Fundamentals of Biostatistics

Cover Page......Page 1
Title Page......Page 4
Copyright Page......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 15
CHAPTER 1 General Overview......Page 21
Reference......Page 24
2.1 Introduction......Page 25
2.2 Measures of Location......Page 26
The Arithmetic Mean......Page 27
The Median......Page 29
Comparison of the Arithmetic Mean and the Median......Page 30
The Mode......Page 31
The Geometric Mean......Page 32
2.3 Some Properties of the Arithmetic Mean......Page 33
The Range......Page 35
Quantiles......Page 36
The Variance and Standard Deviation......Page 37
2.5 Some Properties of the Variance and Standard Deviation......Page 38
2.6 The Coefficient of Variation......Page 40
2.7 Grouped Data......Page 42
2.8 Graphic Methods......Page 44
Stem-and-Leaf Plots......Page 45
Box Plots......Page 46
2.9 Case Study 1: Effects of Lead Exposure on Neurological and Psychological Function in Children......Page 49
2.10 Case Study 2: Effects of Tobacco Use on Bone-Mineral Density in Middle-Aged Women......Page 50
2.12 Summary......Page 51
Hypertension......Page 54
Nutrition......Page 55
Microbiology......Page 56
Endocrinology......Page 57
Infectious Disease......Page 53
3.1 Introduction......Page 58
3.2 Definition of Probability......Page 59
3.3 Some Useful Probabilistic Notation......Page 60
3.4 The Multiplication Law of Probability......Page 62
3.5 The Addition Law of Probability......Page 64
3.6 Conditional Probability......Page 66
3.7 Bayes’ Rule and Screening Tests......Page 71
Bayes’ Rule......Page 73
3.8 Bayesian Inference......Page 76
3.9 ROC Curves......Page 77
3.10 Prevalence and Incidence......Page 79
PROBLEMS......Page 80
Genetics......Page 81
Pulmonary Disease......Page 82
Pulmonary Disease......Page 83
Otolaryngology......Page 84
Mental Health......Page 85
Cardiovascular Disease......Page 86
Genetics......Page 87
Cardiovascular Disease......Page 88
Obstetrics, Health Promotion......Page 89
4.1 Introduction......Page 91
4.2 Random Variables......Page 92
Relationship of Probability Distributions to Frequency Distributions......Page 93
4.4 The Expected Value of a Discrete Random Variable......Page 95
4.5 The Variance of a Discrete Random Variable......Page 96
4.6 The Cumulative-Distribution Function of a Discrete Random Variable......Page 98
4.7 Permutations and Combinations......Page 99
4.8 The Binomial Distribution......Page 103
Using Binomial Tables......Page 104
Using “Electronic” Tables......Page 107
4.9 Expected Value and Variance of the Binomial Distribution......Page 108
4.10 The Poisson Distribution......Page 110
Using Poisson Tables......Page 113
Electronic Tables for the Poisson Distribution......Page 114
4.12 Expected Value and Variance of the Poisson Distribution......Page 115
4.13 Poisson Approximation to the Binomial Distribution......Page 116
PROBLEMS......Page 119
Otolaryngology......Page 120
Pediatrics, Otolaryngology......Page 121
Health Promotion......Page 122
Ophthalmology, Diabetes......Page 123
Endocrinology......Page 124
Genetics, Ophthalmology......Page 125
Obstetrics......Page 126
5.2 General Concepts......Page 128
5.3 The Normal Distribution......Page 131
5.4 Properties of the Standard Normal Distribution......Page 134
Using Normal Tables......Page 135
Using Electronic Tables for the Normal Distribution......Page 138
5.5 Conversion from an N(μ, σ2) Distribution to an N(0,1) Distribution......Page 140
5.6 Linear Combinations of Random Variables......Page 144
Dependent Random Variables......Page 146
5.7 Normal Approximation to the Binomial Distribution......Page 149
5.8 Normal Approximation to the Poisson Distribution......Page 155
5.9 Summary......Page 157
Hypertension......Page 158
Cancer......Page 159
Cardiovascular Disease......Page 160
Hypertension......Page 161
Endocrinology......Page 162
Cardiovascular Disease......Page 163
Ophthalmology......Page 164
Ophthalmology......Page 165
Obstetrics......Page 166
Ophthalmology, Genetics......Page 167
Hypertension......Page 168
6.1 Introduction......Page 169
6.2 The Relationship Between Population and Sample......Page 170
6.3 Random-Number Tables......Page 172
6.4 Randomized Clinical Trials......Page 176
Design Features of Randomized Clinical Trials......Page 178
Point Estimation......Page 180
Standard Error of the Mean......Page 182
Central-Limit Theorem......Page 186
Interval Estimation......Page 188
6.6 Case Study: Effects of Tobacco Use on Bone-Mineral Density (BMD) in Middle-Aged Women......Page 195
Point Estimation......Page 196
The Chi-Square Distribution......Page 197
Interval Estimation......Page 199
Point Estimation......Page 201
Maximum-Likelihood Estimation......Page 202
Interval Estimation—Normal-Theory Methods......Page 204
Interval Estimation—Exact Methods......Page 206
Point Estimation......Page 209
Interval Estimation......Page 210
6.10 One-Sided CIs......Page 213
6.11 Summary......Page 215
Renal Disease......Page 216
Pharmacology......Page 217
Obstetrics......Page 218
Infectious Disease......Page 219
Cardiovascular Disease......Page 220
Sports Medicine......Page 221
Genetics......Page 222
7.2 General Concepts......Page 224
7.3 One-Sample Test for the Mean of a Normal Distribution: One-Sided Alternatives......Page 227
7.4 One-Sample Test for the Mean of a Normal Distribution: Two-Sided Alternatives......Page 235
One-Sample z Test......Page 240
One-Sided Alternatives......Page 241
Two-Sided Alternatives......Page 246
One-Sided Alternatives......Page 248
Sample-Size Determination (Two-Sided Alternatives)......Page 252
Sample-Size Estimation Based on CI Width......Page 253
7.7 The Relationship Between Hypothesis Testing and Confidence Intervals......Page 255
7.8 Bayesian Inference......Page 257
7.9 One-Sample χ2 Test for the Variance of a Normal Distribution......Page 261
Normal-Theory Methods......Page 264
Power and Sample-Size Estimation......Page 269
7.11 One-Sample Inference for the Poisson Distribution......Page 271
7.12 Case Study: Effects of Tobacco Use on Bone-Mineral Density in Middle-Aged Women......Page 276
7.13 Summary......Page 277
Genetics......Page 279
Nutrition......Page 280
Cancer......Page 281
Cancer......Page 282
Endocrinology......Page 283
Environmental Health, Pulmonary Disease......Page 284
Ophthalmology......Page 285
Hypertension, Pediatrics......Page 286
Cancer......Page 287
8.1 Introduction......Page 289
8.2 The Paired t Test......Page 291
8.3 Interval Estimation for the Comparison of Means from Two Paired Samples......Page 295
8.4 Two-Sample t Test for Independent Samples with Equal Variances......Page 296
8.5 Interval Estimation for the Comparison of Means from Two Independent Samples (Equal Variance Case)......Page 300
8.6 Testing for the Equality of Two Variances......Page 301
The F Distribution......Page 302
The F Test......Page 304
8.7 Two-Sample t Test for Independent Samples with Unequal Variances......Page 307
8.8 Case Study: Effects of Lead Exposure on Neurologic and Psychological Function in Children......Page 313
8.9 The Treatment of Outliers......Page 315
Estimation of Sample Size......Page 321
Estimation of Power......Page 323
8.11 Sample-Size Estimation for Longitudinal Studies......Page 324
8.12 Summary......Page 327
Cardiovascular Disease, Pediatrics......Page 329
Ophthalmology......Page 330
Infectious Disease......Page 331
Nutrition......Page 332
Pulmonary Disease......Page 333
Hepatic Disease......Page 334
Hypertension, Pediatrics......Page 335
Hypertension......Page 336
Ophthalmology......Page 337
Cardiovascular Disease......Page 338
Hypertension......Page 339
Health Promotion......Page 340
Cardiovascular Disease......Page 341
Pediatrics......Page 342
Health Promotion......Page 343
Ophthalmology......Page 344
Nutrition......Page 345
9.1 Introduction......Page 347
Normal-Theory Method......Page 349
Exact Method......Page 352
9.3 The Wilcoxon Signed-Rank Test......Page 353
9.4 The Wilcoxon Rank-Sum Test......Page 359
9.6 Summary......Page 364
Otolaryngology, Pediatrics......Page 366
Hypertension......Page 367
Nutrition......Page 368
Cancer......Page 369
Endocrinology......Page 370
10.1 Introduction......Page 372
Normal-Theory Method......Page 373
Contingency-Table Method......Page 377
Significance Testing Using the Contingency-Table Approach......Page 379
Short Computational Form for the Yates-Corrected Chi-Square Test for 2 × 2 Contingency Tables......Page 384
10.3 Fisher’s Exact Test......Page 387
The Hypergeometric Distribution......Page 389
10.4 Two-Sample Test for Binomial Proportions for Matched-Pair Data (McNemar’s Test)......Page 393
Normal-Theory Test......Page 395
Exact Test......Page 397
Independent Samples......Page 401
Paired Samples......Page 403
Sample Size and Power in a Clinical Trial Setting......Page 406
Tests for Association for R × C Contingency Tables......Page 410
Chi-Square Test for Trend in Binomial Proportions......Page 414
Relationship Between the Wilcoxon Rank-Sum Test and the Chi-Square Test for Trend......Page 417
10.7 Chi-Square Goodness-of-Fit Test......Page 421
10.8 The Kappa Statistic......Page 424
10.9 Summary......Page 428
Cardiovascular Disease......Page 429
Cardiovascular Disease......Page 430
Sexually Transmitted Disease......Page 431
Mental Health......Page 432
Pediatrics, Endocrinology......Page 433
Sports Medicine......Page 435
Ophthalmology......Page 436
Zoology......Page 437
Pediatrics, Urology......Page 438
Infectious Disease......Page 439
Health Promotion......Page 440
Mental Health......Page 441
Obstetrics......Page 442
Cardiology......Page 443
Ophthalmology......Page 444
11.1 Introduction......Page 447
11.2 General Concepts......Page 448
11.3 Fitting Regression Lines—The Method of Least Squares......Page 451
11.4 Inferences About Parameters from Regression Lines......Page 455
F Test for Simple Linear Regression......Page 457
t Test for Simple Linear Regression......Page 461
Interval Estimates for Regression Parameters......Page 463
Interval Estimation for Predictions Made from Regression Lines......Page 465
11.6 Assessing the Goodness of Fit of Regression Lines......Page 468
11.7 The Correlation Coefficient......Page 472
Relationship Between the Sample Regression Coefficient (b) and the Sample Correlation Coefficient (r)......Page 473
One-Sample t Test for a Correlation Coefficient......Page 475
One-Sample z Test for a Correlation Coefficient......Page 477
Interval Estimation for Correlation Coefficients......Page 480
Sample-Size Estimation for Correlation Coefficients......Page 482
Two-Sample Test for Correlations......Page 483
Comparison of Dependent Correlation Coefficients......Page 485
Estimation of the Regression Equation......Page 488
Hypothesis Testing......Page 492
Criteria for Goodness of Fit......Page 496
11.10 Case Study: Effects of Lead Exposure on Neurologic and Psychological Function in Children......Page 504
Partial Correlation......Page 511
Multiple Correlation......Page 513
11.12 Rank Correlation......Page 514
11.13 Interval Estimation for Rank-Correlation Coefficients......Page 519
Hematology......Page 524
Cancer......Page 525
Pediatrics, Cardiovascular Disease......Page 526
Pediatrics, Endocrinology......Page 527
Nutrition......Page 528
Ophthalmology......Page 529
Cancer, Endocrinology......Page 530
Ophthalmology......Page 531
Pulmonary Disease......Page 532
Nutrition......Page 534
12.2 One-Way ANOVA—Fixed-Effects Model......Page 536
F Test for Overall Comparison of Group Means......Page 538
t Test for Comparison of Pairs of Groups......Page 542
Linear Contrasts......Page 548
Multiple Comparisons—Bonferroni Approach......Page 551
Multiple-Comparisons Procedures for Linear Contrasts......Page 554
The False-Discovery Rate......Page 556
Application of One-Way ANOVA......Page 558
Relationship Between One-Way ANOVA and Multiple Regression......Page 561
One-Way Analysis of Covariance......Page 565
12.6 Two-Way ANOVA......Page 568
Two-Way ANCOVA......Page 573
12.7 The Kruskal-Wallis Test......Page 575
Comparison of Specific Groups Under the Kruskal-Wallis Test......Page 579
12.8 One-Way ANOVA—The Random-Effects Model......Page 582
12.9 The Intraclass Correlation Coefficient......Page 588
12.10 Mixed Models......Page 592
12.11 Summary......Page 596
Pulmonary Disease......Page 597
Mental Health......Page 598
Bioavailability......Page 599
Endocrinology......Page 600
Environmental Health, Pediatrics......Page 601
Hypertension......Page 602
Cardiovascular Disease......Page 603
Ophthalmology......Page 604
Nutrition, Endocrinology......Page 605
Ophthalmology, Infectious Disease......Page 606
13.2 Study Design......Page 608
13.3 Measures of Effect for Categorical Data......Page 611
The Risk Difference......Page 612
The Risk Ratio......Page 613
The Odds Ratio......Page 615
Interval Estimation for the Odds Ratio......Page 619
13.4 Attributable Risk......Page 621
Confounding......Page 627
Standardization......Page 630
13.6 Methods of Inference for Stratified Categorical Data—The Mantel-Haenszel Test......Page 632
Estimation of the Odds Ratio for Stratified Data......Page 636
Effect Modification......Page 638
Estimation of the OR in Matched-Pair Studies......Page 640
Testing for Trend in the Presence of Confounding—Mantel-Extension Test......Page 642
13.7 Power and Sample-Size Estimation for Stratified Categorical Data......Page 645
General Model......Page 648
Interpretation of Regression Parameters......Page 649
Hypothesis Testing......Page 656
Prediction with Multiple Logistic Regression......Page 662
Assessing Goodness of Fit of Logistic-Regression Models......Page 663
Matched Logistic Regression......Page 669
Polychotomous Logistic Regression......Page 673
Ordinal Logistic Regression......Page 676
13.10 Meta-Analysis......Page 678
Test of Homogeneity of Odds Ratios......Page 681
Inference Based on Confidence-Interval Estimation......Page 683
Sample-Size Estimation for Equivalence Studies......Page 684
13.12 The Cross-Over Design......Page 686
Assessment of Treatment Effects......Page 687
Assessment of Carry-Over Effects......Page 690
Sample-Size Estimation for Cross-Over Studies......Page 692
Hypothesis Testing......Page 694
Power and Sample Size Estimation for Clustered Binary Data......Page 699
Regression Models for Clustered Binary Data......Page 701
13.14 Longitudinal Data Analysis......Page 707
Introduction......Page 716
Measurement-Error Correction with Gold-Standard Exposure......Page 717
Measurement-Error Correction Without a Gold-Standard Exposure......Page 721
13.16 Missing Data......Page 726
13.17 Summary......Page 731
Pulmonary Disease......Page 733
Infectious Disease......Page 734
Cardiovascular Disease......Page 735
Hypertension......Page 736
Cancer, Nutrition......Page 737
Environmental Health, Pediatrics......Page 738
Hypertension......Page 739
Cancer......Page 740
Cancer......Page 741
14.1 Measure of Effect for Person-Time Data......Page 745
Large-Sample Test......Page 747
Confidence Limits for Incidence Rates......Page 749
Hypothesis Testing—General Considerations......Page 750
Normal-Theory Test......Page 751
Exact Test......Page 754
The Rate Ratio......Page 756
Estimation of Power......Page 758
Sample-Size Estimation......Page 760
Hypothesis Testing......Page 762
Estimation of the Rate Ratio......Page 765
Testing the Assumption of Homogeneity of the Rate Ratio across Strata......Page 768
Sample-Size Estimation......Page 770
Estimation of Power......Page 773
14.7 Testing for Trend: Incidence-Rate Data......Page 775
14.8 Introduction to Survival Analysis......Page 778
14.9 Estimation of Survival Curves: The Kaplan-Meier Estimator......Page 780
The Treatment of Censored Data......Page 781
Other Types of Censoring......Page 783
Interval Estimation of Survival Probabilities......Page 784
Estimation of the Hazard Function: The Product-Limit Method......Page 786
14.10 The Log-Rank Test......Page 787
14.11 The Proportional-Hazards Model......Page 794
Testing the Assumptions of the Cox Proportional-Hazards Model......Page 801
Estimation of Power......Page 803
Estimation of Sample Size......Page 806
14.13 Parametric Survival Analysis......Page 807
Estimation of the Parameters of the Weibull Model......Page 809
Estimation of Percentiles of the Weibull Survival Function......Page 813
Assessing Goodness of Fit of the Weibull Model......Page 814
14.14 Parametric Regression Models for Survival Data......Page 815
Estimation of Percentiles for the Weibull Survival Distribution......Page 819
Cancer......Page 822
Infectious Disease......Page 824
Orthopedics......Page 825
Health Promotion......Page 826
Cancer......Page 827
Cancer......Page 828
Infectious Disease......Page 829
APPENDIX Tables......Page 831
Answers to Selected Problems......Page 857
FLOWCHART Methods of Statistical Inference......Page 861
Index of Data Sets......Page 867
Index......Page 869