Preface

Statistics is one of the most widely applied branches of mathematics in science. Among the advances in complex statistical methods through which statisticians can provide a greater understanding of complex processes and mechanisms are applications in medical sciences and health sciences, including generalized linear models, structural equation models, spatial statistical models, statistical methods for clinical trials, Copula models, multi-state models for the analysis of time-to-event data, and multilevel models.

This book is divided into three sections: biostatistical modeling, spatial statistics, and clinical trials. Section 1, 'Biostatistical Modelling', contains five contributions. Chapter 1 proposes the use of binary and ordinal logistic regression techniques to calculate the risk probability for different disabilities (visual, hearing, physical, and intellectual). The author uses criteria such as Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to perform a selection of variables and selected models. Chapter 2 is a detailed introduction to structural equation models in medicine and health sciences and provides an example of their use in the 'red code' process. Chapter 3 illustrates the use of the empirical transition matrix and multi-state modeling to develop advanced optimal infusion controllers and to help nurses encode agitation-sedation scores. Chapter 4 introduces Copula models to capture non-linear dependence and establish the presence of lower- and/or uppertail dependence between the nurse's agitation-sedation rating and the automated sedation dose. Chapter 5 discusses the use of multilevel models in dental research when the response variable is numerical and shows how the bottom-up strategy can be adapted to specify a multilevel model in the Bayesian approach.

Section 2, 'Spatial Statistics', consists of two chapters. Chapter 6 presents spatial models used in epidemiology to predict infectious and non-infectious diseases occurring in a region: generalized linear spatial models, spatial survival models and spatial generalized extreme value models. Chapter 7 demonstrates the application of spatial statistics with the implementation of a generalized linear spatial model for the prediction of dengue disease in the state of Chiapas.

Section 3, 'Clinical Trials' contains two chapters. Chapter 8 discusses practical and near-optimal designs for clinical trials and reviews the strategy of incorporating multiple objectives while advocating a regression-type estimation approach via the generalized estimating equations method. The authors show that the adaptive allocation scheme successfully constructs designs of the desired efficiency, illustrated by practical two- and three-period designs. Chapter 9 reviews fundamental ideas, models, and the construction of optimal designs for N-of-1 trials, and discusses how they may be aggregated to estimate treatment effects for the average patient.

I would like to express my thanks to Karla Skuliber for her support throughout the editorial process of this book.

> **Cruz Vargas-De-León** Professor, División de Investigación, Hospital Juárez de México, Ciudad de México, México

> > Section 1

Biostatistical Modelling

Section 1
