Empirical Likelihood Methods in Biomedicine and Health

Albert Vexler, Jihnhee Yu

• Publisher: Chapman and Hall/CRC
• Year: 2018
• ISBN:
  9781351001502
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Empirical Likelihood Methods in Biomedicine and Health provides a compendium of nonparametric likelihood statistical techniques in the perspective of health research applications. It includes detailed descriptions of the theoretical underpinnings of recently developed empirical likelihood-based methods. The emphasis throughout is on the application of the methods to the health sciences, with worked examples using real data.

• Provides a systematic overview of novel empirical likelihood techniques.
• Presents a good balance of theory, methods, and applications.
• Features detailed worked examples to illustrate the application of the methods.
• Includes R code for implementation.

The book material is attractive and easily understandable to scientists who are new to the research area and may attract statisticians interested in learning more about advanced nonparametric topics including various modern empirical likelihood methods. The book can be used by graduate students majoring in biostatistics, or in a related field, particularly for those who are interested in nonparametric methods with direct applications in Biomedicine.

1

Preliminaries

1.1 Overview: From Statistical Hypotheses to Types of Information for Constructing Statistical Tests

Most experiments in biomedicine and other health-related sciences involve mathematically formalized comparisons, employing appropriate and efficient statistical procedures in designing clinical studies and analyzing data. Decision making through formal rules based on mathematical strategies plays important roles in medical and epidemiological discovery, policy formulation, and clinical practice. In this context, the statistical discipline is commonly required to be applied to make conclusions about populations on the basis of samples from the populations.

The aim of methodologies in decision making is to maximize quantified gains and at the same time minimize losses to reach a conclusion. For example, statements of clinical experiments can target gains such as accuracy of diagnosis of medical conditions, faster healing, and greater patient satisfaction, while they minimize losses such as efforts, durations of screening for disease, and side effects and costs of the experiments.

There are generally many constraints and desirable characteristics for constructing a statistical test. An essential part of the test development is that statistical hypotheses should be clearly and formally set up with respect to objectives of clinical studies. Oftentimes, statistical hypotheses and clinical hypotheses are associated but stated in different forms and orders. In most applications, we are interested in testing characteristics or distributions of one or more populations. In such cases, the statistical hypotheses must be carefully formulated, and formally stated, depicting, e.g., the nature of associations in terms of quantified characteristics or distributions of populations. The term Null Hypothesis, symbolized $H_0$, commonly is used to point out our primary statistical hypothesis. For example, when one wants to test that a biomarker of oxidative stress has different circulating levels for patients with and without atherosclerosis (clinical hypothesis), the null hypothesis (statistical hypothesis) can be proposed corresponding to the assumption that levels of the biomarker in individuals with and without atherosclerosis are distributed equally. Note that the clinical hypothesis points out that we want to show the discriminating power of the biomarker, whereas H₀ says there are no significant associations between the disease and biomarker’s levels. The reason of such null hypothesis specification lies in the ability to formulate H₀ clearly and unambiguously as well as to measure and calculate expected errors in decision making. Probably, if the null hypothesis would be formed in a similar manner to the clinical hypothesis, we could not unambiguously determine which sort of links between the disease and biomarker’s levels should be tested.

The null hypothesis is usually a statement to be statistically tested. In the context of statistical testing that provides a formal test procedure and compares mathematical strategies to make a decision, algorithms for monitoring statistical test characteristics associated with the probability to reject a correct hypothesis should be considered. While developing and applying test procedures, the practical statistician faces a task to control the probability of the event that a test outcome rejects H₀ when in fact H₀ is correct, called a Type I error (TIE) rate.

Obviously, in order to construct statistical tests, we must review the corresponding clinical study, formalizing ob...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• Authors
• 1. Preliminaries
• 2. Basic Ingredients of the Empirical Likelihood
• 3. Empirical Likelihood in Light of Nonparametric Bayesian Inference
• 4. Empirical Likelihood for Probability Weighted Moments
• 5. Two-Group Comparison and Combining Likelihoods Based on Incomplete Data
• 6. Quantile Comparisons
• 7. Empirical Likelihood for a U-Statistic Constraint
• 8. Empirical Likelihood Application to Receiver Operating Characteristic Curve Analysis
• 9. Various Topics
• References
• Name Index
• Subject Index