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Published on September 13, 2017

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2. Principles and Practice of Biostatistics Belavendra Antonisamy PhD, FRSS, FSMS Professor and Head, Department of Biostatistics Christian Medical College Vellore, Tamilnadu Prasanna S. Premkumar PhD Lecturer, Wellcome Trust Research Laboratory & Department of Biostatistics Christian Medical College Vellore, Tamilnadu Solomon Christopher MSc Former Lecturer, Department of Biostatistics Christian Medical College Vellore, Tamilnadu

3. Principles and Practice of Biostatistics, 1e, Antonisamy, Premkumar and Christopher Copyright © 2017, by RELX India Pvt. Ltd. All rights reserved. ISBN: 978-81-312-4887-4 e-Book ISBN: 978-81-312-4942-0 RELX India Pvt. Ltd. Registered Ofﬁce: 818, 8th Floor, Indraprakash Building, 21, Barakhamba Road, New Delhi 110001 Corporate Ofﬁce: 14th Floor, Building No. 10B, DLF Cyber City, Phase II, Gurgaon-122002, Haryana, India No part of this publication may be reproduced or transmitted in any form or by any means, elec- tronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, fur- ther information about the Publisher’s permissions policies and our arrangements with organiza- tions such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notice Knowledge and best practice in this ﬁeld are constantly changing. As new research and experi- ence broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. With respect to any drug or pharmaceutical products identiﬁed, readers are advised to check the most current information provided (i) on procedures featured or (ii) by the manufacturer of each product to be administered, to verify the recommended dose or formula, the method and duration of administration, and contraindications. It is the responsibility of practitioners, relying on their own experience and knowledge of their patients, to make diagnoses, to determine dosages and the best treatment for each individual patient, and to take all appropriate safety precautions. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of product liability, negligence or otherwise, or from any use or operation of any methods, products, in- structions, or ideas contained in the material herein. Although all advertising material is expected to conform to ethical (medical) standards, inclu- sion in this publication does not constitute a guarantee or endorsement of the quality or value of such product or of the claims made of it by its manufacturer. Please consult full prescribing information before issuing prescription for any product mentioned in this publication. Manager - Content Strategy: Renu Rawat Content Strategist (Digital): Nabajyoti Kar Manager – Education Solutions (Digital): Smruti Snigdha Sr Project Manager—Education Solutions: Shabina Nasim Content Development Specialist: Shravan Kumar Project Manager: Devendran Kannan Cover Designer: Milind Majgaonkar Typeset by GW India Printed in India by ………

4. v Foreword Biostatistics is of vital importance in solving problems in Medicine and Public Health. Understanding the principles and practice of biostatistics, however, a daunting task to health professionals because of the complex theoretical and analytical skills required. This book has simplified the principles and practice of biostatistics into a form acceptable and understandable by all the levels of health care profession- als from students to senior faculty. It presents the fundamental paradigms un- derlying statistical methodology, the core applied statistical concepts and methods for the analysis, interpretation and presentation of data, which is no mean task. Public Health, Medical and Life Sciences students and faculty could use this book to conduct and evaluate research and clinical studies. The authors start every chapter by listing the learning objectives clearly. They describe concepts and methods, and include several illustrative examples of data types, analytic methods and interpretation. The graphics relate to practi- cal interesting data and are clear and very helpful. Each chapter ends with re- view questions and exercises to evaluate understanding and knowledge of the material. The collection, summarization, and analysis of data and the interpreta- tion of and the inference from the results have been presented in a lucid and attractive format. It is hoped that this book will provide a valuable resource for students and the wider community. We are fortunate that Professor Belavendra Antonisamy, Mr Solomon Christopher and Dr Prasanna Samuel have responded to the challenge of pre- paring this introduction to statistical procedures. Anna Benjamin Pulimood Principal, Christian Medical College Vellore, India

5. Preface As the entire medical research is evolving towards evidence-based medical practice, medical literature is flooded with application of statistical methods. In medical sciences, anyone who wishes to understand biomedical literature should be able to comprehend and appreciate the use and interpretation of the statistical methods involved. This book aims to provide an understanding of the basic principles and practice of biostatistics. We have attempted to give a com- prehensive insight into the basic aspects of biostatistics that is sound, easy to read, relevant and of useful practical applications. Most often, the subject of statistics is approached with a negative attitude that it is highly abstract and difficult to learn. Our major philosophical objec- tive is to motivate students and readers to develop a positive attitude towards learning statistics. We aimed to raise this positive attitude by means of using mathematical background, formulas and symbols at very minimal level and by introducing the concepts through simple worked out examples. We also felt that there is a gap between academic, educational and research institutions. Our another major objective is to bridge this gap by providing a cohesive and compact text that can serve as a linking guide to rather theoretical students with mathematical or statistical background and introduce them to the realm of applied statistics and statistical consultation. To this end, we have made an attempt, wherever necessary, to demonstrate the concepts, assumptions and interpretation of statistical techniques through graphical methods. Though this book is meant to be an introductory text for biostatistics, it heavily emphasizes its practice in every research aspect. However, there is no compromise in infusing the basic concepts and subject matter through practical examples, making the subject more intuitive than mere theory. Apart from the conventional statistical methods found in other books, this book includes the design of clinical trials and epidemiological studies, collection of data, research methods, clinical measurements, meta-analysis and sample size calculations for various study designs in a more refined manner. This makes it a handbook of biostatistics for students and researchers from the field of medicine, public health, nursing, paramedical sciences, biological and social sciences or in short anyone who encounters the use of biostatistics in his/her respective field. This text can also be used by PhD students who are preparing for their research methodology examination in all the above said fields as it gives a rather com- plete overview on principles of research in theoretical and practical realms. And most importantly, our text does not assume the reader to have any prerequisite

6. viii Preface in research methodology or statistical methods. This book is designed as a teaching and a reference book for the students and practitioners. Each chapter begins with Learning Objectives and ends with summary Key Points and Review Questions for pedagogical reasons. Every topic describing a statistical method is accompanied by an example illustrating its use. In addi- tion, there are two kinds of working exercises at the end of every chapter for the purpose of learning and practice: a limited number of Exercises and a set of ten Multiple Choice Questions (MCQs). Key to the “Exercises” questions is provided just after the “Exercises” and for MCQs at the end of the book, which aid in covering a large volume of material in a short time and also serves for a quick revision. These exercises are also useful from the perspective of univer- sity examination. The first chapter gives an overview of and rationale for statistical methods in biomedical and health sciences. Chapter 2–5 provide a basic introduction to biostatistics including the types of data, descriptive statistics, graphical repre- sentation of data, basic laws of probability, concepts in probability distributions and methods of sampling. Chapter 6 describes the concepts of estimation in- cluding the construction and interpretation of confidence intervals. Chapter 7 explains hypothesis testing and includes the definitions of null and alternative hypothesis, test statistic, critical values and P-values. Besides these, chapters 6 and 7 cover the procedures of estimation and significance testing for the two sample problems involving mean and proportion. Chapter 8 discusses the meth- ods that compare several group means, the inappropriate use of multiple t-test, assumptions involved, relationships between analysis of variance (anova) and multiple regression, analysis of covariance and repeated measures. Chapter 9 explains the analysis of categorical data, which include the Chi-square tests, Fisher’s exact test, McNemar’s paired Chi-square test and Chi-square test for trend. Chapter 10 describes the commonly used non-parametric analytic meth- ods and highlights the difference between parametric and non-parametric ap- proach. Chapter 11 begins with a general introduction to correlation, the esti- mation and interpretation of correlation coefficient. The regression methods, its assumptions and the estimation of parameters are also shown. Chapter 12 presents epidemiological study designs and analysis illustrating the measures of disease frequency, design of epidemiological studies, bias and causality. Chapter 13 covers the design, implementation and analyses of clini- cal trials and a discussion on ethics. Diagnostic tests and measures of diagnos- tic accuracy are included in Chapter 14. Survival analysis is introduced in Chapter 15, which include censoring, survival functions, survival curves and log-rank test. Chapter 16 focuses on clinical measurements, which include ac- curacy and precision, coefficient of variation, intra-class correlation, reference intervals and Bland Altman approach. Chapter 17 provides the sources, mea- sures and methods of demographic data.

7. ixPreface Chapter 18 covers the practical aspects of multiple linear regression, logistic regression, cox proportional regression analysis, and brief discussion on other multivariable methods. Research methods, the importance of data man- agement and the process of obtaining statistical consultations are discussed in Chapter 19. Chapter 20 explains the basics of sample size calculations, its importance and discusses some of the practical issues with it. We conclude this book with a special chapter 21 on meta-analysis providing a background on meta-analytic methods, difference between systematic reviews and meta- analysis, random and fixed effects, and software for meta-analysis. On the whole the chapters can be broadly divided into four broad sections: Basic Biostatistics (chapters 2–11 & 17), Epidemiology and Clinical Trials (chapters 12–14 & 21), Research Methods (chapters 16, 19 & 20), and Advanced Biostatistics (chapters 15 & 18). For a beginner, it is suggested that the chapters in biostatistics are to be read in the order of presentation as the chapters are written in a logical sequence keeping in mind the practical applica- tions, and each require a complete knowledge of the previous chapters. R and STATA software were extensively used for most of the graphics, simulation of hypothetical data, statistical analyses and generation of random number table. Microsoft Excel and PowerPoint were used for few of the graphics. The book has emerged from an equal contribution and collaborative effort of the authors. Almost every chapter has been revised with the frequent consultation between us. Many of the examples and datasets stemmed from our teaching, research and statistical consultation at the Christian Medical College. In addition, we are also giving complimentary access to enhanced e-book along with additional reading materials on www.MedEnact.com. We would like to express our gratitude in particular to Dr. Gagandeep Kang who has been very encouraging and supportive throughout this endeavour. Our heartfelt thanks to the following investigators: Dr. PSS Rao, Dr. P Raghupathy, Dr. George T. John, Dr. Jiji Elizabeth Mathews, Dr. Korula George, Dr. Molly Jacob, Dr. Minnie Faith, Dr. Sivalingam, Dr. KS Dharan, Dr. KS Dhanasekhar, Dr. Subankar Mitra, Dr. Denis Martin and Dr. Tarun Jacob for providing the data for examples. We thank Mr. Narasimhan for assistance in compiling the statistical tables. We would like to thank our Publisher Elsevier, and especially its team of experts, with whom we worked on this edition. We also acknowl- edge the immense support from our institution. We hope that this book will help students and researchers to develop interest and appreciation for the value of medical statistics. We welcome any constructive criticism or suggestions from the readers. Vellore, India BA 2017 PSP SC

8. xi Foreword v Preface vii 1. Role of Biostatistics in Health Sciences 1 2. Summarizing and Presentation of Data 7 3. Probability 24 4. Probability Distributions 36 5. Sampling Methods 59 6. Statistical Inference I – Estimation 71 7. Statistical Inference II – Testing of Hypotheses 86 8. Analysis of Variance and Multiple Comparisons 107 9. Hypothesis Testing – Categorical Data 119 10. Nonparametric Methods 135 11. Correlation and Regression 151 12. Epidemiological Study Designs and Analysis 167 13. Clinical Trials 193 14. Diagnostic Tests 213 15. Introduction to Survival Analysis 227 16. Clinical Measurements 243 17. Demographical Methods and Vital Statistics 260 18. Applied Regression Analysis and Multivariable Methods 273 19. Research Methods 297 20. Sample Size 313 21. Meta-Analysis in Systematic Reviews 333 Contents

9. xii Contents Appendix A Statistical Tables 346 Appendix B Answers to Multiple Choice Questions 367 Appendix C Bibliography 369 Index 373