Converting Data into Evidence

Transcription

1 Converting Data into Evidence

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3 Alfred DeMaris Steven H. Selman Converting Data into Evidence A Statistics Primer for the Medical Practitioner

4 Alfred DeMaris Bowling Green State University Bowling Green, OH, USA Steven H. Selman Department of Urology University of Toledo Toledo, OH, USA ISBN ISBN (ebook) DOI / Springer New York Heidelberg Dordrecht London Library of Congress Control Number: Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (

5 To Gabrielle and Linda

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7 Preface Let us go then, you and I, When the evening is spread out against the sky Like a patient etherized upon a table ; T. S. Elliott Since the term was coined some 22 years ago (Guyatt 1991; Moayyedi 2008), evidence-based medicine, or EBM, has taken center stage in the practice of medicine. Adherence to EBM requires medical practitioners to keep abreast of the results of medical research as reported in the general and specialty journals. At the heart of this research is the science of statistics. It is through statistical techniques that researchers are able to discern the patterns in the data that tell a clinical story worth reporting. Like the astronomer s telescope, statistics uncovers a universe that is invisible to the naked eye. But if you are one of those souls for whom the statistical machinations in the medical literature may as well be cuneiform script, this primer is for you. In it, we invite the reader on a stroll through the landscape of statistical science. We will, moreover, view that landscape while it is, in Elliott s words, etherized upon a table anesthetized, inert, harmless. This primer is intended for anyone who wishes to have a better grasp of the meaning of statistical techniques as they are used in medical research. This includes physicians, nurses, nurse practitioners, physician s assistants, medical students, residents, or even laypersons who enjoy reading research reports in medicine. The book can also be useful for the physician engaged in medical research who is not also a statistician. With the aid of this primer, that researcher will find it easier to communicate with the statisticians on his or her research team. Our intention is to provide a background in statistics that allows readers to understand the application of statistics in journal articles and other research reports in the medical field. It is not our intention to teach individuals how to perform statistical analyses of data or to be statisticians. We leave that enterprise for the many more voluminous works in medical statistics that are out there. Rather the goal in this work is to provide a readerfriendly introduction to the logic and the tools that underlie statistical science. vii

8 viii Preface In pursuit of this goal we have cut to the chase to a considerable degree. We felt that it was important to limit attention to the aspects of statistics that the reader was most likely to encounter on a routine basis. And we believed that it was better to devote more space to a few important topics rather than try to inundate the reader with too many different techniques. Thus, we have omitted extensive coverage of, say, the different ways of graphically displaying data. Other than examples of graphs taken from the medical literature, there is no coverage of histograms, stem-leaf plots, box plots, dot plots, or other such techniques. Similarly, we focus on only the most basic summary measures of variable distributions and omit coverage of, say, the trimmed mean, the harmonic mean, the geometric mean, standard scores, etc. Instead, we have dedicated more space to the subjects that we deem most critical to an understanding of statistics as the discipline is practiced today: causality and causal inference, internal and external validity of statistical results, the sampling distribution of a statistic, the p value, common bivariate statistical procedures, multivariable modeling and the meaning of statistical control, and measures of the predictive efficacy of statistical models, to cite a few examples. Along with this approach, we have avoided the extensive presentation of statistical formulas and sophisticated mathematics. Anyone with even a passing grasp of high-school algebra should have no trouble reading this primer. A few test-statistic formulas are shown to communicate the rationale underlying test statistics. Other than that, however, we simply name the tests that are used in different situations. Some algebraic formulas, however, are unavoidable. It is simply not possible to understand regression modeling in its different incarnations without showing regression equations. Similarly, growth-curve modeling and fixed-effects regression modeling are not understandable without their respective equations. Nevertheless, we have tried to explain, in the narrative, what these equations are conveying in an intuitive sense. And narrative is the operative word. This is not a traditional textbook; there are no exercises and no tables in the back. To the extent that such could be said about a statistics book, our intention was to make it a good read. A feature of the book that we think is especially useful is our extensive presentation of statistical applications from the recent medical literature. Over 30 different articles are explicated herein, taken from such journals as Journal of the American Medical Association, Journal of Urology, British Journal of Urology International, American Journal of Epidemiology, Journal of Internal Medicine, Alcohol and Alcoholism, and BMC Neurology. We deemed it important for readers to see how the various techniques covered in the primer are employed, displayed, and discussed in actual research. In the process we have attempted to translate into English some of the more recondite terminology used in the literature. Hopefully, this enterprise will facilitate the reader s understanding of statistical applications when he or she encounters them in the journals. In the process of writing this primer, many people have been helpful to us. We wish, first, to acknowledge the kind guidance and cheerful flexibility of Marc Strauss, our editor at Springer. We also wish to thank Bowling Green State University, in particular the Center for Family and Demographic Research, as well as the University of Toledo Medical Center, for providing the computer and library

9 Preface ix support that made this work possible. Also deserving of thanks are Annette Mahoney and Kenneth I. Pargament in the Psychology Department at Bowling Green State University for collecting the NAPPS data that are drawn on extensively in Chap. 9. And last, but certainly not least, we wish to gratefully acknowledge our wives, Gabrielle and Linda, for the loving support and encouragement they provided during the writing of this work. And now, let us begin Bowling Green, OH, USA Toledo, OH, USA Alfred DeMaris Steven H. Selman

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11 Contents 1 Statistics and Causality... 1 What Is Statistics?... 1 What Statistics Is... 1 An Example... 2 Populations and Samples... 4 Probability vs. Nonprobability Samples... 4 Sampling to a Population... 4 Statistics and Causal Inference... 5 A Mathematical Definition of Causal Effect... 5 How Do We Estimate the ACE?... 6 Example of Latent Self-Selection... 6 Internal vs. External Validity: A Conundrum Summarizing Data... 9 Descriptive Statistical Techniques... 9 Quantitative vs. Qualitative Data... 9 Describing Data Measuring Center and Spread of a Variable s Distribution The Mean Percentiles and the Median Dispersion Data from the General Social Survey Describing the Population Distribution The Normal and t Distributions Applications: Descriptive Statistics in Action Tarenflurbil Study Hydroxychloroquine Study RALP Study Brachytherapy Study xi

12 xii Contents 3 Testing a Hypothesis The Test of Hypothesis Let s Roll the Dice Testing Whether Al s Die Is Loaded Statement of Hypotheses Testing the Null Hypothesis Making a Decision Statistically Significant Results What About Your Sequence of Die Rolls? Large-Sample Test of Hypothesis About a Mean Assumptions for the Test Statement of Hypotheses Before Going Further: The Sampling Distribution of a Sample Statistic Simple Example of a Sampling Distribution A More Elaborate Example Sampling Distribution of the Mean for the Large-Sample Test of Hypothesis The Central Limit Theorem Test Statistic and P-Value Summary Additional Inferential Procedures Confidence Intervals and the T Test Confidence Intervals Testing the Difference Between Two Means: The T Test Statement of Hypotheses Sample Information and the Sampling Distribution Assumptions for the T Test Computation of the Test Statistic Finding the P Value One-Tailed vs. Two-Tailed Tests Summary: Hypothesis Testing Decision Errors and the Power of the Test Power of the T Test in the Diet Example T Tests for the GSS Data Comments About Statistical Tests P Values, Revisited Sampling from The Population Application: T Tests and Statistical Power in Action Gender Difference in Physician Salaries Power Considerations in Hydroxychloroquine Study Power in the Arterial Inflammation Study Bivariate Statistical Techniques A Nonparametric Test for the Steak-Diet Example Computing the WRST... 58

13 Contents xiii Bivariate Statistics Bivariate Analysis: Other Scenarios Qualitative Treatment with More Than Two Levels: ANOVA Qualitative Treatment and Qualitative Response: χ Calculating the χ 2 Value Minimum and Maximum Values of χ Measuring the Strength of Association Quantitative Treatment and Response: The Correlation Coefficient Testing the Significance of R The Paired t Test: How Correlation Affects the Standard Error Summary of Bivariate Statistics Application: Bivariate Statistics in Action ANOVA: GGT and Alcohol Consumption χ 2 : Second-to-Fourth Digit Ratio Study Paired t Test: Bariatric Surgery and Urinary Function Study Correlation Coefficient: Obesity and Tumor Volume in Prostate Cancer Linear Regression Models Modeling the Study Endpoint Using Regression What Is a Statistical Model? A Regression Model for Exam Scores Other Important Features of Regression Multiple Linear Regression Statistical Control in MULR An Intuitive Sense of Control Statistical Control: Technical Details An Example Using the GSS ANCOVA: A Particular Type of Regression Model Modeling Statistical Interaction The Interaction Model Repeated Measures ANOVA: Interaction in the Foreground A Study of Depressive Symptomatology Analyzing the Data Time, Treatment, and Treatment Time Effects Applications: Regression and Repeated Measures ANOVA in Action Gender Difference in Physician Salaries, Revisited Obesity and Tumor Volume, Revisited Discrimination and Waist Circumference Reducing Alcohol Dependence: An Example of ANCOVA Interaction 1: Evaluating the Six-Minute Walk in MS Interaction 2: Randomized Trial of Methods of Nephrostomy Tract Closure

14 xiv Contents Interaction 3: The Effect of Testosterone Treatment on Aging Symptoms in Men Interaction 4: Spousal Support and Women s Interstitial Cystitis Syndrome Logistic Regression Logistic Regression Model Estimation of Logistic Regression Coefficients An Example Interpreting the Coefficients Predicted Probabilities Test Statistics and Confidence Intervals Examining Model Performance Applications: Logistic Regression in Action Morbidity Following Kidney Surgery Caffeine, Smoking, and Parkinson Disease PSA as a Predictor of Prostate Cancer Vitamin D Deficiency and Frailty Heat Sensitivity in MS Patients Survival Analysis Why Special Methods Are Required Elemental Terms and Concepts An Example Estimating the Survival Function Comparing Survival Functions Across Groups Regression Models for Survival Data Cox s Proportional Hazards Model Modeling the Hazard of Death Due to AIDS Predictive Efficacy of the Cox Model Applications: Survival Analysis in Action Predicting 90-Day Survival After Radical Cystectomy Predicting Biochemical Recurrence After Radical Prostatectomy Survival Following Radical Cystectomy PSA Doubling Time and Metastasis After Radical Prostatectomy Race Differences in the Risk of Prostate Cancer Other Advanced Techniques Multiple Imputation Poisson and Negative-Binomial Regression An Illustrative Example: Pregnancy Stress in the NAPPS Study Propensity Score Analysis An Example: Unintended Pregnancy and Mothers Depression Using Propensity Scores Growth-Curve Modeling

15 Contents xv Estimating the GCA Model An Example: The Trajectory in Mother s Depression Over Time Fixed-Effects Regression Models An Example: Marital Conflict and Mothers Depression Applications Poisson Regression Propensity-Score Analysis and Multiple Imputation Growth-Curve Analysis I Growth-Curve Analysis II Fixed-Effects Regression Conclusion: Looking Back, Looking Forward Looking Back Looking Forward Glossary of Statistical Terms References About the Authors Index