INTRODUCTORY BIOSTATISTICS INTRODUCTORY BIOSTATISTICS CHAP T. LE Distinguished Professor of Biostatistics and Director of Biostatistics Comprehensive Cancer Center University of Minnesota A JOHN WILEY & SONS PUBLICATION Copyright62003byJohnWiley&Sons,Inc.Allrightsreserved. PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey. PublishedsimultaneouslyinCanada. 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LibraryofCongressCataloging-in-PublicationDataIsAvailable ISBN0-471-41816-1 PrintedintheUnitedStatesofAmerica 10 9 8 7 6 5 4 3 2 1 To my wife, Minhha, and my daughters, Mina and Jenna with love CONTENTS Preface xiii 1 Descriptive Methods for CategoricalData 1 1.1 Proportions, 1 1.1.1 Comparative Studies, 2 1.1.2 Screening Tests, 5 1.1.3 Displaying Proportions, 8 1.2 Rates, 11 1.2.1 Changes, 11 1.2.2 Measures of Morbidity and Mortality, 13 1.2.3 Standardization of Rates, 16 1.3 Ratios, 18 1.3.1 Relative Risk, 19 1.3.2 Odds and OddsRatio, 19 1.3.3 Generalized Odds forOrdered 2(cid:1)k Tables, 22 1.3.4 Mantel–Haenszel Method, 26 1.3.5 Standardized MortalityRatio, 30 1.4 Notes onComputations, 31 Exercises, 34 2 Descriptive Methods for Continuous Data 57 2.1 TabularandGraphical Methods, 57 2.1.1 One-Way Scatter Plots, 57 2.1.2 Frequency Distribution, 58 vii viii CONTENTS 2.1.3 Histogramand the Frequency Polygon, 62 2.1.4 Cumulative FrequencyGraphand Percentiles, 67 2.1.5 Stem-and-LeafDiagrams, 70 2.2 NumericalMethods, 72 2.2.1 Mean, 73 2.2.2 Other Measures of Location, 76 2.2.3 Measures of Dispersion, 77 2.2.4 Box Plots, 80 2.3 SpecialCase of Binary Data, 81 2.4 Coe‰cients of Correlation, 83 2.4.1 Pearson’s CorrelationCoe‰cient, 85 2.4.2 Nonparametric Correlation Coe‰cients, 88 2.5 Notes onComputations, 90 Exercises, 92 3 Probability andProbability Models 108 3.1 Probability, 108 3.1.1 Certainty of Uncertainty, 109 3.1.2 Probability, 109 3.1.3 Statistical Relationship, 111 3.1.4 Using Screening Tests, 115 3.1.5 Measuring Agreement, 118 3.2 Normal Distribution, 120 3.2.1 Shape of the Normal Curve, 120 3.2.2 Areas under the Standard Normal Curve, 123 3.2.3 Normal Distribution as a Probability Model, 128 3.3 Probability Models for Continuous Data, 131 3.4 Probability Models for DiscreteData, 132 3.4.1 Binomial Distribution, 133 3.4.2 Poisson Distribution, 136 3.5 Brief Notes onthe Fundamentals, 137 3.5.1 Mean and Variance, 137 3.5.2 Pair-Matched Case–Control Study, 138 3.6 Notes onComputations, 140 Exercises, 141 4 Estimation of Parameters 147 4.1 BasicConcepts, 148 4.1.1 Statistics as Variables, 149 4.1.2 Sampling Distributions, 149 4.1.3 Introduction to Confidence Estimation, 152 4.2 Estimation of Means, 152 4.2.1 Confidence Intervals for aMean, 154 4.2.2 Usesof Small Samples, 156 CONTENTS ix 4.2.3 Evaluationof Interventions, 158 4.3 Estimation of Proportions, 160 4.4 Estimation of Odds Ratios, 165 4.5 Estimation of CorrelationCoe‰cients, 168 4.6 Brief Notes on the Fundamentals, 171 4.7 Notes onComputations, 173 Exercises, 173 5 Introduction toStatistical Testsof Significance 188 5.1 Basic Concepts, 190 5.1.1 Hypothesis Tests, 190 5.1.2 Statistical Evidence, 191 5.1.3 Errors, 192 5.2 Analogies, 194 5.2.1 Trialsby Jury, 194 5.2.2 Medical Screening Tests, 195 5.2.3 Common Expectations, 195 5.3 Summaries and Conclusions, 196 5.3.1 Rejection Region, 197 5.3.2 p Values, 198 5.3.3 Relationshipto Confidence Intervals, 201 5.4 Brief Notes on the Fundamentals, 203 5.4.1 Type I and Type IIErrors, 203 5.4.2 More about Errors and p Values, 203 Exercises, 204 6 Comparisonof PopulationProportions 208 6.1 One-Sample Problem with Binary Data, 208 6.2 Analysisof Pair-MatchedData, 210 6.3 Comparisonof Two Proportions, 213 6.4 Mantel–Haenszel Method, 218 6.5 InferencesforGeneral Two-WayTables, 223 6.6 Fisher’s Exact Test, 229 6.7 Ordered 2(cid:1)k Contingency Tables, 230 6.8 Notes onComputations, 234 Exercises, 234 7 Comparisonof PopulationMeans 246 7.1 One-Sample Problem with Continuous Data, 246 7.2 Analysisof Pair-MatchedData, 248 7.3 Comparisonof Two Means, 253 7.4 Nonparametric Methods, 257 7.4.1 Wilcoxon Rank-Sum Test, 257 7.4.2 Wilcoxon Signed-Rank Test, 261