass populations (CT, R1, R2, R3 and R4) from two cropping systems were studied for resistance patterns and mechanisms. The CT population is from a Christmas tree plantation and was resistant to at least six herbicides with four different mechanisms of action: atrazine, diuron (2.4-fold), glyphosate (7.4-fold), hexazinone (3.1-fold), imazapyr (1.8-fold), and sulfometuron. The resistant indices (RI) for sulfometuron and atrazine could not be calculated because 50% growth reduction for the CT population was not reached even with the highest rates applied, 17.6 kg ai ha⁻¹and 16 kg ai ha⁻¹, respectively, which are 16 times the recommended field application rates for this two herbicides. The CT population accumulated less shikimate than the S population. There were two mutations in the CT population, Trp591 to Leu in the ALS gene and Ser264 to Gly in the psbA gene, which explain the ALS and PII cross resistance, respectively. R1, R2, R3 and R4 were collected from annual cropping systems. All four populations were resistant to flufenacet. RIs for two populations, R2 and R4, were 8.4 and 5.9, respectively. R2 and R4 also were resistant to mesosulfuron-methyl, pinoxaden, quizalofop and clethodim. R4 was resistant to diuron, but R2 was not. An Asp-2078-Gly substitution in the ACCase gene was found in both R2 and R4 populations, while another Ile-2041-Asn substitution in the ACCase gene was found in the R4 population. These mutations explain the ACCase cross resistance in the R2 and R4 populations. The mechanisms for the glyphosate resistance in the CT population and the flufenacet resistance in R1, R2, R3 and R4 populations were not identified in this study. None of the five populations were resistant to the herbicide pyroxasulfone. / Graduation date: 2013

Often predictor variables in regression models are measured with errors. This is known as an errors-in-variables (EIV) problem. The statistical analysis of the data ignoring the EIV is called naive analysis. As a result, the variance of the errors is underestimated. This affects any statistical inference that may subsequently be made about the model parameter estimates or the response prediction. In some cases (e.g. quadratic polynomial models) the parameter estimates and the model prediction is biased. The errors can occur in different ways. These errors are mainly classified into classical (i.e. occur in observational studies) or Berkson type (i.e. occur in designed experiments). This thesis addresses the problem of the Berkson EIV and their effect on the statistical analysis of data fitted using linear and nonlinear models. In particular, the case when the errors are dependent and have heterogeneous variance is studied. Both analytical and empirical tools have been used to develop new approaches for dealing with this type of errors. Two different scenarios are considered: mixture experiments where the model to be estimated is linear in the parameters and the EIV are correlated; and bioassay dose-response studies where the model to be estimated is nonlinear. EIV following Gaussian distribution, as well as the much less investigated non-Gaussian distribution are examined. When the errors occur in mixture experiments both analytical and empirical results showed that the naive analysis produces biased and inefficient estimators for the model parameters. The magnitude of the bias depends on the variances of the EIV for the mixture components, the model and its parameters. First and second Scheffé polynomials are used to fit the response. To adjust for the EIV, four different approaches of corrections are proposed. The statistical properties of the estimators are investigated, and compared with the naive analysis estimators. Analytical and empirical weighted regression calibration methods are found to give the most accurate and efficient results. The approaches require the error variance to be known prior to the analysis. The robustness of the adjusted approaches for misspecified variance was also examined. Different error scenarios of EIV in the settings of concentrations in bioassay dose-response studies are studied (i.e. dependent and independent errors). The scenarios are motivated by real-life examples. Comparisons between the effects of the errors are illustrated using the 4-prameter Hill model. The results show that when the errors are non-Gaussian, the nonlinear least squares approach produces biased and inefficient estimators. An extension of the well-known simulation-extrapolation (SIMEX) method is developed for the case when the EIV lead to biased model parameters estimators, and is called Berkson simulation-extrapolation (BSIMEX). BSIMEX requires the error variance to be known. The robustness of the adjusted approach for misspecified variance is examined. Moreover, it is shown that BSIMEX performs better than the regression calibration methods when the EIV are dependent, while the regression calibration methods are preferable when the EIV are independent.