Ramakrishna HK Medical Statistics For Beginners 123 Medical Statistics Ramakrishna HK Medical Statistics For Beginners Ramakrishna HK Subbaiah Institute of Medical Sciences Shivamogga Karnataka India ISBN 978-981-10-1922-7 ISBN 978-981-10-1923-4 (eBook) DOI 10.1007/978-981-10-1923-4 Library of Congress Control Number: 2016953631 © Springer Science+Business Media Singapore 2017 T his work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifi cally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfi lms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. T he use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specifi c statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. T he publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Science+Business Media Singapore Pte Ltd. T he registered company address is 152 Beach Road, #22-06/08 Gateway East, Singapore 189721, Singapore This book is dedicated To my parents Keshavamurthy and Bhagyalakshmi, who taught me elementary knowledge of how to handle numbers, To my wife Dr. Swarnalatha MC, who gave valuable suggestions, is a constant source of encouragement, and tolerated my odd working hours, To my children Manu and Ajay, who made my life worth living. Foreword I feel privileged to write this foreword to the book on Medical Statistics for Beginners by Dr. H. K. Ramakrishna. H is introduction to the book, sharing his personal experience and journey as an author, is a “must read.” Today, the world is really fl at—one’s effort is the only lim- iting factor. Dr. Ramakrishna has shown what can be done with focused effort. Where you come from and what your offi cial designation is are completely irrele- vant, as far as accomplishments are concerned. Dr Ramakrishna deserves high praise for this work and he should be taken as a “role model” by all surgeons. Statistics is considered a “dry” subject. But it is essential for us to understand at least the basics of statistics to function well as surgeons. This book meets this requirement. The language is simple. The approach is direct and practical. All the principles are explained in a succinct manner. One can see from the screenshots that everything is worked out using basic com- puter tools that are universally available. Several free resources available on the Internet are introduced. With this, every one of us can do the things that are shown in the book. The links to statistical calculators that he has himself developed are a great “value add.” The chapters on “Designing a Study Clinical Trial or Dissertation,” “Evidence- Based Medicine” (EBM), and “Writing an Article for Journals” are very apt. After all, the purpose of statistics is to help us evolve into “scientifi c surgeons.” Every one of us must endeavor to practice EBM and share our vast experience and add to the scientifi c knowledge by formally publishing our work. Finally, I do hope that this book inspires all of us in this country to diligently document our work and publish more often. We fall woefully short of other coun- tries—even small South-East Asian countries—in the fi eld of scientifi c publication! We cannot afford to let the status quo continue. I wish this book every success. It is a landmark effort in the fi eld of surgical publication. Bangalore, India K Lakshman , MS, FRCS vii Opin ion “ Author’s style of writing is easy to read and understand. He gives meaningful examples to explain each new idea and also explains the methodology which at times is quite complex and painstaking. Suggestion to use the computer liberally encourages the reader to learn easy ways of making the complex calculations. The overview of the Biostatistics is nicely covered. I believe that this short book may be a nice book for the medical students and postgraduates to get to know the various statistical terms and methods for them to use in their academic career.” Dr. R. D. Prabhu FRCS ix Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 My Journey from a Rural Surgeon to an Author. . . . . . . . . . . . . . . . . . . . 3 3 Understanding Biostatistics, Probability, and Tests of Significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Skewed Distribution Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4 Understanding Basic Statistical Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Measures of Central Tendency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Measures of Dispersion or Spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Variance and Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Confi dence Interval and Confi dence Level . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Errors Type 1 and Type 2 (Alpha and Beta, Respectively) . . . . . . . . . . . . . . 31 Factors Increasing Type II Error (False Negativity) . . . . . . . . . . . . . . . . . 32 Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Normal or Gaussian Distribution and Skewed Distribution . . . . . . . . . . . 33 5 Tests of Significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Chi-Square Test or Simply Chi Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Fisher’s Exact Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Formula for Fisher’s Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 ! Is the Symbol for Factorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Student’s T Test or Gosset’s Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 One- and Two-Tailed Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Paired T Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Which Test to Use? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Mann–Whitney–Wilcoxon (MWW) Test . . . . . . . . . . . . . . . . . . . . . . . . . 54 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 6 Other Commonly Used Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 ANalysis Of Variance (ANOVA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Rank Test: Wilcoxon Signed-Rank Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 xi xii Contents Risk and Risk Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Odds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Odds Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Relative Risk Reduction (RRR), Absolute Risk Reduction (ARR), and Number Needed to Treat (NNT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Correlation: Relation Between Two Factors . . . . . . . . . . . . . . . . . . . . . . . . . 71 Positive Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Negative Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Correlation Coeffi cient ( r ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Other Types of Regressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Logistic Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Multiple Regression: To Predict an Outcome . . . . . . . . . . . . . . . . . . . . . . 76 The Poisson Regression (Distribution) . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Cox Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Survival Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Kaplan–Meier Estimator or Survival Graph . . . . . . . . . . . . . . . . . . . . . . . 79 Multivariate Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Power of a Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 7 Designing a Study/Clinical Trial/Dissertation, Etc. . . . . . . . . . . . . . . . . . 85 General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Concerns While Designing a Trial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Negative Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Teamwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Phases of Trials: Applies to New Drugs . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Some Commonly Used Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Parallel Studies and Crossover Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Planning and Pilot Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Sample Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Pilot Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Collection and Compilation of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Types of Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Sampling Errors and Nonsampling Errors . . . . . . . . . . . . . . . . . . . . . . . 102 Data Analysis and Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Presentation of Data and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Bar Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Pie Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Line Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Contents xiii Area Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Doughnut Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Difference Between Histogram and Bar Chart . . . . . . . . . . . . . . . . . . . . 120 Clinical Audit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Clinical Audit Versus Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Clinical Audit Is an Ongoing Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Problems with Audit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 8 Writing an Article for Journals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Clear Message . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Type of the Articles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Quality Indicators of a Journal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Indexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Impact Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Uniform Requirement for Manuscript Submission . . . . . . . . . . . . . . . . . 133 What Happens After Submission? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Common Reasons for Rejection of Article or Article Sent Back for Changes (Problems in the Article) . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Best Chance of Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Plagiarism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 Peer Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Copyright . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Scholarly Databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Limitations and Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Open-Access Journals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 Publish or Perish? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 9 Evidence-Based Medicine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 What Is EBM? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Why Do We Need EBM? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 How? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 The Five-Step Approach to EBM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Benefi ts of EBM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Limitations of EBM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 10 Model Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Postoperative Management Protocol to Be Followed . . . . . . . . . . . . . . . . . 168 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179