Computer Assisted Analysis of Mixtures and Applications: Meta Analysis, Disease Mapping, and Others, 1st Edition (Hardback) book cover

Computer Assisted Analysis of Mixtures and Applications

Meta Analysis, Disease Mapping, and Others, 1st Edition

By Dankmar Bohning

Chapman and Hall/CRC

248 pages

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Hardback: 9781584881797
pub: 1999-11-22
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Description

Computer Assisted Analysis of Mixtures summarizes developments in the field over the last 20 years . Along with advancements in theory and algorithms, it explores developments in biometric applications, such as meta-analysis, disease mapping, fertility studies, estimation of prevalence under clustering, and estimation of the distribution of survival times under interval-censoring. The approach is nonparametric for the mixing distribution, including leaving the number of components of the mixing distribution unknown. The text is particularly valuable to statisticians working with pharmaceutical clinical trials, epidemiologists, and social scientists.

Reviews

"…has several valuable features…"

Biometrics, Vol. 56, No. 2, June 2000

"The chapter on disease mapping is interesting and well illustrated…"

Biometrics, Vol. 56, No. 2, June 2000

"Overall, the book provides useful discussion of heterogeneity and algorithms."

Biometrics, Vol. 56, No. 2, June 2000

"This software should permit the interested reader to carry out mixture analysis of their own data with little difficulty and facilitate a better appreciation of the methods presented."

Short Book Reviews, Vol. 20, No. 3, December 2000

"The text is well written and easy to read."

Short Book Reviews, Vol. 20, No. 3, December 2000

Table of Contents

INTRODUCTION

Population Heterogeneity: the Natural Genesis of Mixture Models

Some Examples

Classification Using Posterior Bayes

Parametric or Nonparametric Mixture Models

Connection to Empirical Bayes Estimation

THEORY OF NONPARAMETRIC MIXTURE MODELS

The Likelihood and its Properties

The Directional Derivative and the Gradient Function

The General Mixture Maximum Likelihood Theorem

Applications of the Theorem

ALGORITHMS

Vertex Direction Method

Vertex Exchange Method

Step-Length Choices

C.A. MAN

The EM Algorithm for the Fixed Component Case

THE LIKELIHOOD RATIO TEST FOR THE NUMBER OF COMPONENTS

The Problem

Some Analytical Solutions

Simulation and Bootstrap Solutions

C.A.MAN-APPLICATION: META-ANALYSIS

Conventional Approach

Heterogeneity

C.A.MAN Solution for Modeling Heterogeneity

Classification of Studies Using Posterior Bayes

MOMENT ESTIMATORS OF THE VARIANCE OF MIXING DISTRIBUTION

The DerSimonian-Laird Estimator

The Bohning-Sarol Estimator

Estimation of Binomia- or Poisson Rate Under Heterogeneity

C.A. MAN-APPLICATION: DISEASE MAPPING

Conventional Approach I: Mapping Percentiles

Conventional Approach II: Mapping P-Values

Estimating Map Heterogeneity

OTHER C.A. MAN APPLICATIONS

Fertility Studies

Modeling the Diagnostic Situation

Interval-Censored Survival Data

About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
MED028000
MEDICAL / Epidemiology
MED071000
MEDICAL / Pharmacology