Regression Methods for Medical Research E-Book

Bee Choo Tai

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 516

Veröffentlichungsjahr: 2013

Beschreibung

Regression Methods for Medical Research provides medical researchers with the skills they need to critically read and interpret research using more advanced statistical methods. The statistical requirements of interpreting and publishing in medical journals, together with rapid changes in science and technology, increasingly demands an understanding of more complex and sophisticated analytic procedures.

The text explains the application of statistical models to a wide variety of practical medical investigative studies and clinical trials. Regression methods are used to appropriately answer the key design questions posed and in so doing take due account of any effects of potentially influencing co-variables. It begins with a revision of basic statistical concepts, followed by a gentle introduction to the principles of statistical modelling. The various methods of modelling are covered in a non-technical manner so that the principles can be more easily applied in everyday practice. A chapter contrasting regression modelling with a regression tree approach is included. The emphasis is on the understanding and the application of concepts and methods. Data drawn from published studies are used to exemplify statistical concepts throughout.

Regression Methods for Medical Research is especially designed for clinicians, public health and environmental health professionals, para-medical research professionals, scientists, laboratory-based researchers and students.

Leseprobe

Contents

Preface

1 Introduction

INTRODUCTION

STATISTICAL MODELS

SOME COMPLETED STUDIES

Further reading

TECHNICAL DETAILS

2 Linear Regression: Practical Issues

TYPES OF COVARIATES (INDEPENDENT VARIABLES)

VERIFYING THE ASSUMPTIONS

PRECAUTIONS

STUDY DESIGN

CLINICAL AND STATISTICAL SIGNIFICANCE

REPORTING

TECHNICAL DETAILS

3 Multiple Linear Regression

LINEAR REGRESSION: TWO COVARIATES

HOW GOOD IS THE FITTED MODEL?

QUADRATIC MODELS

MULTIPLE LINEAR REGRESSION

PRECAUTIONS

PARSIMONIOUS MODELS

VERIFYING ASSUMPTIONS

TECHNICAL DETAILS

4 Logistic Regression

THE LOGIT TRANSFORMATION

CATEGORICAL AND CONTINUOUS COVARIATES

MULTIPLE LOGISTIC REGRESSION

MODEL CHECKING

CONDITIONAL LOGISTIC REGRESSION

ORDERED LOGISTIC REGRESSION

TECHNICAL DETAILS

5 Poisson Regression

INTRODUCTION

POISSON OR BINOMIAL MODELS

UNKNOWN POPULATION SIZE AT RISK

OVER-DISPERSION AND ROBUST ESTIMATES

KNOWN POPULATION SIZE AT RISK

KNOWN CUMULATIVE EXPOSURE

ZERO-INFLATED MODELS

RESIDUALS

TECHNICAL DETAILS

6 Time-to-Event Regression

TIME-TO-EVENT DATA

KAPLAN-MEIER SURVIVAL CURVE

THE HAZARD RATE AND HAZARD RATIO

THE COX REGRESSION MODEL

VERIFYING PROPORTIONAL HAZARDS

TECHNICAL DETAILS

7 Model Building

INTRODUCTION

TYPES OF COVARIATES

CASE STUDY

SELECTION PROCEDURES

DERIVING A PROGNOSTIC INDEX

PRACTICAL CONSIDERATIONS

TECHNICAL DETAILS

8 Repeated Measures

LONGITUDINAL STUDIES

AUTO- OR SERIAL-CORRELATION

FIXED-EFFECTS MODELS

MIXED-EFFECTS MODELS

SUBJECT-SPECIFIC VERSUS POPULATION-AVERAGED MODELS

TECHNICAL DETAILS

9 Regression Trees

INTRODUCTION

ILLUSTRATIVE EXAMPLE

TREE BUILDING

TREE PRUNING

PRACTICAL CONSIDERATIONS

STATISTICAL SOFTWARE

10 Further Time-to-Event Models

COMPETING RISKS

PARAMETRIC MODELS

TIME-VARYING COVARIATES

TECHNICAL DETAILS

11 Further Topics

MODEL STRUCTURE

MULTI-LEVEL MODELS

FRACTIONAL POLYNOMIALS

Statistical Tables

References

Index

This edition first published 2014 © 2014 by Bee Choo Tai and David Machin. Published 2014 by John Wiley & Sons, Ltd

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Library of Congress Cataloging-in-Publication Data

Tai, Bee Choo, author.  Regression methods for medical research / Bee Choo Tai, David Machin.        p. ; cm.    Includes bibliographical references and index.

    ISBN 978-1-4443-3144-8 (pbk. : alk. paper) – ISBN 978-1-118-72198-8 – ISBN 978-1-118-72197-1 (Mobi) – ISBN 978-1-118-72196-4 – ISBN 978-1-118-72195-7I. Machin, David, 1939– author. II. Title.[DNLM: 1. Regression Analysis. 2. Biomedical Research. 3. Models, Statistical. WA 950]    R853.S7    610.72′4–dc23

2013018953

A catalogue record for this book is available from the British Library.

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Cover image: Stethoscope - iStock file #13368468 © LevKing. DNA - iStock file#1643638 © Andrey ProkhorovCover design by Meaden Creative

ToIsaac Xu-En Koh and Kheng-Chuan KohandLorna Christine Machin

Preface

In the course of planning a new clinical study, key questions that require answering have to be determined and once this is done the purpose of the study will be to answer the questions posed. Once posed, the next stage of the process is to design the study in detail and this will entail more formally stating the hypotheses of concern and considering how these may be tested. These considerations lead to establishing the statistical models underpinning the research process. Models, once established, will ultimately be fitted to the experimental data collated and the associated statistical techniques will help to establish whether or not the research questions have been answered with the desired reliability. Thus, the chosen statistical models encapsulate the design structure and form the basis for the subsequent analysis, reporting and interpretation. In general terms, such models are termed regression models, of which there are several major types, and the fitting of these to experimental data forms the basis of this text.

Our aim is not to describe regression methods in all their technical detail but more to illustrate the situations in which each is suitable and hence to guide medical researchers of all disciplines to use the methods appropriately. Fortunately, several user-friendly statistical computer packages are available to assist in the model fitting processes. We have used Stata statistical software in the majority of our calculations, and to illustrate the types of commands that may be needed, but this is only one example of packages that can be used for this purpose. Statistical software is continually evolving so that, for example, several and improving versions of Stata have appeared during the time span in which this book has been written. We strongly advise use of the most up-to-date software available and, as we mention within the text itself, one that has excellent graphical facilities. We caution that, although we use real data extensively, our analyses are selective and are for illustration only. They should not be used to draw conclusions from the studies concerned.

We would like to give a general thank you to colleagues and students of the Saw Swee Hock School of Public Health, National University of Singapore and National University Health System, and a specific one for the permission to use the data from the Singapore Cardiovascular Cohort Study 2. Thanks are also due to colleagues at the Skaraborg Institute, Skövde, Sweden. In addition, we would like to thank the following for allowing us to use their studies for illustration: Tin Aung, Singapore Eye Research Institute; Michael J Campbell, University of Sheffield, UK; Boon-Hock Chia, Chia Clinic, Singapore; Siow-Ann Chong, Institute of Mental Health, Singapore; Richard G Grundy, University of Nottingham, UK; James H-P Hui, National University Health System, Singapore; Ronald C-H Lee, National University of Singapore; Daniel P-K Ng, National University of Singapore; R Paul Symonds, University of Leicester, UK; Veronique Viardot-Foucault, KK Women’s and Children’s Hospital, Singapore; Joseph T-S Wee, National Cancer Centre, Singapore; Chinnaiya Anandakumar, Camden Medical Centre, Singapore; and Annapoorna Venkat, National University Health System, Singapore. Finally, we thank Haleh G Maralani for her help with some of the statistical programming.

George EP Box (1979): ‘All models are wrong, but some are useful.’

Bee Choo TaiDavid Machin

1  Introduction

SUMMARY

A very large number of clinical studies with human subjects have and are being ­conducted in a wide range of settings. The design and analysis of such studies demands the use of statistical models in this process. To describe such situations involves specifying the model, including defining population regression coefficients (the parameters), and then stipulating the way these are to be estimated from the data arising from the subjects (the sample) who have been recruited to the study. This chapter introduces the simple linear regression model to describe studies in which the measure made on the subjects can be assumed to be a continuous variable, the value of which is thought to depend either on a single binary or a continuous covariate measure.

  Associated statistical methods are also described defining the null hypothesis, estimating means and standard deviations, comparing groups by use of a z- or t-test, confidence intervals and p-values. We give examples of how a statistical computer package facilitates the relevant analyses and also provides support for suitable graphical display.

  Finally, examples from the medical and associated literature are used to illustrate the wide range of application of regression techniques: further details of some of these examples are included in later chapters.

INTRODUCTION

The aim of this book is to introduce those who are involved with medical studies whether laboratory, clinic, or population based, to the wide range of regression techniques which are pertinent to the design, analysis, and reporting of the studies concerned. Thus our intended readership is expected to range from health care professionals of all disciplines who are concerned with patient care, to those more involved with the non-clinical aspects such as medical support and research in the laboratory and beyond.

Even in the simplest of medical studies in which, for example, recording of a single ­feature from a series of samples taken from individual patients is made, one may ask questions as to why the resulting values differ from each other. It may be that they differ between the genders and/or between the different ages of the patients concerned, or because of the severity of their illnesses. In more formal terms we examine whether or not the value of the observed variable, y, depends on one or more of the (covariate) variables, often termed the x’s. Although the term covariate is used here in a generic sense, we will emphasize that individually they may play different roles in the design and hence analysis of the study of which they are a part. If one or more covariates does influence the outcome, then we are essentially claiming that part of the variation in y is a result of individual patients having different values of the x’s concerned. In which case, any variation remaining after taking into consideration these covariates is termed the residual or random variation. If the covariates do not have influence, then we have not explained (strictly not explained an important part of) the variation in y by the x’s. Nevertheless, there may be other covariates of which we are not aware that would.

Measurements made on human subjects rarely give exactly the same results from one occasion to the next. Even in adults, height varies a little during the course of the day. If one measures the cholesterol levels of an individual on one particular day and then again the following day, under exactly the same conditions, greater variation in this than that of height would be expected. Any variation that we cannot ascribe to one or more covariates is usually termed random variation, although, as we have indicated, it may be that an unknown covariate may account for some of this. The levels of inherent variability may be very high so that, perhaps in the circumstances where a subject has an illness, the oscillations in these measurements may disguise, at least in the early stages of treatment, the beneficial effect of treatment given to improve the condition.