Catálogo de publicaciones - libros

There are a few sources of uncertainty/variability associated with patient recruitment in multicentre clinical trials: uncertainties in prior information, stochasticity in patient arrival and centre initiation processes. Methods of statistical modeling, prediction and adaptive adjustment of recruitment are proposed to address these issues. The procedures for constructing an optimal recruitment design accounting for time and cost constraints are briefly discussed.

Pharmacokinetic (PK) studies with serial sampling which are described by compartmental models are discussed. We focus on intrinsic variability induced by the noise terms in stochastic differential equations (SDE). For several models of intrinsic randomness, we find explicit expressions for mean and covariance functions of the solution of the system of SDE. This, in turn, allows us to construct optimal designs, i.e. find sequences of sampling times that guarantee the most precise estimation of unknown model parameters. The performance of optimal designs is illustrated with several examples, including cost-based designs.

In several scientific disciplines it is often of interest to compare the concentration of the distribution of a categorical variable between two or more populations. The aim is to establish if the heterogeneities of the distributions are equal or not. We propose a nonparametric solution based on a permutation test. The main properties of the test and a Monte Carlo simulation in order to evaluate its behaviour will be discussed.

In I × J balanced factorial designs units are not exchangeable between blocks since their expected values depend on received treatments. It does not seem possible, therefore, to obtain exact and separate tests to respectively assess main factor and interaction effects. Parametric two-way ANOVA F tests are exact tests only under assumption of normal homoschedastic errors, but they are also positively correlated. Instead, it is possible to obtain exact, separate and uncorrelated permutation tests at least for main factors by introducing a restricted kind of permutations, named synchronized permutations. Since these tests are conditional on observed data, they are distribution-free and may be shown to be almost as powerful as their parametric counterpart under normal errors. We obtain the expression of the correlation between the main factor ANOVA tests as a function of the number of replicates in each block, the number of main factor levels and their noncentrality parameters.

Response-adaptive designs may be used in phase III clinical trials to allocate a larger number of patients to the better treatment. Optimal response-adaptive designs are used for the same purpose, but the design is derived from some optimal points of view. The available optimal response-adaptive designs are only for two treatment trials. In the present paper, we extend this idea and derive some optimal response-adaptive designs for phase III clinical trials for more than two treatments. In particular, we work on three treatments. The extension is not trivial, as the designs for three treatments are often iterative, and they need specific algorithms for computation. The proposed approaches are numerically illustrated.

D-optimal experiments for binary response data have been extensively studied in recent years. On the other hand two-level fractional factorials are often used as screening designs at the preliminary stage of an investigation when the outcome is continuous. We explore the performance of the one-half two-level experiments for a logistic model with three factors, and show that the conventional wisdom about this kind of experiment does not apply when the response is binomial.

It is assumed that the covariance matrix of N observations has the form $$ C_\theta = \sum\nolimits_{r = 1}^R {\theta _r U_r } $$ where U _1,..., U _R are known covariance matrices and θ _1,..., θ _R are unknown parameters. Estimators for $$ \sum\nolimits_{r = 1}^R {\theta _r b_r } $$ with known b _1,..., b _R are characterized which minimize the Bayes risk within all invariant quadratic unbiased estimators. In this characterization, the matrix A , which determines the quadratic form of the estimator, is given by a linear equation system which is not of full rank. It is shown that some solutions of the equation system prove to be asymmetric matrices A . Therefore, sufficient conditions are presented which ensures symmetry of the matrix A . Given this result, the influence of designs on the Bayes risk is studied.

In this paper we consider optimal design of experiments for correlated observations. We approximate the error component of the process by an eigenvector expansion of the corresponding covariance function. Furthermore we study the limiting behavior of an additional white noise as a regularization tool. The approach is illustrated by some typical examples.

In clinical studies, continuous endpoints are very commonly seen. However, either for ease of interpretation or to simplify the reporting process, some continuous endpoints are often reported and (unfortunately) analyzed as binary or ordinal responses. We emphasize the usefulness of differentiation between response and utility functions and develop tools to build locally optimal designs for corresponding models. It is also shown that dichotomization of responses may lead to significant loss in statistical precision. We consider an example with two responses and one utility function. The generalization to a larger number of responses and utility functions is straightforward.

In this paper, we discuss quantum nonlocality experiments and show how to optimize them in respect of their experimental setup. The usage of statistical tools from missing data and maximum likelihood are crucial. An aim of this paper is to bring this kind of theory to the statistical community.