Introductory biostatistics

1 Descriptive Methods for Categorical Data 1 1.1 Proportions, 1 1.1.1 Comparative Studies, 2 1.1.2 Screening Tests, 5 1.1.3 Displaying Proportions, 8 1.2 Rates, 11 1.2.1 Changes, 11 1.2.2 Measures of Morbidity and Mortality, 13 1.2.3 Standardization of Rates, 16 1.3 Ratios, 18 1.3.1 Relative Risk, 19 1.3.2 Odds and Odds Ratio, 19 1.3.3 Generalized Odds for Ordered 2
k Tables, 22 1.3.4 Mantel–Haenszel Method, 26 1.3.5 Standardized Mortality Ratio, 30 1.4 Notes on Computations, 31 Exercises, 34 2 Descriptive Methods for Continuous Data 57 2.1 Tabular and Graphical Methods, 57 2.1.1 One-Way Scatter Plots, 57 2.1.2 Frequency Distribution, 58 vii 2.1.3 Histogram and the Frequency Polygon, 62 2.1.4 Cumulative Frequency Graph and Percentiles, 67 2.1.5 Stem-and-Leaf Diagrams, 70 2.2 Numerical Methods, 72 2.2.1 Mean, 73 2.2.2 Other Measures of Location, 76 2.2.3 Measures of Dispersion, 77 2.2.4 Box Plots, 80 2.3 Special Case of Binary Data, 81 2.4 Coe‰cients of Correlation, 83 2.4.1 Pearson’s Correlation Coe‰cient, 85 2.4.2 Nonparametric Correlation Coe‰cients, 88 2.5 Notes on Computations, 90 Exercises, 92 3 Probability and Probability Models 108 3.1 Probability, 108 3.1.1 Certainty of Uncertainty, 109 3.1.2 Probability, 109 3.1.3 Statistical Relationship, 111 3.1.4 Using Screening Tests, 115 3.1.5 Measuring Agreement, 118 3.2 Normal Distribution, 120 3.2.1 Shape of the Normal Curve, 120 3.2.2 Areas under the Standard Normal Curve, 123 3.2.3 Normal Distribution as a Probability Model, 128 3.3 Probability Models for Continuous Data, 131 3.4 Probability Models for Discrete Data, 132 3.4.1 Binomial Distribution, 133 3.4.2 Poisson Distribution, 136 3.5 Brief Notes on the Fundamentals, 137 3.5.1 Mean and Variance, 137 3.5.2 Pair-Matched Case–Control Study, 138 3.6 Notes on Computations, 140 Exercises, 141 4 Estimation of Parameters 147 4.1 Basic Concepts, 148 4.1.1 Statistics as Variables, 149 4.1.2 Sampling Distributions, 149 4.1.3 Introduction to Confidence Estimation, 152 4.2 Estimation of Means, 152 4.2.1 Confidence Intervals for a Mean, 154 4.2.2 Uses of Small Samples, 156 viii CONTENTS 4.2.3 Evaluation of Interventions, 158 4.3 Estimation of Proportions, 160 4.4 Estimation of Odds Ratios, 165 4.5 Estimation of Correlation Coe‰cients, 168 4.6 Brief Notes on the Fundamentals, 171 4.7 Notes on Computations, 173 Exercises, 173 5 Introduction to Statistical Tests of Significance 188 5.1 Basic Concepts, 190 5.1.1 Hypothesis Tests, 190 5.1.2 Statistical Evidence, 191 5.1.3 Errors, 192 5.2 Analogies, 194 5.2.1 Trials by Jury, 194 5.2.2 Medical Screening Tests, 195 5.2.3 Common Expectations, 195 5.3 Summaries and Conclusions, 196 5.3.1 Rejection Region, 197 5.3.2 p Values, 198 5.3.3 Relationship to Confidence Intervals, 201 5.4 Brief Notes on the Fundamentals, 203 5.4.1 Type I and Type II Errors, 203 5.4.2 More about Errors and p Values, 203 Exercises, 204 6 Comparison of Population Proportions 208 6.1 One-Sample Problem with Binary Data, 208 6.2 Analysis of Pair-Matched Data, 210 6.3 Comparison of Two Proportions, 213 6.4 Mantel–Haenszel Method, 218 6.5 Inferences for General Two-Way Tables, 223 6.6 Fisher’s Exact Test, 229 6.7 Ordered 2
k Contingency Tables, 230 6.8 Notes on Computations, 234 Exercises, 234 7 Comparison of Population Means 246 7.1 One-Sample Problem with Continuous Data, 246 7.2 Analysis of Pair-Matched Data, 248 7.3 Comparison of Two Means, 253 7.4 Nonparametric Methods, 257 7.4.1 Wilcoxon Rank-Sum Test, 257 7.4.2 Wilcoxon Signed-Rank Test, 261 CONTENTS ix 7.5 One-Way Analysis of Variance, 263 7.6 Brief Notes on the Fundamentals, 269 7.7 Notes on Computations, 270 Exercises, 270 8 Correlation and Regression 282 8.1 Simple Regression Analysis, 283 8.1.1 Simple Linear Regression Model, 283 8.1.2 Scatter Diagram, 283 8.1.3 Meaning of Regression Parameters, 284 8.1.4 Estimation of Parameters, 285 8.1.5 Testing for Independence, 289 8.1.6 Analysis-of-Variance Approach, 292 8.2 Multiple Regression Analysis, 294 8.2.1 Regression Model with Several Independent Variables, 294 8.2.2 Meaning of Regression Parameters, 295 8.2.3 E¤ect Modifications, 295 8.2.4 Polynomial Regression, 296 8.2.5 Estimation of Parameters, 296 8.2.6 Analysis-of-Variance Approach, 297 8.2.7 Testing Hypotheses in Multiple Linear Regression, 298 8.3 Notes on Computations, 305 Exercises, 306 9 Logistic Regression 314 9.1 Simple Regression Analysis, 316 9.1.1 Simple Logistic Regression Model, 317 9.1.2 Measure of Association, 318 9.1.3 E¤ect of Measurement Scale, 320 9.1.4 Tests of Association, 321 9.1.5 Use of the Logistic Model for Di¤erent Designs, 322 9.1.6 Overdispersion, 323 9.2 Multiple Regression Analysis, 325 9.2.1 Logistic Regression Model with Several Covariates, 326 9.2.2 E¤ect Modifications, 327 9.2.3 Polynomial Regression, 328 9.2.4 Testing Hypotheses in Multiple Logistic Regression, 329 9.2.5 Receiver Operating Characteristic Curve, 336 9.2.6 ROC Curve and Logistic Regression, 337 9.3 Brief Notes on the Fundamentals, 339 Exercise, 341 x CONTENTS 10 Methods for Count Data 350 10.1 Poisson Distribution, 350 10.2 Testing Goodness of Fit, 354 10.3 Poisson Regression Model, 356 10.3.1 Simple Regression Analysis, 357 10.3.2 Multiple Regression Analysis, 360 10.3.3 Overdispersion, 368 10.3.4 Stepwise Regression, 370 Exercise, 372 11 Analysis of Survival Data and Data from Matched Studies 379 11.1 Survival Data, 381 11.2 Introductory Survival Analyses, 384 11.2.1 Kaplan–Meier Curve, 384 11.2.2 Comparison of Survival Distributions, 386 11.3 Simple Regression and Correlation, 390 11.3.1 Model and Approach, 391 11.3.2 Measures of Association, 392 11.3.3 Tests of Association, 395 11.4 Multiple Regression and Correlation, 395 11.4.1 Proportional Hazards Model with Several Covariates, 396 11.4.2 Testing Hypotheses in Multiple Regression, 397 11.4.3 Time-Dependent Covariates and Applications, 401 11.5 Pair-Matched Case–Control Studies, 405 11.5.1 Model, 406 11.5.2 Analysis, 407 11.6 Multiple Matching, 409 11.6.1 Conditional Approach, 409 11.6.2 Estimation of the Odds Ratio, 410 11.6.3 Testing for Exposure E¤ect, 411 11.7 Conditional Logistic Regression, 413 11.7.1 Simple Regression Analysis, 414 11.7.2 Multiple Regression Analysis, 418 Exercises, 426 12 Study Designs 445 12.1 Types of Study Designs, 446 12.2 Classification of Clinical Trials, 447 12.3 Designing Phase I Cancer Trials, 448 12.4 Sample Size Determination for Phase II Trials and Surveys, 451 12.5 Sample Sizes for Other Phase II Trials, 453 CONTENTS xi 12.5.1 Continuous Endpoints, 454 12.5.2 Correlation Endpoints, 454 12.6 About Simon’s Two-Stage Phase II Design, 456 12.7 Phase II Designs for Selection, 457 12.7.1 Continuous Endpoints, 457 12.7.2 Binary Endpoints, 458 12.8 Toxicity Monitoring in Phase II Trials, 459 12.9 Sample Size Determination for Phase III Trials, 461 12.9.1 Comparison of Two Means, 462 12.9.2 Comparison of Two Proportions, 464 12.9.3 Survival Time as the Endpoint, 466 12.10 Sample Size Determination for Case–Control Studies, 469 12.10.1 Unmatched Designs for a Binary Exposure, 469 12.10.2 Matched Designs for a Binary Exposure, 471 12.10.3 Unmatched Designs for a Continuous Exposure, 473 Exercises, 476 Bibliography 483 Appendices 489 Answers to Selected Exercises 499 Index