Introductory Biostatistics

INTRODUCTORY
BIOSTATISTICS......Page 4
Copyright......Page 5
CONTENTS......Page 8
PREFACE......Page 14
1.1 PROPORTIONS......Page 18
1.1.1 Comparative Studies......Page 19
1.1.2 Screening Tests......Page 22
1.1.3 Displaying Proportions......Page 25
1.2.1 Changes......Page 28
1.2.2 Measures of Morbidity and Mortality......Page 30
1.2.3 Standardization of Rates......Page 33
1.3 RATIOS......Page 35
1.3.2 Odds and Odds Ratio......Page 36
1.3.3 Generalized Odds for Ordered 2Dk Tables......Page 39
1.3.4 Mantel ¨C Haenszel Method......Page 43
1.3.5 Standardized Mortality Ratio......Page 47
1.4 NOTES ON COMPUTATIONS......Page 48
EXERCISES......Page 51
2.1.1 One- Way Scatter Plots......Page 74
2.1.2 Frequency Distribution......Page 75
2.1.3 Histogram and the Frequency Polygon......Page 79
2.1.4 Cumulative Frequency Graph and Percentiles......Page 84
2.1.5 Stem- and- Leaf Diagrams......Page 87
2.2 NUMERICAL METHODS......Page 89
2.2.1 Mean......Page 90
2.2.2 Other Measures of Location......Page 93
2.2.3 Measures of Dispersion......Page 94
2.2.4 Box Plots......Page 97
2.3 SPECIAL CASE OF BINARY DATA......Page 98
2.4 COEFFICIENTS OF CORRELATION......Page 100
2.4.1 Pearson¡¯s Correlation Coe¡ë cient......Page 102
2.4.2 Nonparametric Correlation Coe¡ë cients......Page 105
2.5 NOTES ON COMPUTATIONS......Page 107
EXERCISES......Page 109
3.1 PROBABILITY......Page 125
3.1.2 Probability......Page 126
3.1.3 Statistical Relationship......Page 128
3.1.4 Using Screening Tests......Page 132
3.1.5 Measuring Agreement......Page 135
3.2.1 Shape of the Normal Curve......Page 137
3.2.2 Areas under the Standard Normal Curve......Page 140
3.2.3 Normal Distribution as a Probability Model......Page 145
3.3 PROBABILITY MODELS FOR CONTINUOUS DATA......Page 148
3.4 PROBABILITY MODELS FOR DISCRETE DATA......Page 149
3.4.1 Binomial Distribution......Page 150
3.4.2 Poisson Distribution......Page 153
3.5.1 Mean and Variance......Page 154
3.5.2 Pair- Matched Case ¨C Control Study......Page 155
3.6 NOTES ON COMPUTATIONS......Page 157
EXERCISES......Page 158
4 Estimation of Parameters......Page 164
4.1 BASIC CONCEPTS......Page 165
4.1.2 Sampling Distributions......Page 166
4.2 ESTIMATION OF MEANS......Page 169
4.2.1 Con . dence Intervals for a Mean......Page 171
4.2.2 Uses of Small Samples......Page 173
4.2.3 Evaluation of Interventions......Page 175
4.3 ESTIMATION OF PROPORTIONS......Page 177
4.4 ESTIMATION OF ODDS RATIOS......Page 182
4.5 ESTIMATION OF CORRELATION COEFFICIENTS......Page 185
4.6 BRIEF NOTES ON THE FUNDAMENTALS......Page 188
EXERCISES......Page 190
5 Introduction to Statistical Tests of Signi.cance......Page 205
5.1.1 Hypothesis Tests......Page 207
5.1.2 Statistical Evidence......Page 208
5.1.3 Errors......Page 209
5.2.1 Trials by Jury......Page 211
5.2.3 Common Expectations......Page 212
5.3 SUMMARIES AND CONCLUSIONS......Page 213
5.3.1 Rejection Region......Page 214
5.3.2 p Values......Page 215
5.3.3 Relationship to Con . dence Intervals......Page 218
5.4.2 More about Errors and p Values......Page 220
EXERCISES......Page 221
6.1 ONE- SAMPLE PROBLEM WITH BINARY DATA......Page 225
6.2 ANALYSIS OF PAIR- MATCHED DATA......Page 227
6.3 COMPARISON OF TWO PROPORTIONS......Page 230
6.4 MANTEL ¨C HAENSZEL METHOD......Page 235
6.5 INFERENCES FOR GENERAL TWO- WAY TABLES......Page 240
6.6 FISHER¡¯S EXACT TEST......Page 246
6.7 ORDERED 2Dk CONTINGENCY TABLES......Page 247
EXERCISES......Page 251
7.1 ONE- SAMPLE PROBLEM WITH CONTINUOUS DATA......Page 263
7.2 ANALYSIS OF PAIR- MATCHED DATA......Page 265
7.3 COMPARISON OF TWO MEANS......Page 270
7.4.1 Wilcoxon Rank- Sum Test......Page 274
7.4.2 Wilcoxon Signed- Rank Test......Page 278
7.5 ONE- WAY ANALYSIS OF VARIANCE......Page 280
7.6 BRIEF NOTES ON THE FUNDAMENTALS......Page 286
EXERCISES......Page 287
8 Correlation and Regression......Page 299
8.1.2 Scatter Diagram......Page 300
8.1.3 Meaning of Regression Parameters......Page 301
8.1.4 Estimation of Parameters......Page 302
8.1.5 Testing for Independence......Page 306
8.1.6 Analysis- of- Variance Approach......Page 309
8.2.1 Regression Model with Several Independent Variables......Page 311
8.2.3 E ¤ ect Modi . cations......Page 312
8.2.5 Estimation of Parameters......Page 313
8.2.6 Analysis- of- Variance Approach......Page 314
8.2.7 Testing Hypotheses in Multiple Linear Regression......Page 315
8.3 NOTES ON COMPUTATIONS......Page 322
EXERCISES......Page 323
9 Logistic Regression......Page 331
9.1 SIMPLE REGRESSION ANALYSIS......Page 333
9.1.1 Simple Logistic Regression Model......Page 334
9.1.2 Measure of Association......Page 335
9.1.3 E ¤ ect of Measurement Scale......Page 337
9.1.4 Tests of Association......Page 338
9.1.5 Use of the Logistic Model for Di ¤ erent Designs......Page 339
9.1.6 Overdispersion......Page 340
9.2 MULTIPLE REGRESSION ANALYSIS......Page 342
9.2.1 Logistic Regression Model with Several Covariates......Page 343
9.2.2 E ¤ ect Modi . cations......Page 344
9.2.3 Polynomial Regression......Page 345
9.2.4 Testing Hypotheses in Multiple Logistic Regression......Page 346
9.2.5 Receiver Operating Characteristic Curve......Page 353
9.2.6 ROC Curve and Logistic Regression......Page 354
9.3 BRIEF NOTES ON THE FUNDAMENTALS......Page 356
EXERCISE......Page 358
10.1 POISSON DISTRIBUTION......Page 367
10.2 TESTING GOODNESS OF FIT......Page 371
10.3 POISSON REGRESSION MODEL......Page 373
10.3.1 Simple Regression Analysis......Page 374
10.3.2 Multiple Regression Analysis......Page 377
10.3.3 Overdispersion......Page 385
10.3.4 Stepwise Regression......Page 387
EXERCISE......Page 389
11 Analysis of Survival Data and Data from Matched Studies......Page 396
11.1 SURVIVAL DATA......Page 398
11.2.1 Kaplan ¨C Meier Curve......Page 401
11.2.2 Comparison of Survival Distributions......Page 403
11.3 SIMPLE REGRESSION AND CORRELATION......Page 407
11.3.1 Model and Approach......Page 408
11.3.2 Measures of Association......Page 409
11.4 MULTIPLE REGRESSION AND CORRELATION......Page 412
11.4.1 Proportional Hazards Model with Several Covariates......Page 413
11.4.2 Testing Hypotheses in Multiple Regression......Page 414
11.4.3 Time- Dependent Covariates and Applications......Page 418
11.5 PAIR- MATCHED CASE ¨C CONTROL STUDIES......Page 422
11.5.1 Model......Page 423
11.5.2 Analysis......Page 424
11.6.1 Conditional Approach......Page 426
11.6.2 Estimation of the Odds Ratio......Page 427
11.6.3 Testing for Exposure E ¤ ect......Page 428
11.7 CONDITIONAL LOGISTIC REGRESSION......Page 430
11.7.1 Simple Regression Analysis......Page 431
11.7.2 Multiple Regression Analysis......Page 435
EXERCISES......Page 443
12 Study Designs......Page 462
12.1 TYPES OF STUDY DESIGNS......Page 463
12.2 CLASSIFICATION OF CLINICAL TRIALS......Page 464
12.3 DESIGNING PHASE I CANCER TRIALS......Page 465
12.4 SAMPLE SIZE DETERMINATION FOR PHASE II TRIALS AND SURVEYS......Page 468
12.5 SAMPLE SIZES FOR OTHER PHASE II TRIALS......Page 470
12.5.2 Correlation Endpoints......Page 471
12.6 ABOUT SIMON¡¯S TWO- STAGE PHASE II DESIGN......Page 473
12.7.1 Continuous Endpoints......Page 474
12.7.2 Binary Endpoints......Page 475
12.8 TOXICITY MONITORING IN PHASE II TRIALS......Page 476
12.9 SAMPLE SIZE DETERMINATION FOR PHASE III TRIALS......Page 478
12.9.1 Comparison of Two Means......Page 479
12.9.2 Comparison of Two Proportions......Page 481
12.9.3 Survival Time as the Endpoint......Page 483
12.10.1 Unmatched Designs for a Binary Exposure......Page 486
12.10.2 Matched Designs for a Binary Exposure......Page 488
12.10.3 Unmatched Designs for a Continuous Exposure......Page 490
EXERCISES......Page 493
BIBLIOGRAPHY......Page 500
APPENDICES......Page 506
APPENDIX A: TABLE OF RANDOM NUMBERS......Page 507
APPENDIX B: AREA UNDER THE STANDARD NORMAL CURVE......Page 508
APPENDIX C: PERCENTILES OF THE t DISTRIBUTION......Page 510
APPENDIX D: PERCENTILES OF CHI- SQUARE DISTRIBUTIONS......Page 512
APPENDIX E: PERCENTILES OF THE F DISTRIBUTION......Page 514
Answers to Selected Exercises......Page 516
INDEX......Page 548