Medical biostatistics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2008
|
| Edition: | 2. ed. |
| Series: | Chapman & Hall/CRC biostatistics series
25 |
| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xlvii, 771 p. ill. 25 cm |
| ISBN: | 9781584888871 1584888873 |
Staff View
MARC
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| 245 | 1 | 0 | |a Medical biostatistics |c A. Indrayan |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2008 | |
| 300 | |a xlvii, 771 p. |b ill. |c 25 cm | ||
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| 490 | 1 | |a Chapman & Hall/CRC biostatistics series |v 25 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Medical statistics | |
| 650 | 4 | |a Biometry | |
| 650 | 4 | |a Biometry |x methods | |
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Record in the Search Index
| _version_ | 1804137661777051648 |
|---|---|
| adam_text | Contents
Preface to Second Edition xxix
Summary Tables xxxi
Frequently Used Notations xxxix
Abbreviations xliii
1 Medical Uncertainties 1
1.1 Uncertainties in Health and Disease 2
1.1.1 Uncertainties due to Intrinsic Variation 3
1.1.1.1 Biologic Variability 3
1.1.1.2 Genetic Variability 3
1.1.1.3 Variation in Behavior and Other Host Factors 4
1.1.1.4 Environmental Variability 4
1.1.1.5 Chance Variability 4
1.1.1.6 Sampling Fluctuation 5
1.1.2 Natural Variation in Assessment 5
1.1.2.1 Observer Variability 5
1.1.2.2 Variability in Treatment Strategies 6
1.1.2.3 Instrument and Laboratory Variability 6
1.1.2.4 Imperfect Tools 7
1.1.2.5 Incomplete Information on the Patient 7
1.1.2.6 Poor Compliance with the Regimen 7
1.1.3 Inadequate Knowledge 8
1.1.3.1 Epistemic Uncertainties 8
1.1.3.2 Diagnostic, Therapeutic, and Prognostic
Uncertainties 8
1.1.3.3 Predictive and Other Uncertainties 9
1.2 Uncertainties in Medical Research 9
1.2.1 Empiricism in Medical Research 10
1.2.1.1 Laboratory Experiments 10
1.2.1.2 Clinical Trials 10
1.2.1.3 Surgical Procedures 10
1.2.1.4 Epidemiological Research 11
1.2.2 Elements of Minimizing the Impact of Uncertainties
on Research 11
1.2.2.1 Proper Design 12
vii
viii Contents
1.2.2.2 Improved Medical Methods 12
1.2.2.3 Analysis and Synthesis 13
1.2.3 Critique of a Report of a Medical Study 13
1.2.3.1 Introduction 14
1.2.3.2 Methodology 14
1.2.3.3 Results 15
1.2.3.4 Discussion and Conclusions 16
1.3 Uncertainties in Health Planning and Evaluation 16
1.3.1 Health Situation Analysis 17
1.3.1.1 Identification of the Specifics of the Problem 17
1.3.1.2 Size of the Target Population 18
1.3.1.3 Magnitude of the Problem 19
1.3.1.4 Health Infrastructure 20
1.3.1.5 Feasibility of Remedial Steps 21
1.3.2 Evaluation of Health Programs 21
1.4 Management of Uncertainties: About This Book 22
1.4.1 Contents of the Book 23
1.4.2 Salient Features of the Text 25
1.4.2.1 System of Notations 26
1.4.2.2 Guide Chart of the Biostatistical Methods 27
References 27
2 Basics of Medical Studies 29
2.1 Study Protocol 30
2.1.1 The Problem, Objectives, and Hypotheses 30
2.1.1.1 The Problem 30
2.1.1.2 Objectives 31
2.1.1.3 Hypotheses 31
2.1.2 Protocol Content 32
2.2 Types of Medical Studies 35
2.2.1 Elements of Design 36
2.2.1.1 Broad Objective of the Study 37
2.2.2 Basic Types of Study Design 38
2.2.2.1 Descriptive Studies 38
2.2.2.2 Analytical Studies 40
2.2.2.3 Basic Types of Analytical Studies 40
2.2.3 Choosing a Design 41
2.2.3.1 Recommended Design for Particular Setups 41
2.2.3.2 Choice of Design by Level of Evidence 42
2.3 Data Collection 44
2.3.1 Nature of Data 44
2.3.1.1 Factual, Knowledge-Based, and Opinion-Based Data... 44
2.3.1.2 Method of Obtaining the Data 45
2.3.2 Tools of Data Collection 46
2.3.2.1 Existing Records 46
2.3.2.2 Questionnaires and Schedules 47
Contents ix
2.3.3 Pretesting and Pilot Study 49
2.4 Nonsampling Errors and Other Biases 49
2.4.1 Nonresponse 50
2.4.2 Variety of Biases to Guard Against 50
2.4.2.1 List of Biases 50
2.4.2.2 Steps for Minimizing Bias 56
References 58
3 Sampling Methods 59
3.1 Sampling Concepts 59
3.1.1 Advantages and Limitations of Sampling 60
3.1.1.1 Sampling Fluctuations 60
3.1.1.2 Advantages of Sampling 61
3.1.1.3 Limitations of Sampling 61
3.1.2 Some Special Terms Used in Sampling 61
3.1.2.1 Unit 61
3.1.2.2 Sampling Frame 62
3.1.2.3 Parameters and Statistics 62
3.1.2.4 Sample Size 62
3.1.2.5 Nonrandom and Random Sampling 63
3.2 Common Methods of Random Sampling 63
3.2.1 Simple Random Sampling 63
3.2.2 Stratified Random Sampling 64
3.2.3 Multistage Random Sampling 67
3.2.4 Cluster Random Sampling 68
3.2.5 Systematic Random Sampling 70
3.2.6 Choice of Method of Random Sampling 72
3.3 Some Other Methods of Sampling 72
3.3.1 Other Random Methods of Sampling 73
3.3.1.1 Probability Proportional to Size Sampling 73
3.3.1.2 Area Sampling 74
3.3.1.3 Inverse Sampling 74
3.3.1.4 Consecutive Subjects Attending a Clinic 74
3.3.1.5 Sequential Sampling 75
3.3.2 Nonrandom Methods of Sampling 75
3.3.2.1 Convenience Samples 75
3.3.2.2 Other Types of Purposive Samples 76
3.4 Some Examples of Sample Surveys 77
3.4.1 National Health and Nutrition Examination Survey
in the United States 77
3.4.1.1 Sample Design 77
3.4.1.2 Logistics and Other Details 78
3.4.2 A Small-Scale Survey of an Elderly Population in Australia 78
3.4.2.1 Sample Design 79
3.4.2.2 Logistics and Other Details 79
References 80
x Contents
4 Designs for Observational Studies 81
4.1 Prospective Studies 84
4.1.1 Variations of Prospective Studies 84
4.1.1.1 Cohort Study 84
4.1.1.2 Longitudinal Study 86
4.1.2 Comparison Group in a Prospective Study 86
4.1.3 Selection of Subjects for a Prospective Study 87
4.1.4 Potential Biases in Prospective Studies 88
4.1.4.1 Selection Bias 88
4.1.4.2 Bias due to Loss in Follow-Up 88
4.1.4.3 Assessment Bias and Errors 89
4.1.4.4 Bias due to Change in the Status 89
4.1.4.5 Confounding Bias 89
4.1.4.6 Post Hoc Bias 90
4.1.4.7 Validity Bias 90
4.1.5 Merits and Demerits of Prospective Studies 90
4.1.5.1 Merits of Prospective Studies 90
4.1.5.2 Demerits of Prospective Studies 91
4.2 Retrospective Studies 91
4.2.1 Case-Control Design 92
4.2.1.1 Nested Case-Control Design 93
4.2.2 Selection of Cases and Controls 94
4.2.2.1 Sampling Methods in Retrospective Studies 94
4.2.2.2 Confounders and Matching 95
4.2.3 Merits and Demerits of Case-Control Studies 96
4.2.3.1 Merits of Case-Control Studies 96
4.2.3.2 Demerits of Case-Control Studies 96
4.3 Cross-Sectional Studies 97
4.3.1 Selection of Subjects for a Cross-Sectional Study 98
4.3.2 Merits and Demerits of Cross-Sectional Studies 98
4.3.2.1 Demerits of Cross-Sectional Studies 98
4.3.2.2 Merits of Cross-Sectional Studies 99
4.4 Comparative Performance of Prospective, Retrospective,
and Cross-Sectional Studies 100
4.4.1 Performance of Prospective Studies 101
4.4.2 Performance of Retrospective Studies 103
4.4.3 Performance of Cross-Sectional Studies 103
References 104
5 Medical Experiments 107
5.1 Basic Features of Medical Experiments 108
5.1.1 Statistical Principles of Experimentation 109
5.1.1.1 Control Group 109
5.1.1.2 Randomization 110
5.1.1.3 Replication 110
5.1.2 Advantages and Limitations of Experiments Ill
Contents xi
5.1.2.1 Advantages Ill
5.1.2.2 Limitations 112
5.2 Design of Experiments 112
5.2.1 Classical Designs: One-Way, Two-Way, and Factorial 113
5.2.1.1 One-Way Design 113
5.2.1.2 Two-Way Design 114
5.2.1.3 AT-Way and Factorial Experiments 116
5.2.2 Some Unconventional Designs 117
5.2.2.1 Repeated Measures Design 117
5.2.2.2 Crossover Design 118
5.2.2.3 Other Complex Designs 120
5.3 Choice and Sampling of Units for Laboratory Experiments 120
5.3.1 Choice of Experimental Unit 121
5.3.2 Sampling Methods in Laboratory Experiments 122
5.3.3 Choosing a Design of Experiment 123
References 123
6 Clinical Trials 125
6.1 Therapeutic Trials 126
6.1.1 Phases of a Clinical Trial 126
6.1.1.1 Phase I Trial 126
6.1.1.2 Phase II Trial 126
6.1.1.3 Phase HI Trial 127
6.1.1.4 Phase IV: Postmarketing Surveillance 128
6.1.2 Selection of Subjects 128
6.1.2.1 Selection of Participants for RCT 129
6.1.2.2 Control Group in a Clinical Trial 130
6.1.3 Randomization and Matching 132
6.1.3.1 Randomization 132
6.1.3.2 Matching 133
6.1.4 Methods of Random Allocation 134
6.1.4.1 Allocation out of a Large Number of Available
Subjects 134
6.1.4.2 Random Allocation of Consecutive Patients
Coming to a Clinic 134
6.1.5 Blinding and Masking 136
6.1.5.1 Blinding 136
6.1.5.2 Masking 137
6.2 Issues in Clinical Trials 138
6.2.1 Efficacy, Effectiveness, and Pragmatic Trials 138
6.2.1.1 End-Points or Outcome 138
6.2.1.2 Causal Inference 139
6.2.1.3 Side Effects 139
6.2.2 Various Equivalences in Clinical Trials 140
6.2.2.1 Superiority, Equivalence, and Noninferiority Trials.... 140
6.2.2.2 Therapeutic Equivalence and Bioequivalence 141
xii Contents
6.2.3 Designs for Clinical Trials 142
6.2.3.1 One-Way, Two-Way, and Factorial Designs 142
6.2.3.2 Crossover and Repeated Measures Designs 142
6.2.3.3 N-of-1, Up-and-Down, and Sequential Designs 143
6.2.3.4 Choosing a Design for a Clinical Trial 145
6.2.4 Biostatistical Ethics for Clinical Trials 146
6.2.4.1 Equipoise 146
6.2.4.2 Ethical Cautions 147
6.2.4.3 Statistical Considerations in a Multicentric Trial 148
6.2.4.4 Multiple Treatments with Different Outcomes
in the Same Trial 148
6.2.4.5 Size of the Trial 148
6.2.4.6 Compliance 149
6.2.5 Reporting Results of a Clinical Trial 149
6.2.5.1 CONSORT 150
6.2.5.2 Open Access 150
6.3 Trials Other than for Therapeutics 151
6.3.1 Clinical Trials for Diagnostic and Prophylactic Modalities 151
6.3.1.1 Diagnostic Trials 151
6.3.1.2 Prophylactic Trials in Clinics 152
6.3.2 Field Trials for Screening, Prophylaxis, and Vaccines 153
6.3.2.1 Screening Trials 153
6.3.2.2 Prophylactic Trials in the Field 154
6.3.2.3 Vaccine Trials 154
6.3.3 Issues in Field Trials 155
6.3.3.1 Randomization and Blinding in Field Trials 155
6.3.3.2 Designs for Field Trials 156
References 156
7 Numerical Methods for Representing Variation 159
7.1 Types of Measurement 159
7.1.1 Nominal, Metric, and Ordinal Scales 160
7.1.1.1 Nominal Scale 160
7.1.1.2 Metric Scale 161
7.1.1.3 Ordinal Scale 161
7.1.1.4 Grouping of a Metric Scale 162
7.1.2 Other Classifications of the Types of Measurement 164
7.1.2.1 Discrete and Continuous Variables 164
7.1.2.2 Qualitative and Quantitative Data 165
7.1.2.3 Stochastic and Deterministic Variables 166
7.2 Tabular Presentation 166
7.2.1 Contingency Tables and Frequency Distribution 167
7.2.1.1 Empty Cells 168
7.2.1.2 Problems in Preparing a Contingency Table
on Metric Data 169
7.2.2 Multiple Response Tables and Other Features 169
Contents xiii
7.2.2.1 Features of a Table 170
7.2.3 Other Statistical Tables 171
7.2.3.1 What Is a Good Statistical Table? 171
7.3 Rates and Ratios 172
7.3.1 Proportion, Rate, and Ratio 172
7.3.1.1 Proportion 172
7.3.1.2 Rate 172
7.3.1.3 Ratio 173
7.4 Central and Other Locations 174
7.4.1 Central Values: Mean, Median, and Mode 174
7.4.1.1 Understanding Mean, Median, and Mode 174
7.4.1.2 Calculation in Case of Grouped Data 175
7.4.1.3 Which Central Value to Use? 176
7.4.1.4 Geometric Mean 178
7.4.1.5 Harmonic Mean 178
7.4.2 Other Locations: Quantiles 180
7.4.2.1 Quantiles in Ungrouped Data 180
7.4.2.2 Quantiles in Grouped Data 180
7.4.2.3 Interpretation 182
7.5 Measuring Variability 183
7.5.1 Variance and Standard Deviation 184
7.5.1.1 Variance and Standard Deviation
in Ungrouped Data 185
7.5.1.2 Variance and Standard Deviation in Grouped Data 186
7.5.2 Coefficient of Variation 186
References 188
8 Presentation of Variation by Figures 189
8.1 Graphs for Frequency Distribution 190
8.1.1 Histogram and Its Variants 190
8.1.1.1 Histogram 190
8.1.1.2 Stem-and-Leaf Plot 192
8.1.1.3 Line Histogram 192
8.1.2 Polygon and Its Variants 192
8.1.2.1 Frequency Polygon 193
8.1.2.2 Area Diagram 193
8.1.3 Frequency Curve 193
8.2 Pie, Bar, and Line Diagrams 194
8.2.1 Pie Diagram 194
8.2.1.1 Useful Features of Pie Diagram 194
8.2.2 Bar Diagram 195
8.2.3 Scatter and Line Diagrams 197
8.2.3.1 Scatter Diagram 197
8.2.3.2 Line Diagram 198
8.2.3.3 Complex Line Diagrams 199
8.2.4 Choice and Cautions in Visual Display of Data 200
xiv Contents
8.2.5 Mixed and Three-Dimensional Diagrams 202
8.2.5.1 Mixed Diagram 202
8.2.5.2 Box-and-Whiskers Plot 202
8.2.5.3 Three-Dimensional Diagram 204
8.2.5.4 Biplot 204
8.2.5.5 Nomogram 204
8.3 Special Diagrams in Health and Medicine 206
8.3.1 Diagrams Used in Public Health 206
8.3.1.1 Epidemic Curve 206
8.3.1.2 Lexis Diagram 207
8.3.2 Diagrams Used in Individual Care and Research 208
8.3.2.1 Growth Charts 208
8.3.2.2 Partogram 209
8.3.2.3 Dendrogram 210
8.4 Charts and Maps 211
8.4.1 Charts 211
8.4.1.1 Schematic Chart 212
8.4.1.2 Pedigree Chart 212
8.4.2 Maps 213
8.4.2.1 Spot Map 213
8.4.2.2 Thematic Choroplethic Map 214
8.4.2.3 Cartogram 215
References 215
9 Some Quantitative Aspects of Medicine 219
9.1 Some Epidemiological Measures of Health and Disease 220
9.1.1 Epidemiological Indicators of Neonatal Health 221
9.1.1.1 Birth Weight 221
9.1.1.2 Apgar Score 222
9.1.2 Epidemiological Indicators of Growth in Children 222
9.1.2.1 Weight-for-Age 223
9.1.2.2 Weight-for-Height and Height-for-Age 223
9.1.2.3 Z-Scores and Percent of Median 223
9.1.2.4 Growth Velocity 225
9.1.2.5 Skinfold Thickness 225
9.1.2.6 Development 226
9.1.3 Epidemiological Indicators of Adolescent Health 226
9.1.3.1 Growth in Height and Weight in Adolescence 226
9.1.3.2 Sexual Maturity Rating 227
9.1.4 Epidemiological Indicators of Adult Health 227
9.1.4.1 Obesity 227
9.1.4.2 Smoking 228
9.1.4.3 Physiological Functions 231
9.1.4.4 Quality of Life 231
9.1.5 Epidemiological Indicators of Geriatric Health 232
9.1.5.1 Activities of Daily Living 232
Contents xv
9.1.5.2 Mental Health of the Elderly 232
9.2 Reference Values 233
9.2.1 Gaussian and Other Distributions 233
9.2.1.1 Properties of a Gaussian Distribution 234
9.2.1.2 Other Distributions 235
9.2.2 Reference or Normal Values 236
9.2.2.1 Implications of Normal Values 237
9.2.3 Normal Range 237
9.2.3.1 Disease Threshold 238
9.2.3.2 Clinical Threshold 238
9.2.3.3 Statistical Threshold 239
9.3 Measurement of Uncertainty: Probability 241
9.3.1 Elementary Laws of Probability 241
9.3.1.1 Law of Multiplication 241
9.3.1.2 Law of Addition 242
9.3.2 Probability in Clinical Assessments 244
9.3.2.1 Probabilities in Diagnosis 244
9.3.2.2 Forwarding Diagnosis 246
9.3.2.3 Assessment of Prognosis 246
9.3.2.4 Choice of Treatment 247
9.3.3 Further on Diagnosis: Bayes Rule 247
9.3.3.1 Bayes Rule 247
9.3.3.2 Extension of Bayes Rule 249
9.4 Validity of Medical Tests 250
9.4.1 Sensitivity and Specificity 251
9.4.1.1 Features of Sensitivity and Specificity 252
9.4.1.2 Likelihood Ratio 253
9.4.2 Predictivities 254
9.4.2.1 Positive and Negative Predictivity 254
9.4.2.2 Predictivity and Prevalence 255
9.4.2.3 The Meaning of Prevalence for Predictivity 257
9.4.2.4 Features of Positive and Negative Predictivities 257
9.4.3 Combination of Tests 259
9.4.3.1 Tests in Series 259
9.4.3.2 Tests in Parallel 259
9.4.3.3 Gains from a Test 260
9.4.3.4 When Can a Test Be Avoided? 262
9.4.5 Search for the Best Criterion: ROC Curve 263
9.4.5.1 Sensitivity-Specificity Based ROC Curve 263
9.4.5.2 Predictivities Based ROC Curve 265
References 267
10 Clinimetrics and Evidence-Based Medicine 271
10.1 Indicators, Indexes, and Scores 272
10.1.1 Indicators 272
10.1.1.1 Merits and Demerits of Indicators 272
xvi Contents
10.1.1.2 Choice of Indicators 273
10.1.2 Indexes 274
10.1.2.1 Some Commonly Used Indexes 274
10.1.2.2 Advantages and Limitations of Indexes 275
10.1.3 Scores 276
10.1.3.1 Scoring System for Diagnosis 277
10.1.3.2 Scoring for Gradation of Severity 279
10.2 Clinimetrics 280
10.2.1 Method of Scoring 280
10.2.1.1 Method of Scoring for Graded Characteristics.... 280
10.2.1.2 Method of Scoring for Diagnosis 281
10.2.2 Validity and Reliability of a Scoring System 283
10.2.2.1 Validity of Scoring System 284
10.2.2.2 Reliability of a Scoring System 285
10.3 Evidence-Based Medicine 285
10.3.1 Decision Analysis 286
10.3.1.1 Decision Tree 286
10.3.2 Statistical Tools for Evidence-Based Medicine 291
10.3.2.1 Etiology Diagram 291
10.3.2.2 Expert System 292
References 294
11 Measurement of Community Health 299
11.1 Indicators of Mortality 300
11.1.1 Crude and Standardized Death Rates 300
11.1.1.1 Crude Death Rate 300
11.1.1.2 Age-Specific Death Rate 300
11.1.1.3 Standardized Death Rate 301
11.1.1.4 Comparative Mortality Ratio 305
11.1.2 Specific Mortality Rates 305
11.1.2.1 Fetal Deaths and Mortality in Children 305
11.1.2.2 Maternal Mortality 309
11.1.2.3 Adult Mortality 309
11.1.2.4 Other Measures of Mortality 310
11.1.3 Death Spectrum 311
11.2 Measures of Morbidity 312
11.2.1 Prevalence and Incidence 312
11.2.1.1 Point Prevalence 312
11.2.1.2 Period Prevalence 313
11.2.1.3 Incidence 313
11.2.1.4 The Concept of Person-Time 314
11.2.1.5 Capture-Recapture Methodology 314
11.2.2 Duration of Morbidity 316
11.2.2.1 Prevalence in Relation to Duration
of Morbidity 316
11.2.2.2 Incidence from Prevalence 317
Contents xvii
11.2.2.3 Epidemiologically Consistent Estimates 318
11.2.3 Morbidity Measures for Acute Conditions 319
11.2.3.1 Attack Rates 319
11.2.3.2 Disease Spectrum 320
11.3 Indicators of Social and Mental Health 322
11.3.1 Indicators of Social Health 322
11.3.1.1 Education 322
11.3.1.2 Income 323
11.3.1.3 Occupation 324
11.3.1.4 Socioeconomic Status 324
11.3.1.5 Gender Empowerment 325
11.3.1.6 Dependency Ratio 326
11.3.2 Indicators of Health Resources 326
11.3.2.1 Health Infrastructure 327
11.3.2.2 Health Expenditure 328
11.3.3 Indicators of Lack of Mental Health 329
11.3.3.1 Smoking and Other Addictions 329
11.3.3.2 Divorces 329
11.3.3.3 Vehicular Accidents and Crimes 329
11.3.3.4 Others Measures of Lack of Mental Health 330
11.4 Composite Indexes of Health 331
11.4.1 Indexes of Status of Comprehensive Health 331
11.4.1.1 Human Development Index 331
11.4.1.2 Quality of Life Index 332
11.4.2 Indexes of Health Gap 333
11.4.2.1 DALYs Lost 333
11.4.2.2 Human Poverty Index 334
11.4.2.3 Index of Need for Health Resources 335
References 335
12 Confidence Intervals, Principles of Tests of Significance,
and Sample Size 337
12.1 Sampling Distributions 338
12.1.1 Basic Concepts 338
12.1.1.1 Sampling Error 338
12.1.1.2 Point Estimate 338
12.1.1.3 Standard Error of p and x 339
12.1.2 Sampling Distribution of p and x 341
12.1.2.1 Gaussian Conditions 341
12.1.2.2 Assessing Gaussian Pattern for Small n 343
12.1.3 Obtaining Probabilities from a Gaussian Distribution 343
12.1.3.1 Gaussian Probability 344
12.1.3.2 Continuity Correction 345
12.1.3.3 Probabilities Relating to the Mean
and the Proportion 346
12.1.4 The Case of a Not Known (/-Distribution) 347
xviii Contents
12.2 Confidence Intervals 348
12.2.1 Confidence Interval for ir (Large n) and fi
(Gaussian Conditions) 348
12.2.1.1 Confidence Interval for
Proportion tt (Large ri) 349
12.2.1.2 Lower and Upper Bounds for tt (Large ri) 351
12.2.1.3 Confidence Interval for Mean fi (Large n) 351
12.2.1.4 Confidence Bounds for Mean fi 354
12.2.2 Confidence Interval for Differences (Large n) 355
12.2.2.1 Two Independent Samples 355
12.2.2.2 Paired Samples 356
12.2.3 Confidence Interval for it (Small n)
and fj. (Small n): Non-Gaussian Conditions 358
12.2.3.1 Confidence Interval for tt (Small ri) 358
12.2.3.2 Confidence Bound for tt When the Success or
the Failure Rate in the Sample Is Zero Percent.... 360
12.2.3.3 Confidence Interval for Median
(Small ri): Non-Gaussian Conditions 362
12.3 P-Values and Statistical Significance 364
12.3.1 What Is Statistical Significance? 364
12.3.1.1 Court Judgment 364
12.3.1.2 Errors in Diagnosis 365
12.3.1.3 Null Hypothesis 365
12.3.1.4 Philosophical Basis of Statistical Tests 366
12.3.1.5 Alternative Hypothesis 367
12.3.1.6 One-Sided Alternatives: Which Tail
Is Wagging? 367
12.3.2 Errors, P-Values, and Power 368
12.3.2.1 Type-I Error 368
12.3.2.2 Type-H Error 369
12.3.2.3 Type-Hi Error 370
12.3.2.4 Power 370
12.3.3 General Procedure to Obtain P-value 371
12.4 Initial Debate on Statistical Significance 375
12.4.1 Confidence Interval versus Test of Ho 376
12.4.2 Medical Significance versus Statistical Significance 377
12.5 Sample Size Determination in Some Cases 379
12.5.1 Sample Size Required in Estimation Setup 380
12.5.1.1 General Considerations in the Estimation
Setup 380
12.5.1.2 General Procedure for Determining Size
of Sample for Estimation 382
12.5.1.3 Formulas for Sample Size Calculation
for Estimation in Simple Situations 384
12.5.2 Sample Size for Testing a Hypothesis
with Specified Power 386
Contents xix
12.5.2.1 General Considerations in a
Testing-of-Hypothesis Setup 387
12.5.2.2 Sample Size Formulas for Test
of Hypothesis in Simple Situations 388
12.5.2.3 Nomograms and Tables of Sample Size 391
12.5.2.4 Thumb Rules 392
12.5.2.5 Power Analysis 392
References 393
13 Inference from Proportions 395
13.1 One Qualitative Variable 396
13.1.1 Dichotomous Categories: Binomial Distribution 396
13.1.1.1 Binomial Distribution 396
13.1.1.2 Large n: Gaussian Approximation to Binomial... 398
13.1.2 Polytomous Categories (Large n):
Goodness-of-Fit Test 399
13.1.2.1 Chi-Square and Its Explanation 400
13.1.2.2 Degrees of Freedom 401
13.1.2.3 Cautions in Using Chi-Square 402
13.1.2.4 Further Analysis (Partitioning of Table) 404
13.1.3 Polytomous Categories (Small n):
Exact Multinomial Test 405
13.1.3.1 Goodness-of-Fit in Small Samples 405
13.2 Proportions in 2 X 2 Tables 407
13.2.1 Structure of 2 X 2 Table in Different Types of Study 408
13.2.1.1 Structure in Prospective Study 408
13.2.1.2 Structure in Retrospective Study 408
13.2.1.3 Structure in Cross-Sectional Study 408
13.2.2 Two Independent Samples (Large n): Chi-Square Test 408
13.2.2.1 Chi-Square Test 409
13.2.2.2 Yate s Correction for Continuity 410
13.2.2.3 Z-Test for Proportions 411
13.2.2.4 Detecting a Medically Important Difference
in Proportions 411
13.2.2.5 Equivalence Tests 413
13.2.2.6 Crossover Design with Binary Response
(Large n) 415
13.2.3 Two Independent Samples (Small n): Fisher s Exact Test 417
13.2.3.1 Fisher s Exact Test 417
13.2.3.2 Crossover Design (Small n) 417
13.2.4 Proportions in Matched Pairs: McNemar s Test
(Large n) and Exact Test (Small n) 418
13.2.4.1 Large n: McNemar s Test 419
13.2.4.2 Small n: Exact Test (Matched Pairs) 420
13.2.4.3 Comparison of Two Tests for Sensitivity
and Specificity 421
xx Contents
13.3 Analysis of R X C Tables (Large ri) 423
13.3.1 One Dichototnous and the Other Polytomous
Variable (2 X C Table) 423
13.3.1.1 The Test Criterion 424
13.3.1.2 Trend in Proportions in Ordinal Categories 425
13.3.2 Two Polytomous Variables 427
13.4 Three-Way Tables 429
13.4.1 Assessment of Association in Three-Way Tables 430
13.4.2 Log-Linear Models 433
13.4.2.1 Log-Linear Model for Two-Way Tables 433
13.4.2.2 Log-Linear Model for Three-Way Tables 434
References 436
14 Relative Risk and Odds Ratio 439
14.1 Relative and Attributable Risks (Large n) 439
14.1.1 Risk, Hazard, and Odds 439
14.1.1.1 Risk 440
14.1.1.2 Hazard 440
14.1.1.3 Odds 440
14.1.1.4 Ratios of Risks and Odds 440
14.1.2 Relative Risk 441
14.1.2.1 RR in Independent Samples 441
14.1.2.2 Confidence Interval for RR
(Independent Samples) 443
14.1.2.3 Test of Hypothesis on RR
(Independent Samples) 445
14.1.2.4 RR in the Case of Matched Pairs 446
14.1.3 Attributable Risk 447
14.1.3.1 AR in Independent Samples 447
14.1.3.2 AR in Matched Pairs 448
14.1.3.3 Number Needed to Treat 450
14.1.3.4 Relative Risk Reduction 451
14.1.3.5 Population Attributable Risk 451
14.2 Odds Ratio 452
14.2.1 OR in Two Independent Samples 452
14.2.1.1 CI for OR (Independent Samples) 455
14.2.1.2 Test of Hypothesis on OR
(Independent Samples) 455
14.2.2 OR in Matched Pairs 457
14.2.2.1 Confidence Interval for OR (Matched Pairs) 458
14.2.2.2 Test of Hypothesis on OR (Matched Pairs) 458
14.2.2.3 Multiple Controls 460
14.3 Stratified Analysis and Sample Size 460
14.3.1 Mantel-Haenszel Procedure 461
14.3.2 Sample Size Requirement for Inference on RR and OR 464
References 468
Contents xxi
15 Inference from Means 469
15.1 Comparison of Means in One and Two Groups
(Gaussian Conditions): Student s /-Test 470
15.1.1 Comparison with a Prespecified Mean 470
15.1.1.1 Student s/-Test for One Sample 471
15.1.2 Difference in Means in Two Samples 473
15.1.2.1 Paired Samples Setup 473
15.1.2.2 Unpaired (Independent) Samples Setup 474
15.1.2.3 Some Features of Student s / 476
15.1.2.4 Difference-in-Differences Approach 478
15.1.3 Analysis of Crossover Designs 478
15.1.3.1 Test for Group Effect 479
15.1.3.2 Test for Carry-Over Effect 480
15.1.3.3 Test for Treatment Effect 480
15.1.4 Analysis of Data of Up-and-Down Trials 481
15.2 Comparison of Means in Three or More Groups
(Gaussian Conditions): ANOVA F-Test 482
15.2.1 One-Way ANOVA 483
15.2.1.1 Mathematical Details 484
15.2.1.2 The Procedure to Test H,, 485
15.2.1.3 Checking the Validity of the Assumptions
of ANOVA 489
15.2.2 Two-Way ANOVA 490
15.2.2.1 Two-Factor Design 490
15.2.2.2 The Hypotheses and Their Test 491
15.2.2.3 Main Effect and Interaction (Effect) 494
15.2.2.4 Repeated Measures 496
15.2.3 Multiple Comparisons: Bonferroni and Tukey Tests 497
15.2.3.1 Bonferroni Procedure 497
15.2.3.2 Tukey Test 498
15.3 Non-Gaussian Conditions: Nonparametric Tests for Location 499
15.3.1 Comparison of Two Groups: Wilcoxon Tests 500
15.3.1.1 Case I: Paired Data 500
15.3.1.2 Case II: Independent Samples 504
15.3.2 Comparison of Three or More Groups:
Kruskal-Wallis Test 506
15.3.3 Two-Way Layout: Friedman Test 508
15.4 When Significant Is Not Significant 511
15.4.1 The Nature of Statistical Significance 511
15.4.2 Testing for Presence of Medically Important
Difference in Means 517
15.4.2.1 Detecting Specified Difference in Mean 518
15.4.2.2 Equivalence Tests 519
15.4.3 Power and Level of Significance 519
15.4.3.1 Balancing Type-I and Type-II Error 522
References 522
xxii Contents
16 Relationships: Quantitative Data 525
16.1 Some General Features of a Regression Setup 527
16.1.1 Dependent and Independent Variables 527
16.1.1.1 Simple, Multiple, and Multivariate
Regression 528
16.1.2 Linear, Curvilinear, and Nonlinear Regressions 529
16.1.2.1 Linear Regression 529
16.1.2.2 Curvilinear Regression 531
16.1.2.3 Nonlinear Relationships 531
16.1.3 The Concept of Residuals 533
16.1.4 General Method of Fitting a Regression 533
16.2 Linear Regression Models 535
16.2.1 Testing Adequacy of a Regression Fit 537
16.2.1.1 Goodness of Fit and R2 537
16.2.1.2 Stepwise Procedure 538
16.2.1.3 Statistical Significance of Individual
Regression Coefficients 539
16.2.1.4 Validity of Assumptions 539
16.2.2 Interpretation of the Regression Coefficients 544
16.3 Some Issues in Regression 547
16.3.1 Confidence Interval, Confidence Band, and Tests 547
16.3.1.1 SEs and CIs for the Regression 547
16.3.1.2 Confidence Band 548
16.3.1.3 Equality of Two Regression Lines 549
16.3.1.4 Difference-in-Differences Approach with
Regression 550
16.3.2 Some Variations of Regression 551
16.3.2.1 Ridge Regression 551
16.3.2.2 Multilevel Regression 551
16.3.2.3 Analysis of Covariance 553
16.4 Measuring the Strength of Quantitative Relationship 554
16.4.1 Product-Moment and Related Correlations 554
16.4.1.1 Multiple Correlation 554
16.4.1.2 Product-Moment Correlation 555
16.4.1.3 Covariance 555
16.4.1.4 Statistical Significance of r 559
16.4.1.5 Intraclass Correlation 560
16.4.1.6 Serial Correlation 560
16.4.2 Rank Correlation 560
16.4.2.1 Spearman s Rho 561
16.4.2.2 Kendall s Tau and Goodman-Kruskal
Gamma 562
16.5 Assessment of Agreement 563
16.5.1 Agreement in Quantitative Measurements 563
16.5.1.1 Statistical Formulation of the Problem 564
Contents xxiii
16.5.2 Approaches for Measuring Quantitative Agreement 564
16.5.2.1 Limits of Disagreement Approach 564
16.5.2.2 Intraclass Correlation as a Measure
of Agreement 566
16.5.2.3 Relative Merits of the Two Methods 567
References 569
17 Relationships: Qualitative Dependent 571
17.1 Binary Dependent: Logistic Regression (Large n) 572
17.1.1 Meaning of a Logistic Model 572
17.1.2 Assessing Overall Adequacy of a Logistic
Regression 575
17.1.2.1 Log Likelihood 575
17.1.2.2 Classification Accuracy 577
17.1.2.3 Hosmer-Lemeshow Test 577
17.2 Inference from Logistic Coefficients 578
17.2.1 Interpretation of the Logistic Coefficients 578
17.2.1.1 Dichotomous Predictors 578
17.2.1.2 Polytomous and Continuous Predictors 580
17.2.2 Confidence Interval and Test of Hypothesis
on Logistic Coefficients 581
17.3 Issues in Logistic Regression 583
17.3.1 Conditional Logistic for Matched Data 583
17.3.2 Polytomous Dependent 584
17.3.2.1 Nominal Categories: Multinomial Logistic 584
17.3.2.2 Ordinal Categories 585
17.4 Some Models for Qualitative Data 586
17.4.1 Cox Regression for Hazards 587
17.4.2 Classification and Regression Trees 589
17.5 Strength of Relationship in Qualitative Variables 590
17.5.1 Both Variables Qualitative 590
17.5.1.1 Dichotomous Categories 590
17.5.1.2 Polytomous Categories 592
17.5.1.3 Proportional Reduction in Error 594
17.5.2 One Qualitative and the Other Quantitative Variable 596
17.5.3 Agreement in Qualitative Measurements 597
17.5.3.1 The Meaning of Qualitative Agreement 597
17.5.3.2 Cohen s Kappa 598
References 599
18 Survival Analysis 601
18.1 Life Expectancy 602
18.1.1 Life Table 602
18.1.2 Other Forms of Life Expectancy 606
18.1.2.1 Potential Years of Life Lost 606
18.1.2.2 Healthy Life Expectancy 607
xxiv Contents
18.1.2.3 Life Expectation Related to a Cause of Death 607
18.1.2.4 Application to Other Setups 607
18.2 Analysis of Survival Data 608
18.2.1 Nature of Survival Data 609
18.2.1.1 Types of Censoring 609
18.2.1.2 Collection of Survival Time Data 610
18.2.2 Survival Observed in Time Intervals:
Life Table Method 611
18.2.2.1 Life Table Method 611
18.2.2.2 Survival Function 612
18.2.3 Continuous Observation of Survival Time:
Kaplan-Meier Method 614
18.2.3.1 Kaplan-Meier Method 614
18.2.3.2 Hazard Function 617
18.3 Issues in Survival Analysis 619
18.3.1 Comparison of Survival in Two Groups 619
18.3.1.1 Comparing Survival Rates 619
18.3.1.2 Comparing Survival Experience:
Log-Rank Test 620
18.3.2 Factors Affecting Survival: Cox Model 623
18.3.2.1 Parametric Models 623
18.3.2.2 Cox Model for Survival 623
18.3.3 Sample Size for Survival Studies 625
References 626
19 Simultaneous Consideration of Several Variables 627
19.1 Scope of Multivariate Methods 628
19.1.1 The Essentials of a Multivariate Setup 628
19.1.2 Statistical Limitation on the Number of Variables 630
19.2 Dependent and Independent Sets of Variables 630
19.2.1 Dependents and Independents Both Quantitative:
Multivariate Multiple Regression 631
19.2.2 Quantitative Dependents and Qualitative Independents:
Multivariate Analysis of Variance (MANOVA) 635
19.2.3 Classification of Subjects into Known Groups:
Discriminant Analysis 638
19.2.3.1 Discriminant Analysis 638
19.2.3.2 Classification Rule 639
19.2.3.3 Classification Accuracy 640
19.3 Identification of Structure in the Observationas 643
19.3.1 Identification of Clusters of Subjects: Cluster Analysis 644
19.3.1.1 Measures of Similarity 644
19.3.1.2 Hierarchical Agglomerative Algorithm 645
19.3.1.3 Deciding on the Number of Natural Clusters 646
19.3.2 Identification of Unobservable Underlying Factors:
Factor Analysis 648
Contents xxv
19.3.2.1 Factor Analysis 649
19.3.2.2 Features of a Successful Factor Analysis 651
19.3.2.3 Factor Scores 652
References 653
20 Quality Considerations 655
20.1 Statistical Quality Control in Medical Care 656
20.1.1 Statistical Control of Medical Care Errors 657
20.1.1.1 Adverse Patient Outcomes 657
20.1.1.2 Monitoring Fatality 658
20.1.1.3 Limits of Tolerance 658
20.1.2 Quality of Lots 659
20.1.2.1 The Lot Quality Method 660
20.1.2.2 LQAS in Health Assessment 660
20.1.3 Quality Control in a Medical Laboratory 661
20.1.3.1 Control Chart 661
20.1.3.2 Cusum Chart 662
20.2 Quality of Measurements 664
20.2.1 Validity of Instruments 664
20.2.1.1 Types of Validity 665
20.2.2 Reliability of Instruments 666
20.2.2.1 Internal Consistency 667
20.2.2.2 Cronbach s Alpha 667
20.2.2.3 Test-Retest Reliability 669
20.3 Quality of Statistical Models: Robustness 670
20.3.1 External Validation 672
20.3.1.1 Split-Sample Method 672
20.3.1.2 Another Sample Method 672
20.3.2 Sensitivity Analysis and Uncertainty Analysis 673
20.3.2.1 Sensitivity Analysis 673
20.3.2.2 Uncertainty Analysis 674
20.3.3 Resampling 675
20.3.3.1 Bootstrapping 676
20.3.3.2 Jackknife Resampling 676
20.4 Quality of Data 677
20.4.1 Errors in Measurement 677
20.4.1.1 Lack of Standardization in Definitions 677
20.4.1.2 Lack of Care in Obtaining or Recording
Information 677
20.4.1.3 Inability of the Observer to Get Confidence
of the Respondent 678
20.4.1.4 Bias of the Observer 678
20.4.1.5 Variable Competence of the Observers 678
20.4.2 Missing Values 679
20.4.2.1 Handling Nonresponse 680
20.4.2.2 Imputations 683
xxvi Contents
20.4.2.3 Intention-to-Treat Analysis 683
20.4.3 Lack of Standardization in Values 685
20.4.3.1 Standardization Methods Already
Described 685
20.4.3.2 Standardization for Calculating
Adjusted Rates 685
20.4.3.3 Standardized Mortality Ratio 686
References 688
21 Statistical Fallacies 691
21.1 Problems with the Sample 692
21.1.1 Biased Sample 692
21.1.1.1 Survivors 692
21.1.1.2 Volunteers 693
21.1.1.3 Clinical Subjects 693
21.1.1.4 Inadequate Size of the Sample 694
21.1.1.5 Publication Bias 695
21.1.1.6 Inadequate Specification of Sampling
Method 695
21.1.1.7 Abrupt Series 695
21.1.2 Incomparable Groups 695
21.1.2.1 Differential in Group Composition 695
21.1.2.2 Differential Definitions 697
21.1.2.3 Differential Compliance 698
21.1.2.4 Variable Periods of Exposure 698
21.1.2.5 Improper Denominator 699
21.1.3 Mixing of Distinct Groups 700
21.1.3.1 Effect on Regression 701
21.1.3.2 Effect on Shape of the Distribution 702
21.1.3.3 Lack of Intragroup Homogeneity 702
21.2 Errors in Presentation of Findings 703
21.2.1 Misuse of Percentages and Means 703
21.2.1.1 Misuse of Percentages 703
21.2.1.2 Misuse of Means 704
21.2.1.3 Unnecessary Decimals 705
21.2.2 Problems in Reporting 706
21.2.2.1 Incomplete Reporting 706
21.2.2.2 Over-Reporting 707
21.2.2.3 Self-Reporting versus Objective
Measurement 707
21.2.2.4 Misuse of Graphs 708
21.3 Inadequate Analysis 709
21.3.1 Ignoring Reality 709
21.3.1.1 Looking for Linearity 709
21.3.1.2 Assumptions Overlooked 709
Contents xxvii
21.3.1.3 Area under the Concentration Curve 710
21.3.1.4 Anomalous Person-Years 711
21.3.2 Mean or Proportion? 711
21.3.3 Forgetting Baseline Values 712
21.3.4 Misuse of Statistical Packages 713
21.3.4.1 Over-Analysis 713
21.3.4.2 Data Dredging 714
21.3.4.3 Quantitative Analysis of Codes 714
21.3.4.4 Soft Data versus Hard Data 714
21.4 Misinterpretation 715
21.4.1 Misuse of P-Values 715
21.4.1.1 Magic Threshold 0.05 715
21.4.1.2 One-Tail or Two-Tail P-Values 716
21.4.1.3 Multiple Comparisons 716
21.4.1.4 Dramatic P-Values 716
21.4.1.5 P-Values for Nonrandom Sample 716
21.4.1.6 Normal with Respect to Several
Parameters 717
21.4.2 Correlation versus Cause-Effect Relationship 717
21.4.2.1 Criteria for Cause-Effect 718
21.4.2.2 Other Considerations 719
21.4.3 Sundry Issues 720
21.4.3.1 Diagnostic Test Is Only an Additional
Adjunct 720
21.4.3.2 Medical Significance versus Statistical
Significance 720
21.4.3.3 Interpretation of Standard Error (p) 721
21.4.3.4 Univariate Analysis but Multivariate
Conclusions 721
21.4.3.5 Limitation of Relative Risk 722
21.4.4 Final Comments 722
References 723
Appendix 1 Statistical Software 727
Al.l General Purpose Statistical Software 727
A1.2 Special Purpose Statistical Software 729
Appendix 2 Some Statistical Tables 731
Index 737
|
| adam_txt |
Contents
Preface to Second Edition xxix
Summary Tables xxxi
Frequently Used Notations xxxix
Abbreviations xliii
1 Medical Uncertainties 1
1.1 Uncertainties in Health and Disease 2
1.1.1 Uncertainties due to Intrinsic Variation 3
1.1.1.1 Biologic Variability 3
1.1.1.2 Genetic Variability 3
1.1.1.3 Variation in Behavior and Other Host Factors 4
1.1.1.4 Environmental Variability 4
1.1.1.5 Chance Variability 4
1.1.1.6 Sampling Fluctuation 5
1.1.2 Natural Variation in Assessment 5
1.1.2.1 Observer Variability 5
1.1.2.2 Variability in Treatment Strategies 6
1.1.2.3 Instrument and Laboratory Variability 6
1.1.2.4 Imperfect Tools 7
1.1.2.5 Incomplete Information on the Patient 7
1.1.2.6 Poor Compliance with the Regimen 7
1.1.3 Inadequate Knowledge 8
1.1.3.1 Epistemic Uncertainties 8
1.1.3.2 Diagnostic, Therapeutic, and Prognostic
Uncertainties 8
1.1.3.3 Predictive and Other Uncertainties 9
1.2 Uncertainties in Medical Research 9
1.2.1 Empiricism in Medical Research 10
1.2.1.1 Laboratory Experiments 10
1.2.1.2 Clinical Trials 10
1.2.1.3 Surgical Procedures 10
1.2.1.4 Epidemiological Research 11
1.2.2 Elements of Minimizing the Impact of Uncertainties
on Research 11
1.2.2.1 Proper Design 12
vii
viii Contents
1.2.2.2 Improved Medical Methods 12
1.2.2.3 Analysis and Synthesis 13
1.2.3 Critique of a Report of a Medical Study 13
1.2.3.1 Introduction 14
1.2.3.2 Methodology 14
1.2.3.3 Results 15
1.2.3.4 Discussion and Conclusions 16
1.3 Uncertainties in Health Planning and Evaluation 16
1.3.1 Health Situation Analysis 17
1.3.1.1 Identification of the Specifics of the Problem 17
1.3.1.2 Size of the Target Population 18
1.3.1.3 Magnitude of the Problem 19
1.3.1.4 Health Infrastructure 20
1.3.1.5 Feasibility of Remedial Steps 21
1.3.2 Evaluation of Health Programs 21
1.4 Management of Uncertainties: About This Book 22
1.4.1 Contents of the Book 23
1.4.2 Salient Features of the Text 25
1.4.2.1 System of Notations 26
1.4.2.2 Guide Chart of the Biostatistical Methods 27
References 27
2 Basics of Medical Studies 29
2.1 Study Protocol 30
2.1.1 The Problem, Objectives, and Hypotheses 30
2.1.1.1 The Problem 30
2.1.1.2 Objectives 31
2.1.1.3 Hypotheses 31
2.1.2 Protocol Content 32
2.2 Types of Medical Studies 35
2.2.1 Elements of Design 36
2.2.1.1 Broad Objective of the Study 37
2.2.2 Basic Types of Study Design 38
2.2.2.1 Descriptive Studies 38
2.2.2.2 Analytical Studies 40
2.2.2.3 Basic Types of Analytical Studies 40
2.2.3 Choosing a Design 41
2.2.3.1 Recommended Design for Particular Setups 41
2.2.3.2 Choice of Design by Level of Evidence 42
2.3 Data Collection 44
2.3.1 Nature of Data 44
2.3.1.1 Factual, Knowledge-Based, and Opinion-Based Data. 44
2.3.1.2 Method of Obtaining the Data 45
2.3.2 Tools of Data Collection 46
2.3.2.1 Existing Records 46
2.3.2.2 Questionnaires and Schedules 47
Contents ix
2.3.3 Pretesting and Pilot Study 49
2.4 Nonsampling Errors and Other Biases 49
2.4.1 Nonresponse 50
2.4.2 Variety of Biases to Guard Against 50
2.4.2.1 List of Biases 50
2.4.2.2 Steps for Minimizing Bias 56
References 58
3 Sampling Methods 59
3.1 Sampling Concepts 59
3.1.1 Advantages and Limitations of Sampling 60
3.1.1.1 Sampling Fluctuations 60
3.1.1.2 Advantages of Sampling 61
3.1.1.3 Limitations of Sampling 61
3.1.2 Some Special Terms Used in Sampling 61
3.1.2.1 Unit 61
3.1.2.2 Sampling Frame 62
3.1.2.3 Parameters and Statistics 62
3.1.2.4 Sample Size 62
3.1.2.5 Nonrandom and Random Sampling 63
3.2 Common Methods of Random Sampling 63
3.2.1 Simple Random Sampling 63
3.2.2 Stratified Random Sampling 64
3.2.3 Multistage Random Sampling 67
3.2.4 Cluster Random Sampling 68
3.2.5 Systematic Random Sampling 70
3.2.6 Choice of Method of Random Sampling 72
3.3 Some Other Methods of Sampling 72
3.3.1 Other Random Methods of Sampling 73
3.3.1.1 Probability Proportional to Size Sampling 73
3.3.1.2 Area Sampling 74
3.3.1.3 Inverse Sampling 74
3.3.1.4 Consecutive Subjects Attending a Clinic 74
3.3.1.5 Sequential Sampling 75
3.3.2 Nonrandom Methods of Sampling 75
3.3.2.1 Convenience Samples 75
3.3.2.2 Other Types of Purposive Samples 76
3.4 Some Examples of Sample Surveys 77
3.4.1 National Health and Nutrition Examination Survey
in the United States 77
3.4.1.1 Sample Design 77
3.4.1.2 Logistics and Other Details 78
3.4.2 A Small-Scale Survey of an Elderly Population in Australia 78
3.4.2.1 Sample Design 79
3.4.2.2 Logistics and Other Details 79
References 80
x Contents
4 Designs for Observational Studies 81
4.1 Prospective Studies 84
4.1.1 Variations of Prospective Studies 84
4.1.1.1 Cohort Study 84
4.1.1.2 Longitudinal Study 86
4.1.2 Comparison Group in a Prospective Study 86
4.1.3 Selection of Subjects for a Prospective Study 87
4.1.4 Potential Biases in Prospective Studies 88
4.1.4.1 Selection Bias 88
4.1.4.2 Bias due to Loss in Follow-Up 88
4.1.4.3 Assessment Bias and Errors 89
4.1.4.4 Bias due to Change in the Status 89
4.1.4.5 Confounding Bias 89
4.1.4.6 Post Hoc Bias 90
4.1.4.7 Validity Bias 90
4.1.5 Merits and Demerits of Prospective Studies 90
4.1.5.1 Merits of Prospective Studies 90
4.1.5.2 Demerits of Prospective Studies 91
4.2 Retrospective Studies 91
4.2.1 Case-Control Design 92
4.2.1.1 Nested Case-Control Design 93
4.2.2 Selection of Cases and Controls 94
4.2.2.1 Sampling Methods in Retrospective Studies 94
4.2.2.2 Confounders and Matching 95
4.2.3 Merits and Demerits of Case-Control Studies 96
4.2.3.1 Merits of Case-Control Studies 96
4.2.3.2 Demerits of Case-Control Studies 96
4.3 Cross-Sectional Studies 97
4.3.1 Selection of Subjects for a Cross-Sectional Study 98
4.3.2 Merits and Demerits of Cross-Sectional Studies 98
4.3.2.1 Demerits of Cross-Sectional Studies 98
4.3.2.2 Merits of Cross-Sectional Studies 99
4.4 Comparative Performance of Prospective, Retrospective,
and Cross-Sectional Studies 100
4.4.1 Performance of Prospective Studies 101
4.4.2 Performance of Retrospective Studies 103
4.4.3 Performance of Cross-Sectional Studies 103
References 104
5 Medical Experiments 107
5.1 Basic Features of Medical Experiments 108
5.1.1 Statistical Principles of Experimentation 109
5.1.1.1 Control Group 109
5.1.1.2 Randomization 110
5.1.1.3 Replication 110
5.1.2 Advantages and Limitations of Experiments Ill
Contents xi
5.1.2.1 Advantages Ill
5.1.2.2 Limitations 112
5.2 Design of Experiments 112
5.2.1 Classical Designs: One-Way, Two-Way, and Factorial 113
5.2.1.1 One-Way Design 113
5.2.1.2 Two-Way Design 114
5.2.1.3 AT-Way and Factorial Experiments 116
5.2.2 Some Unconventional Designs 117
5.2.2.1 Repeated Measures Design 117
5.2.2.2 Crossover Design 118
5.2.2.3 Other Complex Designs 120
5.3 Choice and Sampling of Units for Laboratory Experiments 120
5.3.1 Choice of Experimental Unit 121
5.3.2 Sampling Methods in Laboratory Experiments 122
5.3.3 Choosing a Design of Experiment 123
References 123
6 Clinical Trials 125
6.1 Therapeutic Trials 126
6.1.1 Phases of a Clinical Trial 126
6.1.1.1 Phase I Trial 126
6.1.1.2 Phase II Trial 126
6.1.1.3 Phase HI Trial 127
6.1.1.4 Phase IV: Postmarketing Surveillance 128
6.1.2 Selection of Subjects 128
6.1.2.1 Selection of Participants for RCT 129
6.1.2.2 Control Group in a Clinical Trial 130
6.1.3 Randomization and Matching 132
6.1.3.1 Randomization 132
6.1.3.2 Matching 133
6.1.4 Methods of Random Allocation 134
6.1.4.1 Allocation out of a Large Number of Available
Subjects 134
6.1.4.2 Random Allocation of Consecutive Patients
Coming to a Clinic 134
6.1.5 Blinding and Masking 136
6.1.5.1 Blinding 136
6.1.5.2 Masking 137
6.2 Issues in Clinical Trials 138
6.2.1 Efficacy, Effectiveness, and Pragmatic Trials 138
6.2.1.1 End-Points or Outcome 138
6.2.1.2 Causal Inference 139
6.2.1.3 Side Effects 139
6.2.2 Various Equivalences in Clinical Trials 140
6.2.2.1 Superiority, Equivalence, and Noninferiority Trials. 140
6.2.2.2 Therapeutic Equivalence and Bioequivalence 141
xii Contents
6.2.3 Designs for Clinical Trials 142
6.2.3.1 One-Way, Two-Way, and Factorial Designs 142
6.2.3.2 Crossover and Repeated Measures Designs 142
6.2.3.3 N-of-1, Up-and-Down, and Sequential Designs 143
6.2.3.4 Choosing a Design for a Clinical Trial 145
6.2.4 Biostatistical Ethics for Clinical Trials 146
6.2.4.1 Equipoise 146
6.2.4.2 Ethical Cautions 147
6.2.4.3 Statistical Considerations in a Multicentric Trial 148
6.2.4.4 Multiple Treatments with Different Outcomes
in the Same Trial 148
6.2.4.5 Size of the Trial 148
6.2.4.6 Compliance 149
6.2.5 Reporting Results of a Clinical Trial 149
6.2.5.1 CONSORT 150
6.2.5.2 Open Access 150
6.3 Trials Other than for Therapeutics 151
6.3.1 Clinical Trials for Diagnostic and Prophylactic Modalities 151
6.3.1.1 Diagnostic Trials 151
6.3.1.2 Prophylactic Trials in Clinics 152
6.3.2 Field Trials for Screening, Prophylaxis, and Vaccines 153
6.3.2.1 Screening Trials 153
6.3.2.2 Prophylactic Trials in the Field 154
6.3.2.3 Vaccine Trials 154
6.3.3 Issues in Field Trials 155
6.3.3.1 Randomization and Blinding in Field Trials 155
6.3.3.2 Designs for Field Trials 156
References 156
7 Numerical Methods for Representing Variation 159
7.1 Types of Measurement 159
7.1.1 Nominal, Metric, and Ordinal Scales 160
7.1.1.1 Nominal Scale 160
7.1.1.2 Metric Scale 161
7.1.1.3 Ordinal Scale 161
7.1.1.4 Grouping of a Metric Scale 162
7.1.2 Other Classifications of the Types of Measurement 164
7.1.2.1 Discrete and Continuous Variables 164
7.1.2.2 Qualitative and Quantitative Data 165
7.1.2.3 Stochastic and Deterministic Variables 166
7.2 Tabular Presentation 166
7.2.1 Contingency Tables and Frequency Distribution 167
7.2.1.1 Empty Cells 168
7.2.1.2 Problems in Preparing a Contingency Table
on Metric Data 169
7.2.2 Multiple Response Tables and Other Features 169
Contents xiii
7.2.2.1 Features of a Table 170
7.2.3 Other Statistical Tables 171
7.2.3.1 What Is a Good Statistical Table? 171
7.3 Rates and Ratios 172
7.3.1 Proportion, Rate, and Ratio 172
7.3.1.1 Proportion 172
7.3.1.2 Rate 172
7.3.1.3 Ratio 173
7.4 Central and Other Locations 174
7.4.1 Central Values: Mean, Median, and Mode 174
7.4.1.1 Understanding Mean, Median, and Mode 174
7.4.1.2 Calculation in Case of Grouped Data 175
7.4.1.3 Which Central Value to Use? 176
7.4.1.4 Geometric Mean 178
7.4.1.5 Harmonic Mean 178
7.4.2 Other Locations: Quantiles 180
7.4.2.1 Quantiles in Ungrouped Data 180
7.4.2.2 Quantiles in Grouped Data 180
7.4.2.3 Interpretation 182
7.5 Measuring Variability 183
7.5.1 Variance and Standard Deviation 184
7.5.1.1 Variance and Standard Deviation
in Ungrouped Data 185
7.5.1.2 Variance and Standard Deviation in Grouped Data 186
7.5.2 Coefficient of Variation 186
References 188
8 Presentation of Variation by Figures 189
8.1 Graphs for Frequency Distribution 190
8.1.1 Histogram and Its Variants 190
8.1.1.1 Histogram 190
8.1.1.2 Stem-and-Leaf Plot 192
8.1.1.3 Line Histogram 192
8.1.2 Polygon and Its Variants 192
8.1.2.1 Frequency Polygon 193
8.1.2.2 Area Diagram 193
8.1.3 Frequency Curve 193
8.2 Pie, Bar, and Line Diagrams 194
8.2.1 Pie Diagram 194
8.2.1.1 Useful Features of Pie Diagram 194
8.2.2 Bar Diagram 195
8.2.3 Scatter and Line Diagrams 197
8.2.3.1 Scatter Diagram 197
8.2.3.2 Line Diagram 198
8.2.3.3 Complex Line Diagrams 199
8.2.4 Choice and Cautions in Visual Display of Data 200
xiv Contents
8.2.5 Mixed and Three-Dimensional Diagrams 202
8.2.5.1 Mixed Diagram 202
8.2.5.2 Box-and-Whiskers Plot 202
8.2.5.3 Three-Dimensional Diagram 204
8.2.5.4 Biplot 204
8.2.5.5 Nomogram 204
8.3 Special Diagrams in Health and Medicine 206
8.3.1 Diagrams Used in Public Health 206
8.3.1.1 Epidemic Curve 206
8.3.1.2 Lexis Diagram 207
8.3.2 Diagrams Used in Individual Care and Research 208
8.3.2.1 Growth Charts 208
8.3.2.2 Partogram 209
8.3.2.3 Dendrogram 210
8.4 Charts and Maps 211
8.4.1 Charts 211
8.4.1.1 Schematic Chart 212
8.4.1.2 Pedigree Chart 212
8.4.2 Maps 213
8.4.2.1 Spot Map 213
8.4.2.2 Thematic Choroplethic Map 214
8.4.2.3 Cartogram 215
References 215
9 Some Quantitative Aspects of Medicine 219
9.1 Some Epidemiological Measures of Health and Disease 220
9.1.1 Epidemiological Indicators of Neonatal Health 221
9.1.1.1 Birth Weight 221
9.1.1.2 Apgar Score 222
9.1.2 Epidemiological Indicators of Growth in Children 222
9.1.2.1 Weight-for-Age 223
9.1.2.2 Weight-for-Height and Height-for-Age 223
9.1.2.3 Z-Scores and Percent of Median 223
9.1.2.4 Growth Velocity 225
9.1.2.5 Skinfold Thickness 225
9.1.2.6 Development 226
9.1.3 Epidemiological Indicators of Adolescent Health 226
9.1.3.1 Growth in Height and Weight in Adolescence 226
9.1.3.2 Sexual Maturity Rating 227
9.1.4 Epidemiological Indicators of Adult Health 227
9.1.4.1 Obesity 227
9.1.4.2 Smoking 228
9.1.4.3 Physiological Functions 231
9.1.4.4 Quality of Life 231
9.1.5 Epidemiological Indicators of Geriatric Health 232
9.1.5.1 Activities of Daily Living 232
Contents xv
9.1.5.2 Mental Health of the Elderly 232
9.2 Reference Values 233
9.2.1 Gaussian and Other Distributions 233
9.2.1.1 Properties of a Gaussian Distribution 234
9.2.1.2 Other Distributions 235
9.2.2 Reference or Normal Values 236
9.2.2.1 Implications of Normal Values 237
9.2.3 Normal Range 237
9.2.3.1 Disease Threshold 238
9.2.3.2 Clinical Threshold 238
9.2.3.3 Statistical Threshold 239
9.3 Measurement of Uncertainty: Probability 241
9.3.1 Elementary Laws of Probability 241
9.3.1.1 Law of Multiplication 241
9.3.1.2 Law of Addition 242
9.3.2 Probability in Clinical Assessments 244
9.3.2.1 Probabilities in Diagnosis 244
9.3.2.2 Forwarding Diagnosis 246
9.3.2.3 Assessment of Prognosis 246
9.3.2.4 Choice of Treatment 247
9.3.3 Further on Diagnosis: Bayes' Rule 247
9.3.3.1 Bayes' Rule 247
9.3.3.2 Extension of Bayes' Rule 249
9.4 Validity of Medical Tests 250
9.4.1 Sensitivity and Specificity 251
9.4.1.1 Features of Sensitivity and Specificity 252
9.4.1.2 Likelihood Ratio 253
9.4.2 Predictivities 254
9.4.2.1 Positive and Negative Predictivity 254
9.4.2.2 Predictivity and Prevalence 255
9.4.2.3 The Meaning of Prevalence for Predictivity 257
9.4.2.4 Features of Positive and Negative Predictivities 257
9.4.3 Combination of Tests 259
9.4.3.1 Tests in Series 259
9.4.3.2 Tests in Parallel 259
9.4.3.3 Gains from a Test 260
9.4.3.4 When Can a Test Be Avoided? 262
9.4.5 Search for the Best Criterion: ROC Curve 263
9.4.5.1 Sensitivity-Specificity Based ROC Curve 263
9.4.5.2 Predictivities Based ROC Curve 265
References 267
10 Clinimetrics and Evidence-Based Medicine 271
10.1 Indicators, Indexes, and Scores 272
10.1.1 Indicators 272
10.1.1.1 Merits and Demerits of Indicators 272
xvi Contents
10.1.1.2 Choice of Indicators 273
10.1.2 Indexes 274
10.1.2.1 Some Commonly Used Indexes 274
10.1.2.2 Advantages and Limitations of Indexes 275
10.1.3 Scores 276
10.1.3.1 Scoring System for Diagnosis 277
10.1.3.2 Scoring for Gradation of Severity 279
10.2 Clinimetrics 280
10.2.1 Method of Scoring 280
10.2.1.1 Method of Scoring for Graded Characteristics. 280
10.2.1.2 Method of Scoring for Diagnosis 281
10.2.2 Validity and Reliability of a Scoring System 283
10.2.2.1 Validity of Scoring System 284
10.2.2.2 Reliability of a Scoring System 285
10.3 Evidence-Based Medicine 285
10.3.1 Decision Analysis 286
10.3.1.1 Decision Tree 286
10.3.2 Statistical Tools for Evidence-Based Medicine 291
10.3.2.1 Etiology Diagram 291
10.3.2.2 Expert System 292
References 294
11 Measurement of Community Health 299
11.1 Indicators of Mortality 300
11.1.1 Crude and Standardized Death Rates 300
11.1.1.1 Crude Death Rate 300
11.1.1.2 Age-Specific Death Rate 300
11.1.1.3 Standardized Death Rate 301
11.1.1.4 Comparative Mortality Ratio 305
11.1.2 Specific Mortality Rates 305
11.1.2.1 Fetal Deaths and Mortality in Children 305
11.1.2.2 Maternal Mortality 309
11.1.2.3 Adult Mortality 309
11.1.2.4 Other Measures of Mortality 310
11.1.3 Death Spectrum 311
11.2 Measures of Morbidity 312
11.2.1 Prevalence and Incidence 312
11.2.1.1 Point Prevalence 312
11.2.1.2 Period Prevalence 313
11.2.1.3 Incidence 313
11.2.1.4 The Concept of Person-Time 314
11.2.1.5 Capture-Recapture Methodology 314
11.2.2 Duration of Morbidity 316
11.2.2.1 Prevalence in Relation to Duration
of Morbidity 316
11.2.2.2 Incidence from Prevalence 317
Contents xvii
11.2.2.3 Epidemiologically Consistent Estimates 318
11.2.3 Morbidity Measures for Acute Conditions 319
11.2.3.1 Attack Rates 319
11.2.3.2 Disease Spectrum 320
11.3 Indicators of Social and Mental Health 322
11.3.1 Indicators of Social Health 322
11.3.1.1 Education 322
11.3.1.2 Income 323
11.3.1.3 Occupation 324
11.3.1.4 Socioeconomic Status 324
11.3.1.5 Gender Empowerment 325
11.3.1.6 Dependency Ratio 326
11.3.2 Indicators of Health Resources 326
11.3.2.1 Health Infrastructure 327
11.3.2.2 Health Expenditure 328
11.3.3 Indicators of Lack of Mental Health 329
11.3.3.1 Smoking and Other Addictions 329
11.3.3.2 Divorces 329
11.3.3.3 Vehicular Accidents and Crimes 329
11.3.3.4 Others Measures of Lack of Mental Health 330
11.4 Composite Indexes of Health 331
11.4.1 Indexes of Status of Comprehensive Health 331
11.4.1.1 Human Development Index 331
11.4.1.2 Quality of Life Index 332
11.4.2 Indexes of Health Gap 333
11.4.2.1 DALYs Lost 333
11.4.2.2 Human Poverty Index 334
11.4.2.3 Index of Need for Health Resources 335
References 335
12 Confidence Intervals, Principles of Tests of Significance,
and Sample Size 337
12.1 Sampling Distributions 338
12.1.1 Basic Concepts 338
12.1.1.1 Sampling Error 338
12.1.1.2 Point Estimate 338
12.1.1.3 Standard Error of p and x 339
12.1.2 Sampling Distribution of p and x 341
12.1.2.1 Gaussian Conditions 341
12.1.2.2 Assessing Gaussian Pattern for Small n 343
12.1.3 Obtaining Probabilities from a Gaussian Distribution 343
12.1.3.1 Gaussian Probability 344
12.1.3.2 Continuity Correction 345
12.1.3.3 Probabilities Relating to the Mean
and the Proportion 346
12.1.4 The Case of a Not Known (/-Distribution) 347
xviii Contents
12.2 Confidence Intervals 348
12.2.1 Confidence Interval for ir (Large n) and fi
(Gaussian Conditions) 348
12.2.1.1 Confidence Interval for
Proportion tt (Large ri) 349
12.2.1.2 Lower and Upper Bounds for tt (Large ri) 351
12.2.1.3 Confidence Interval for Mean fi (Large n) 351
12.2.1.4 Confidence Bounds for Mean fi 354
12.2.2 Confidence Interval for Differences (Large n) 355
12.2.2.1 Two Independent Samples 355
12.2.2.2 Paired Samples 356
12.2.3 Confidence Interval for it (Small n)
and fj. (Small n): Non-Gaussian Conditions 358
12.2.3.1 Confidence Interval for tt (Small ri) 358
12.2.3.2 Confidence Bound for tt When the Success or
the Failure Rate in the Sample Is Zero Percent. 360
12.2.3.3 Confidence Interval for Median
(Small ri): Non-Gaussian Conditions 362
12.3 P-Values and Statistical Significance 364
12.3.1 What Is Statistical Significance? 364
12.3.1.1 Court Judgment 364
12.3.1.2 Errors in Diagnosis 365
12.3.1.3 Null Hypothesis 365
12.3.1.4 Philosophical Basis of Statistical Tests 366
12.3.1.5 Alternative Hypothesis 367
12.3.1.6 One-Sided Alternatives: Which Tail
Is Wagging? 367
12.3.2 Errors, P-Values, and Power 368
12.3.2.1 Type-I Error 368
12.3.2.2 Type-H Error 369
12.3.2.3 Type-Hi Error 370
12.3.2.4 Power 370
12.3.3 General Procedure to Obtain P-value 371
12.4 Initial Debate on Statistical Significance 375
12.4.1 Confidence Interval versus Test of Ho 376
12.4.2 Medical Significance versus Statistical Significance 377
12.5 Sample Size Determination in Some Cases 379
12.5.1 Sample Size Required in Estimation Setup 380
12.5.1.1 General Considerations in the Estimation
Setup 380
12.5.1.2 General Procedure for Determining Size
of Sample for Estimation 382
12.5.1.3 Formulas for Sample Size Calculation
for Estimation in Simple Situations 384
12.5.2 Sample Size for Testing a Hypothesis
with Specified Power 386
Contents xix
12.5.2.1 General Considerations in a
Testing-of-Hypothesis Setup 387
12.5.2.2 Sample Size Formulas for Test
of Hypothesis in Simple Situations 388
12.5.2.3 Nomograms and Tables of Sample Size 391
12.5.2.4 Thumb Rules 392
12.5.2.5 Power Analysis 392
References 393
13 Inference from Proportions 395
13.1 One Qualitative Variable 396
13.1.1 Dichotomous Categories: Binomial Distribution 396
13.1.1.1 Binomial Distribution 396
13.1.1.2 Large n: Gaussian Approximation to Binomial. 398
13.1.2 Polytomous Categories (Large n):
Goodness-of-Fit Test 399
13.1.2.1 Chi-Square and Its Explanation 400
13.1.2.2 Degrees of Freedom 401
13.1.2.3 Cautions in Using Chi-Square 402
13.1.2.4 Further Analysis (Partitioning of Table) 404
13.1.3 Polytomous Categories (Small n):
Exact Multinomial Test 405
13.1.3.1 Goodness-of-Fit in Small Samples 405
13.2 Proportions in 2 X 2 Tables 407
13.2.1 Structure of 2 X 2 Table in Different Types of Study 408
13.2.1.1 Structure in Prospective Study 408
13.2.1.2 Structure in Retrospective Study 408
13.2.1.3 Structure in Cross-Sectional Study 408
13.2.2 Two Independent Samples (Large n): Chi-Square Test 408
13.2.2.1 Chi-Square Test 409
13.2.2.2 Yate's Correction for Continuity 410
13.2.2.3 Z-Test for Proportions 411
13.2.2.4 Detecting a Medically Important Difference
in Proportions 411
13.2.2.5 Equivalence Tests 413
13.2.2.6 Crossover Design with Binary Response
(Large n) 415
13.2.3 Two Independent Samples (Small n): Fisher's Exact Test 417
13.2.3.1 Fisher's Exact Test 417
13.2.3.2 Crossover Design (Small n) 417
13.2.4 Proportions in Matched Pairs: McNemar's Test
(Large n) and Exact Test (Small n) 418
13.2.4.1 Large n: McNemar's Test 419
13.2.4.2 Small n: Exact Test (Matched Pairs) 420
13.2.4.3 Comparison of Two Tests for Sensitivity
and Specificity 421
xx Contents
13.3 Analysis of R X C Tables (Large ri) 423
13.3.1 One Dichototnous and the Other Polytomous
Variable (2 X C Table) 423
13.3.1.1 The Test Criterion 424
13.3.1.2 Trend in Proportions in Ordinal Categories 425
13.3.2 Two Polytomous Variables 427
13.4 Three-Way Tables 429
13.4.1 Assessment of Association in Three-Way Tables 430
13.4.2 Log-Linear Models 433
13.4.2.1 Log-Linear Model for Two-Way Tables 433
13.4.2.2 Log-Linear Model for Three-Way Tables 434
References 436
14 Relative Risk and Odds Ratio 439
14.1 Relative and Attributable Risks (Large n) 439
14.1.1 Risk, Hazard, and Odds 439
14.1.1.1 Risk 440
14.1.1.2 Hazard 440
14.1.1.3 Odds 440
14.1.1.4 Ratios of Risks and Odds 440
14.1.2 Relative Risk 441
14.1.2.1 RR in Independent Samples 441
14.1.2.2 Confidence Interval for RR
(Independent Samples) 443
14.1.2.3 Test of Hypothesis on RR
(Independent Samples) 445
14.1.2.4 RR in the Case of Matched Pairs 446
14.1.3 Attributable Risk 447
14.1.3.1 AR in Independent Samples 447
14.1.3.2 AR in Matched Pairs 448
14.1.3.3 Number Needed to Treat 450
14.1.3.4 Relative Risk Reduction 451
14.1.3.5 Population Attributable Risk 451
14.2 Odds Ratio 452
14.2.1 OR in Two Independent Samples 452
14.2.1.1 CI for OR (Independent Samples) 455
14.2.1.2 Test of Hypothesis on OR
(Independent Samples) 455
14.2.2 OR in Matched Pairs 457
14.2.2.1 Confidence Interval for OR (Matched Pairs) 458
14.2.2.2 Test of Hypothesis on OR (Matched Pairs) 458
14.2.2.3 Multiple Controls 460
14.3 Stratified Analysis and Sample Size 460
14.3.1 Mantel-Haenszel Procedure 461
14.3.2 Sample Size Requirement for Inference on RR and OR 464
References 468
Contents xxi
15 Inference from Means 469
15.1 Comparison of Means in One and Two Groups
(Gaussian Conditions): Student's /-Test 470
15.1.1 Comparison with a Prespecified Mean 470
15.1.1.1 Student's/-Test for One Sample 471
15.1.2 Difference in Means in Two Samples 473
15.1.2.1 Paired Samples Setup 473
15.1.2.2 Unpaired (Independent) Samples Setup 474
15.1.2.3 Some Features of Student's / 476
15.1.2.4 Difference-in-Differences Approach 478
15.1.3 Analysis of Crossover Designs 478
15.1.3.1 Test for Group Effect 479
15.1.3.2 Test for Carry-Over Effect 480
15.1.3.3 Test for Treatment Effect 480
15.1.4 Analysis of Data of Up-and-Down Trials 481
15.2 Comparison of Means in Three or More Groups
(Gaussian Conditions): ANOVA F-Test 482
15.2.1 One-Way ANOVA 483
15.2.1.1 Mathematical Details 484
15.2.1.2 The Procedure to Test H,, 485
15.2.1.3 Checking the Validity of the Assumptions
of ANOVA 489
15.2.2 Two-Way ANOVA 490
15.2.2.1 Two-Factor Design 490
15.2.2.2 The Hypotheses and Their Test 491
15.2.2.3 Main Effect and Interaction (Effect) 494
15.2.2.4 Repeated Measures 496
15.2.3 Multiple Comparisons: Bonferroni and Tukey Tests 497
15.2.3.1 Bonferroni Procedure 497
15.2.3.2 Tukey Test 498
15.3 Non-Gaussian Conditions: Nonparametric Tests for Location 499
15.3.1 Comparison of Two Groups: Wilcoxon Tests 500
15.3.1.1 Case I: Paired Data 500
15.3.1.2 Case II: Independent Samples 504
15.3.2 Comparison of Three or More Groups:
Kruskal-Wallis Test 506
15.3.3 Two-Way Layout: Friedman Test 508
15.4 When Significant Is Not Significant 511
15.4.1 The Nature of Statistical Significance 511
15.4.2 Testing for Presence of Medically Important
Difference in Means 517
15.4.2.1 Detecting Specified Difference in Mean 518
15.4.2.2 Equivalence Tests 519
15.4.3 Power and Level of Significance 519
15.4.3.1 Balancing Type-I and Type-II Error 522
References 522
xxii Contents
16 Relationships: Quantitative Data 525
16.1 Some General Features of a Regression Setup 527
16.1.1 Dependent and Independent Variables 527
16.1.1.1 Simple, Multiple, and Multivariate
Regression 528
16.1.2 Linear, Curvilinear, and Nonlinear Regressions 529
16.1.2.1 Linear Regression 529
16.1.2.2 Curvilinear Regression 531
16.1.2.3 Nonlinear Relationships 531
16.1.3 The Concept of Residuals 533
16.1.4 General Method of Fitting a Regression 533
16.2 Linear Regression Models 535
16.2.1 Testing Adequacy of a Regression Fit 537
16.2.1.1 Goodness of Fit and R2 537
16.2.1.2 Stepwise Procedure 538
16.2.1.3 Statistical Significance of Individual
Regression Coefficients 539
16.2.1.4 Validity of Assumptions 539
16.2.2 Interpretation of the Regression Coefficients 544
16.3 Some Issues in Regression 547
16.3.1 Confidence Interval, Confidence Band, and Tests 547
16.3.1.1 SEs and CIs for the Regression 547
16.3.1.2 Confidence Band 548
16.3.1.3 Equality of Two Regression Lines 549
16.3.1.4 Difference-in-Differences Approach with
Regression 550
16.3.2 Some Variations of Regression 551
16.3.2.1 Ridge Regression 551
16.3.2.2 Multilevel Regression 551
16.3.2.3 Analysis of Covariance 553
16.4 Measuring the Strength of Quantitative Relationship 554
16.4.1 Product-Moment and Related Correlations 554
16.4.1.1 Multiple Correlation 554
16.4.1.2 Product-Moment Correlation 555
16.4.1.3 Covariance 555
16.4.1.4 Statistical Significance of r 559
16.4.1.5 Intraclass Correlation 560
16.4.1.6 Serial Correlation 560
16.4.2 Rank Correlation 560
16.4.2.1 Spearman's Rho 561
16.4.2.2 Kendall's Tau and Goodman-Kruskal
Gamma 562
16.5 Assessment of Agreement 563
16.5.1 Agreement in Quantitative Measurements 563
16.5.1.1 Statistical Formulation of the Problem 564
Contents xxiii
16.5.2 Approaches for Measuring Quantitative Agreement 564
16.5.2.1 Limits of Disagreement Approach 564
16.5.2.2 Intraclass Correlation as a Measure
of Agreement 566
16.5.2.3 Relative Merits of the Two Methods 567
References 569
17 Relationships: Qualitative Dependent 571
17.1 Binary Dependent: Logistic Regression (Large n) 572
17.1.1 Meaning of a Logistic Model 572
17.1.2 Assessing Overall Adequacy of a Logistic
Regression 575
17.1.2.1 Log Likelihood 575
17.1.2.2 Classification Accuracy 577
17.1.2.3 Hosmer-Lemeshow Test 577
17.2 Inference from Logistic Coefficients 578
17.2.1 Interpretation of the Logistic Coefficients 578
17.2.1.1 Dichotomous Predictors 578
17.2.1.2 Polytomous and Continuous Predictors 580
17.2.2 Confidence Interval and Test of Hypothesis
on Logistic Coefficients 581
17.3 Issues in Logistic Regression 583
17.3.1 Conditional Logistic for Matched Data 583
17.3.2 Polytomous Dependent 584
17.3.2.1 Nominal Categories: Multinomial Logistic 584
17.3.2.2 Ordinal Categories 585
17.4 Some Models for Qualitative Data 586
17.4.1 Cox Regression for Hazards 587
17.4.2 Classification and Regression Trees 589
17.5 Strength of Relationship in Qualitative Variables 590
17.5.1 Both Variables Qualitative 590
17.5.1.1 Dichotomous Categories 590
17.5.1.2 Polytomous Categories 592
17.5.1.3 Proportional Reduction in Error 594
17.5.2 One Qualitative and the Other Quantitative Variable 596
17.5.3 Agreement in Qualitative Measurements 597
17.5.3.1 The Meaning of Qualitative Agreement 597
17.5.3.2 Cohen's Kappa 598
References 599
18 Survival Analysis 601
18.1 Life Expectancy 602
18.1.1 Life Table 602
18.1.2 Other Forms of Life Expectancy 606
18.1.2.1 Potential Years of Life Lost 606
18.1.2.2 Healthy Life Expectancy 607
xxiv Contents
18.1.2.3 Life Expectation Related to a Cause of Death 607
18.1.2.4 Application to Other Setups 607
18.2 Analysis of Survival Data 608
18.2.1 Nature of Survival Data 609
18.2.1.1 Types of Censoring 609
18.2.1.2 Collection of Survival Time Data 610
18.2.2 Survival Observed in Time Intervals:
Life Table Method 611
18.2.2.1 Life Table Method 611
18.2.2.2 Survival Function 612
18.2.3 Continuous Observation of Survival Time:
Kaplan-Meier Method 614
18.2.3.1 Kaplan-Meier Method 614
18.2.3.2 Hazard Function 617
18.3 Issues in Survival Analysis 619
18.3.1 Comparison of Survival in Two Groups 619
18.3.1.1 Comparing Survival Rates 619
18.3.1.2 Comparing Survival Experience:
Log-Rank Test 620
18.3.2 Factors Affecting Survival: Cox Model 623
18.3.2.1 Parametric Models 623
18.3.2.2 Cox Model for Survival 623
18.3.3 Sample Size for Survival Studies 625
References 626
19 Simultaneous Consideration of Several Variables 627
19.1 Scope of Multivariate Methods 628
19.1.1 The Essentials of a Multivariate Setup 628
19.1.2 Statistical Limitation on the Number of Variables 630
19.2 Dependent and Independent Sets of Variables 630
19.2.1 Dependents and Independents Both Quantitative:
Multivariate Multiple Regression 631
19.2.2 Quantitative Dependents and Qualitative Independents:
Multivariate Analysis of Variance (MANOVA) 635
19.2.3 Classification of Subjects into Known Groups:
Discriminant Analysis 638
19.2.3.1 Discriminant Analysis 638
19.2.3.2 Classification Rule 639
19.2.3.3 Classification Accuracy 640
19.3 Identification of Structure in the Observationas 643
19.3.1 Identification of Clusters of Subjects: Cluster Analysis 644
19.3.1.1 Measures of Similarity 644
19.3.1.2 Hierarchical Agglomerative Algorithm 645
19.3.1.3 Deciding on the Number of Natural Clusters 646
19.3.2 Identification of Unobservable Underlying Factors:
Factor Analysis 648
Contents xxv
19.3.2.1 Factor Analysis 649
19.3.2.2 Features of a Successful Factor Analysis 651
19.3.2.3 Factor Scores 652
References 653
20 Quality Considerations 655
20.1 Statistical Quality Control in Medical Care 656
20.1.1 Statistical Control of Medical Care Errors 657
20.1.1.1 Adverse Patient Outcomes 657
20.1.1.2 Monitoring Fatality 658
20.1.1.3 Limits of Tolerance 658
20.1.2 Quality of Lots 659
20.1.2.1 The Lot Quality Method 660
20.1.2.2 LQAS in Health Assessment 660
20.1.3 Quality Control in a Medical Laboratory 661
20.1.3.1 Control Chart 661
20.1.3.2 Cusum Chart 662
20.2 Quality of Measurements 664
20.2.1 Validity of Instruments 664
20.2.1.1 Types of Validity 665
20.2.2 Reliability of Instruments 666
20.2.2.1 Internal Consistency 667
20.2.2.2 Cronbach's Alpha 667
20.2.2.3 Test-Retest Reliability 669
20.3 Quality of Statistical Models: Robustness 670
20.3.1 External Validation 672
20.3.1.1 Split-Sample Method 672
20.3.1.2 Another Sample Method 672
20.3.2 Sensitivity Analysis and Uncertainty Analysis 673
20.3.2.1 Sensitivity Analysis 673
20.3.2.2 Uncertainty Analysis 674
20.3.3 Resampling 675
20.3.3.1 Bootstrapping 676
20.3.3.2 Jackknife Resampling 676
20.4 Quality of Data 677
20.4.1 Errors in Measurement 677
20.4.1.1 Lack of Standardization in Definitions 677
20.4.1.2 Lack of Care in Obtaining or Recording
Information 677
20.4.1.3 Inability of the Observer to Get Confidence
of the Respondent 678
20.4.1.4 Bias of the Observer 678
20.4.1.5 Variable Competence of the Observers 678
20.4.2 Missing Values 679
20.4.2.1 Handling Nonresponse 680
20.4.2.2 Imputations 683
xxvi Contents
20.4.2.3 Intention-to-Treat Analysis 683
20.4.3 Lack of Standardization in Values 685
20.4.3.1 Standardization Methods Already
Described 685
20.4.3.2 Standardization for Calculating
Adjusted Rates 685
20.4.3.3 Standardized Mortality Ratio 686
References 688
21 Statistical Fallacies 691
21.1 Problems with the Sample 692
21.1.1 Biased Sample 692
21.1.1.1 Survivors 692
21.1.1.2 Volunteers 693
21.1.1.3 Clinical Subjects 693
21.1.1.4 Inadequate Size of the Sample 694
21.1.1.5 Publication Bias 695
21.1.1.6 Inadequate Specification of Sampling
Method 695
21.1.1.7 Abrupt Series 695
21.1.2 Incomparable Groups 695
21.1.2.1 Differential in Group Composition 695
21.1.2.2 Differential Definitions 697
21.1.2.3 Differential Compliance 698
21.1.2.4 Variable Periods of Exposure 698
21.1.2.5 Improper Denominator 699
21.1.3 Mixing of Distinct Groups 700
21.1.3.1 Effect on Regression 701
21.1.3.2 Effect on Shape of the Distribution 702
21.1.3.3 Lack of Intragroup Homogeneity 702
21.2 Errors in Presentation of Findings 703
21.2.1 Misuse of Percentages and Means 703
21.2.1.1 Misuse of Percentages 703
21.2.1.2 Misuse of Means 704
21.2.1.3 Unnecessary Decimals 705
21.2.2 Problems in Reporting 706
21.2.2.1 Incomplete Reporting 706
21.2.2.2 Over-Reporting 707
21.2.2.3 Self-Reporting versus Objective
Measurement 707
21.2.2.4 Misuse of Graphs 708
21.3 Inadequate Analysis 709
21.3.1 Ignoring Reality 709
21.3.1.1 Looking for Linearity 709
21.3.1.2 Assumptions Overlooked 709
Contents xxvii
21.3.1.3 Area under the Concentration Curve 710
21.3.1.4 Anomalous Person-Years 711
21.3.2 Mean or Proportion? 711
21.3.3 Forgetting Baseline Values 712
21.3.4 Misuse of Statistical Packages 713
21.3.4.1 Over-Analysis 713
21.3.4.2 Data Dredging 714
21.3.4.3 Quantitative Analysis of Codes 714
21.3.4.4 Soft Data versus Hard Data 714
21.4 Misinterpretation 715
21.4.1 Misuse of P-Values 715
21.4.1.1 Magic Threshold 0.05 715
21.4.1.2 One-Tail or Two-Tail P-Values 716
21.4.1.3 Multiple Comparisons 716
21.4.1.4 Dramatic P-Values 716
21.4.1.5 P-Values for Nonrandom Sample 716
21.4.1.6 "Normal" with Respect to Several
Parameters 717
21.4.2 Correlation versus Cause-Effect Relationship 717
21.4.2.1 Criteria for Cause-Effect 718
21.4.2.2 Other Considerations 719
21.4.3 Sundry Issues 720
21.4.3.1 Diagnostic Test Is Only an Additional
Adjunct 720
21.4.3.2 Medical Significance versus Statistical
Significance 720
21.4.3.3 Interpretation of Standard Error (p) 721
21.4.3.4 Univariate Analysis but Multivariate
Conclusions 721
21.4.3.5 Limitation of Relative Risk 722
21.4.4 Final Comments 722
References 723
Appendix 1 Statistical Software 727
Al.l General Purpose Statistical Software 727
A1.2 Special Purpose Statistical Software 729
Appendix 2 Some Statistical Tables 731
Index 737 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Indrayan, Abhaya |
| author_facet | Indrayan, Abhaya |
| author_role | aut |
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| building | Verbundindex |
| bvnumber | BV023322375 |
| callnumber-first | R - Medicine |
| callnumber-label | RA407 |
| callnumber-raw | RA407 |
| callnumber-search | RA407 |
| callnumber-sort | RA 3407 |
| callnumber-subject | RA - Public Medicine |
| classification_rvk | SK 950 |
| ctrlnum | (OCoLC)156994633 (DE-599)BVBBV023322375 |
| dewey-full | 610.7/27 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 610 - Medicine and health |
| dewey-raw | 610.7/27 |
| dewey-search | 610.7/27 |
| dewey-sort | 3610.7 227 |
| dewey-tens | 610 - Medicine and health |
| discipline | Mathematik Medizin |
| discipline_str_mv | Mathematik Medizin |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV023322375 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:54:15Z |
| indexdate | 2024-07-09T21:15:51Z |
| institution | BVB |
| isbn | 9781584888871 1584888873 |
| language | English |
| lccn | 2007030353 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016506449 |
| oclc_num | 156994633 |
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| owner | DE-20 DE-19 DE-BY-UBM |
| owner_facet | DE-20 DE-19 DE-BY-UBM |
| physical | xlvii, 771 p. ill. 25 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Chapman & Hall/CRC biostatistics series |
| series2 | Chapman & Hall/CRC biostatistics series |
| spelling | Indrayan, Abhaya Verfasser aut Medical biostatistics A. Indrayan 2. ed. Boca Raton [u.a.] Chapman & Hall/CRC 2008 xlvii, 771 p. ill. 25 cm txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC biostatistics series 25 Includes bibliographical references and index Medical statistics Biometry Biometry methods Medizinische Statistik (DE-588)4127563-9 gnd rswk-swf Biostatistik (DE-588)4729990-3 gnd rswk-swf Medizinische Statistik (DE-588)4127563-9 s Biostatistik (DE-588)4729990-3 s DE-604 Chapman & Hall/CRC biostatistics series 25 (DE-604)BV023097394 25 http://www.loc.gov/catdir/enhancements/fy0733/2007030353-d.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016506449&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Indrayan, Abhaya Medical biostatistics Chapman & Hall/CRC biostatistics series Medical statistics Biometry Biometry methods Medizinische Statistik (DE-588)4127563-9 gnd Biostatistik (DE-588)4729990-3 gnd |
| subject_GND | (DE-588)4127563-9 (DE-588)4729990-3 |
| title | Medical biostatistics |
| title_auth | Medical biostatistics |
| title_exact_search | Medical biostatistics |
| title_exact_search_txtP | Medical biostatistics |
| title_full | Medical biostatistics A. Indrayan |
| title_fullStr | Medical biostatistics A. Indrayan |
| title_full_unstemmed | Medical biostatistics A. Indrayan |
| title_short | Medical biostatistics |
| title_sort | medical biostatistics |
| topic | Medical statistics Biometry Biometry methods Medizinische Statistik (DE-588)4127563-9 gnd Biostatistik (DE-588)4729990-3 gnd |
| topic_facet | Medical statistics Biometry Biometry methods Medizinische Statistik Biostatistik |
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