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Applied Medical Statistics

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en Limba Engleză Hardback – 29 Apr 2022

An up-to-date exploration of foundational concepts in statistics and probability for medical students and researchers

Medical journals and researchers are increasingly recognizing the need for improved statistical rigor in medical science. In Applied Medical Statistics, renowned statistician and researcher Dr. Jingmei Jiang delivers a clear, coherent, and accessible introduction to basic statistical concepts, ideal for medical students and medical research practitioners. The book will help readers master foundational concepts in statistical analysis and assist in the development of a critical understanding of the basic rationale of statistical analysis techniques.

The distinguished author presents information without assuming the reader has a background in specialized mathematics, statistics, or probability. All of the described methods are illustrated with up-to-date examples based on real-world medical research, supplemented by exercises and case discussions to help solidify the concepts and give readers an opportunity to critically evaluate different research scenarios.

Readers will also benefit from the inclusion of:

  • A thorough introduction to basic concepts in statistics, including foundational terms and definitions, location and spread of data distributions, population parameters estimation, and statistical hypothesis tests
  • Explorations of commonly used statistical methods, including t-tests, analysis of variance, and linear regression
  • Discussions of advanced analysis topics, including multiple linear regression and correlation, logistic regression, and survival analysis
  • Substantive exercises and case discussions at the end of each chapter

Perfect for postgraduate medical students, clinicians, and medical and biomedical researchers, Applied Medical Statistics will also earn a place on the shelf of any researcher with an interest in biostatistics or applying statistical methods to their own field of research.

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Specificații

ISBN-13: 9781119716709
ISBN-10: 1119716705
Pagini: 640
Dimensiuni: 186 x 262 x 39 mm
Greutate: 1.23 kg
Editura: Wiley
Locul publicării: Hoboken, United States

Cuprins

Preface xiii Acknowledgments xv About the Companion Website xvii 1 What is Biostatistics 1 1.1 Overview 1 1.2 Some Statistical Terminology 2 1.2.1 Population and Sample 2 1.2.2 Homogeneity and Variation 3 1.2.3 Parameter and Statistic 4 1.2.4 Types of Data 4 1.2.5 Error 5 1.3 Workflow of Applied Statistics 6 1.4 Statistics and Its Related Disciplines 6 1.5 Statistical Thinking 7 1.6 Summary 7 1.7 Exercises 8 2 Descriptive Statistics 11 2.1 Frequency Tables and Graphs 12 2.1.1 Frequency Distribution of Numerical Data 12 2.1.2 Frequency Distribution of Categorical Data 16 2.2 Descriptive Statistics of Numerical Data 17 2.2.1 Measures of Central Tendency 17 2.2.2 Measures of Dispersion 26 2.3 Descriptive Statistics of Categorical Data 31 2.3.1 Relative Numbers 31 2.3.2 Standardization of Rates 34 2.4 Constructing Statistical Tables and Graphs 38 2.4.1 Statistical Tables 38 2.4.2 Statistical Graphs 40 2.5 Summary 47 2.6 Exercises 48 3 Fundamentals of Probability 53 3.1 Sample Space and Random Events 54 3.1.1 Definitions of Sample Space and Random Events 54 3.1.2 Operation of Events 55 3.2 Relative Frequency and Probability 58 3.2.1 Definition of Probability 59 3.2.2 Basic Properties of Probability 59 3.3 Conditional Probability and Independence of Events 60 3.3.1 Conditional Probability 60 3.3.2 Independence of Events 60 3.4 Multiplication Law of Probability 61 3.5 Addition Law of Probability 62 3.5.1 General Addition Law 62 3.5.2 Addition Law of Mutually Exclusive Events 62 3.6 Total Probability Formula and Bayes' Rule 63 3.6.1 Total Probability Formula 63 3.6.2 Bayes' Rule 64 3.7 Summary 65 3.8 Exercises 65 4 Discrete Random Variable 69 4.1 Concept of the Random Variable 69 4.2 Probability Distribution of the Discrete Random Variable 70 4.2.1 Probability Mass Function 70 4.2.2 Cumulative Distribution Function 71 4.2.3 Association Between the Probability Distribution and Relative Frequency Distribution 72 4.3 Numerical Characteristics 73 4.3.1 Expected Value 73 4.3.2 Variance and Standard Deviation 74 4.4 Commonly Used Discrete Probability Distributions 75 4.4.1 Binomial Distribution 75 4.4.2 Multinomial Distribution 80 4.4.3 Poisson Distribution 82 4.5 Summary 87 4.6 Exercises 87 5 Continuous Random Variable 91 5.1 Concept of Continuous Random Variable 92 5.2 Numerical Characteristics 93 5.3 Normal Distribution 94 5.3.1 Concept of the Normal Distribution 94 5.3.2 Standard Normal Distribution 96 5.3.3 Descriptive Methods for Assessing Normality 99 5.4 Application of the Normal Distribution 102 5.4.1 Normal Approximation to the Binomial Distribution 102 5.4.2 Normal Approximation to the Poisson Distribution 105 5.4.3 Determining the Medical Reference Interval 108 5.5 Summary 109 5.6 Exercises 110 6 Sampling Distribution and Parameter Estimation 113 6.1 Samples and Statistics 114 6.2 Sampling Distribution of a Statistic 114 6.2.1 Sampling Distribution of the Mean 115 6.2.2 Sampling Distribution of the Variance 120 6.2.3 Sampling Distribution of the Rate (Normal Approximation) 122 6.3 Estimation of One Population Parameter 124 6.3.1 Point Estimation and Its Quality Evaluation 124 6.3.2 Interval Estimation for the Mean 126 6.3.3 Interval Estimation for the Variance 130 6.3.4 Interval Estimation for the Rate (Normal Approximation Method) 131 6.4 Estimation of Two Population Parameters 132 6.4.1 Estimation of the Difference in Means 132 6.4.2 Estimation of the Ratio of Variances 136 6.4.3 Estimation of the Difference Between Rates (Normal Approximation Method) 139 6.5 Summary 141 6.6 Exercises 141 7 Hypothesis Testing for One Parameter 145 7.1 Overview 145 7.1.1 Concepts and Procedures 146 7.1.2 Type I and Type II Errors 150 7.1.3 One-sided and Two-sided Hypothesis 152 7.1.4 Association Between Hypothesis Testing and Interval Estimation 153 7.2 Hypothesis Testing for One Parameter 155 7.2.1 Hypothesis Tests for the Mean 155 7.2.1.1 Power of the Test 156 7.2.1.2 Sample Size Determination 160 7.2.2 Hypothesis Tests for the Rate (Normal Approximation Methods) 162 7.2.2.1 Power of the Test 163 7.2.2.2 Sample Size Determination 164 7.3 Further Considerations on Hypothesis Testing 164 7.3.1 About the Significance Level 164 7.3.2 Statistical Significance and Clinical Significance 165 7.4 Summary 165 7.5 Exercises 166 8 Hypothesis Testing for Two Population Parameters 169 8.1 Testing the Difference Between Two Population Means: Paired Samples 170 8.2 Testing the Difference Between Two Population Means: Independent Samples 173 8.2.1 t-Test for Means with Equal Variances 173 8.2.2 F-Test for the Equality of Two Variances 176 8.2.3 Approximation t-Test for Means with Unequal Variances 178 8.2.4 Z-Test for Means with Large-Sample Sizes 181 8.2.5 Power for Comparing Two Means 182 8.2.6 Sample Size Determination 183 8.3 Testing the Difference Between Two Population Rates (Normal Approximation Method) 185 8.3.1 Power for Comparing Two Rates 186 8.3.2 Sample Size Determination 187 8.4 Summary 188 8.5 Exercises 189 9 One-way Analysis of Variance 193 9.1 Overview 193 9.1.1 Concept of ANOVA 194 9.1.2 Data Layout and Modeling Assumption 195 9.2 Procedures of ANOVA 196 9.3 Multiple Comparisons of Means 204 9.3.1 Tukey's Test 204 9.3.2 Dunnett's Test 206 9.3.3 Least Significant Difference (LSD) Test 209 9.4 Checking ANOVA Assumptions 211 9.4.1 Check for Normality 211 9.4.2 Test for Homogeneity of Variances 213 9.4.2.1 Bartlett's Test 213 9.4.2.2 Levene's Test 215 9.5 Data Transformations 217 9.6 Summary 218 9.7 Exercises 218 10 Analysis of Variance in Different Experimental Designs 221 10.1 ANOVA for Randomized Block Design 221 10.1.1 Data Layout and Model Assumptions 223 10.1.2 Procedure of ANOVA 224 10.2 ANOVA for Two-factor Factorial Design 229 10.2.1 Concept of Factorial Design 230 10.2.2 Data Layout and Model Assumptions 233 10.2.3 Procedure of ANOVA 234 10.3 ANOVA for Repeated Measures Design 240 10.3.1 Characteristics of Repeated Measures Data 240 10.3.2 Data Layout and Model Assumptions 242 10.3.3 Procedure of ANOVA 243 10.3.4 Sphericity Test of Covariance Matrix 245 10.3.5 Multiple Comparisons of Means 248 10.4 ANOVA for 2 × 2 Crossover Design 251 10.4.1 Concept of a 2 × 2 Crossover Design 251 10.4.2 Data Layout and Model Assumptions 252 10.4.3 Procedure of ANOVA 254 10.5 Summary 256 10.6 Exercises 257 11 chi² Test 261 11.1 Contingency Table 262 11.1.1 General Form of Contingency Table 263 11.1.2 Independence of Two Categorical Variables 264 11.1.3 Significance Testing Using the Contingency Table 265 11.2 chi² Test for a 2 × 2 Contingency Table 266 11.2.1 Test of Independence 266 11.2.2 Yates' Corrected chi² test for a 2 × 2 Contingency Table 269 11.2.3 Paired Samples Design chi² Test 269 11.2.4 Fisher's Exact Tests for Completely Randomized Design 272 11.2.5 Exact McNemar's Test for Paired Samples Design 275 11.3 chi² Test for R × C Contingency Tables 276 11.3.1 Comparison of Multiple Independent Proportions 276 11.3.2 Multiple Comparisons of Proportions 278 11.4 chi² Goodness-of-Fit Test 280 11.4.1 Normal Distribution Goodness-of-Fit Test 281 11.4.2 Poisson Distribution Goodness-of-Fit Test 283 11.5 Summary 284 11.6 Exercises 285 12 Nonparametric Tests Based on Rank 289 12.1 Concept of Order Statistics 289 12.2 Wilcoxon's Signed-Rank Test for Paired Samples 290 12.3 Wilcoxon's Rank-Sum Test for Two Independent Samples 295 12.4 Kruskal-Wallis Test for Multiple Independent Samples 299 12.4.1 Kruskal-Wallis Test 299 12.4.2 Multiple Comparisons 301 12.5 Friedman's Test for Randomized Block Design 303 12.6 Further Considerations About Nonparametric Tests 306 12.7 Summary 306 12.8 Exercises 306 13 Simple Linear Regression 311 13.1 Concept of Simple Linear Regression 311 13.2 Establishment of Regression Model 314 13.2.1 Least Squares Estimation of a Regression Coefficient 314 13.2.2 Basic Properties of the Regression Model 316 13.2.3 Hypothesis Testing of Regression Model 317 13.3 Application of Regression Model 321 13.3.1 Confidence Interval Estimation of a Regression Coefficient 321 13.3.2 Confidence Band Estimation of Regression Model 322 13.3.3 Prediction Band Estimation of Individual Response Values 323 13.4 Evaluation of Model Fitting 325 13.4.1 Coefficient of Determination 325 13.4.2 Residual Analysis 326 13.5 Summary 327 13.6 Exercises 328 14 Simple Linear Correlation 331 14.1 Concept of Simple Linear Correlation 331 14.1.1 Definition of Correlation Coefficient 331 14.1.2 Interpretation of Correlation Coefficient 334 14.2 Hypothesis Testing of Correlation Coefficient 336 14.3 Confidence Interval Estimation for Correlation Coefficient 338 14.4 Spearman's Rank Correlation 340 14.4.1 Concept of Spearman's Rank Correlation Coefficient 340 14.4.2 Hypothesis Testing of Spearman's Rank Correlation Coefficient 342 14.5 Summary 342 14.6 Exercises 343 15 Multiple Linear Regression 345 15.1 Multiple Linear Regression Model 346 15.1.1 Concept of the Multiple Linear Regression 346 15.1.2 Least Squares Estimation of Regression Coefficient 349 15.1.3 Properties of the Least Squares Estimators 351 15.1.4 Standardized Partial-Regression Coefficient 351 15.2 Hypothesis Testing 352 15.2.1 F-Test for Overall Regression Model 352 15.2.2 t-Test for Partial-Regression Coefficients 354 15.3 Evaluation of Model Fitting 356 15.3.1 Coefficient of Determination and Adjusted Coefficient of Determination 356 15.3.2 Residual Analysis and Outliers 357 15.4 Other Aspects of Regression 359 15.4.1 Multicollinearity 359 15.4.2 Selection of Independent Variables 361 15.4.3 Sample Size 364 15.5 Summary 364 15.6 Exercises 364 16 Logistic Regression 369 16.1 Logistic Regression Model 370 16.1.1 Linear Probability Model 371 16.1.2 Probability, Odds, and Logit Transformation 371 16.1.3 Definition of Logistic Regression 373 16.1.4 Inference for Logistic Regression 375 16.1.4.1 Estimation of Model Coefficient 375 16.1.4.2 Interpretation of Model Coefficient 378 16.1.4.3 Hypothesis Testing of Model Coefficient 380 16.1.4.4 Interval Estimation of Model Coefficient 382 16.1.5 Evaluation of Model Fitting 385 16.2 Conditional Logistic Regression Model 388 16.2.1 Characteristics of Conditional Logistic Regression Model 390 16.2.2 Estimation of Regression Coefficient 390 16.2.3 Hypothesis Testing of Regression Coefficient 393 16.3 Additional Remarks 394 16.3.1 Sample Size 394 16.3.2 Types of Independent Variables 394 16.3.3 Selection of Independent Variables 395 16.3.4 Missing Data 395 16.4 Summary 395 16.5 Exercises 396 17 Survival Analysis 399 17.1 Overview 400 17.1.1 Concept of Survival Analysis 400 17.1.2 Basic Functions of Survival Time 402 17.2 Description of the Survival Process 405 17.2.1 Product Limit Method 405 17.2.2 Life Table Method 408 17.3 Comparison of Survival Processes 410 17.3.1 Log-Rank Test 410 17.3.2 Other Methods for Comparing Survival Processes 413 17.4 Cox's Proportional Hazards Model 414 17.4.1 Concept and Model Assumptions 415 17.4.2 Estimation of Model Coefficient 417 17.4.3 Hypothesis Testing of Model Coefficient 419 17.4.4 Evaluation of Model Fitting 420 17.5 Other Aspects of Cox's Proportional Hazard Model 421 17.5.1 Hazard Index 421 17.5.2 Sample Size 421 17.6 Summary 422 17.7 Exercises 423 18 Evaluation of Diagnostic Tests 431 18.1 Basic Characteristics of Diagnostic Tests 431 18.1.1 Sensitivity and Specificity 433 18.1.2 Composite Measures of Sensitivity and Specificity 435 18.1.3 Predictive Values 438 18.1.4 Sensitivity and Specificity Comparison of Two Diagnostic Tests 440 18.2 Agreement Between Diagnostic Tests 443 18.2.1 Agreement of Categorical Data 444 18.2.2 Agreement of Numerical Data 447 18.3 Receiver Operating Characteristic Curve Analysis 448 18.3.1 Concept of an ROC Curve 449 18.3.2 Area Under the ROC Curve 450 18.3.3 Comparison of Areas Under ROC Curves 453 18.4 Summary 456 18.5 Exercises 457 19 Observational Study Design 461 19.1 Cross-Sectional Studies 462 19.1.1 Types of Cross-Sectional Studies 462 19.1.2 Probability Sampling Methods 462 19.1.3 Sample Size for Surveys 466 19.1.4 Cross-Sectional Studies for Clues of Etiology 468 19.2 Cohort Studies 469 19.2.1 Measures of Association in Cohort Studies 469 19.2.2 Sample Size for Cohort Studies 470 19.3 Case-Control Studies 472 19.3.1 Measures of Association in Case-Control Studies 472 19.3.2 Sample Size for Case-Control Studies 473 19.4 Summary 474 19.5 Exercises 475 20 Experimental Study Design 477 20.1 Overview 478 20.1.1 Basic Components of an Experimental Study 478 20.1.2 Principles of Experimental Study Design 480 20.1.3 Blinding Procedures in Clinical Trials 482 20.2 Completely Randomized Design 483 20.2.1 Concept of Completely Randomized Design 483 20.2.2 Sample Size for Completely Randomized Design 485 20.3 Randomized Block Design 486 20.3.1 Concepts of Randomized Block Design 486 20.3.2 Sample Size for Randomized Block Design 488 20.4 Factorial Design 489 20.5 Crossover Design 491 20.5.1 Concepts of Crossover Design 491 20.5.2 Sample Size for 2 × 2 Crossover Design 492 20.6 Summary 493 20.7 Exercises 493 Appendix 495 References 549 Index 557