Applied Medical Statistics

ISBN-13: 9781119716709 / Angielski / Twarda / 2022 / 640 str.

Jingmei Jiang

Spis treści

Preface xiiiAcknowledgments xvAbout the Companion Website xvii1 What is Biostatistics 11.1 Overview 11.2 Some Statistical Terminology 21.2.1 Population and Sample 21.2.2 Homogeneity and Variation 31.2.3 Parameter and Statistic 41.2.4 Types of Data 41.2.5 Error 51.3 Workflow of Applied Statistics 61.4 Statistics and Its Related Disciplines 61.5 Statistical Thinking 71.6 Summary 71.7 Exercises 82 Descriptive Statistics 112.1 Frequency Tables and Graphs 122.1.1 Frequency Distribution of Numerical Data 122.1.2 Frequency Distribution of Categorical Data 162.2 Descriptive Statistics of Numerical Data 172.2.1 Measures of Central Tendency 172.2.2 Measures of Dispersion 262.3 Descriptive Statistics of Categorical Data 312.3.1 Relative Numbers 312.3.2 Standardization of Rates 342.4 Constructing Statistical Tables and Graphs 382.4.1 Statistical Tables 382.4.2 Statistical Graphs 402.5 Summary 472.6 Exercises 483 Fundamentals of Probability 533.1 Sample Space and Random Events 543.1.1 Definitions of Sample Space and Random Events 543.1.2 Operation of Events 553.2 Relative Frequency and Probability 583.2.1 Definition of Probability 593.2.2 Basic Properties of Probability 593.3 Conditional Probability and Independence of Events 603.3.1 Conditional Probability 603.3.2 Independence of Events 603.4 Multiplication Law of Probability 613.5 Addition Law of Probability 623.5.1 General Addition Law 623.5.2 Addition Law of Mutually Exclusive Events 623.6 Total Probability Formula and Bayes' Rule 633.6.1 Total Probability Formula 633.6.2 Bayes' Rule 643.7 Summary 653.8 Exercises 654 Discrete Random Variable 694.1 Concept of the Random Variable 694.2 Probability Distribution of the Discrete Random Variable 704.2.1 Probability Mass Function 704.2.2 Cumulative Distribution Function 714.2.3 Association Between the Probability Distribution and Relative Frequency Distribution 724.3 Numerical Characteristics 734.3.1 Expected Value 734.3.2 Variance and Standard Deviation 744.4 Commonly Used Discrete Probability Distributions 754.4.1 Binomial Distribution 754.4.2 Multinomial Distribution 804.4.3 Poisson Distribution 824.5 Summary 874.6 Exercises 875 Continuous Random Variable 915.1 Concept of Continuous Random Variable 925.2 Numerical Characteristics 935.3 Normal Distribution 945.3.1 Concept of the Normal Distribution 945.3.2 Standard Normal Distribution 965.3.3 Descriptive Methods for Assessing Normality 995.4 Application of the Normal Distribution 1025.4.1 Normal Approximation to the Binomial Distribution 1025.4.2 Normal Approximation to the Poisson Distribution 1055.4.3 Determining the Medical Reference Interval 1085.5 Summary 1095.6 Exercises 1106 Sampling Distribution and Parameter Estimation 1136.1 Samples and Statistics 1146.2 Sampling Distribution of a Statistic 1146.2.1 Sampling Distribution of the Mean 1156.2.2 Sampling Distribution of the Variance 1206.2.3 Sampling Distribution of the Rate (Normal Approximation) 1226.3 Estimation of One Population Parameter 1246.3.1 Point Estimation and Its Quality Evaluation 1246.3.2 Interval Estimation for the Mean 1266.3.3 Interval Estimation for the Variance 1306.3.4 Interval Estimation for the Rate (Normal Approximation Method) 1316.4 Estimation of Two Population Parameters 1326.4.1 Estimation of the Difference in Means 1326.4.2 Estimation of the Ratio of Variances 1366.4.3 Estimation of the Difference Between Rates (Normal Approximation Method) 1396.5 Summary 1416.6 Exercises 1417 Hypothesis Testing for One Parameter 1457.1 Overview 1457.1.1 Concepts and Procedures 1467.1.2 Type I and Type II Errors 1507.1.3 One-sided and Two-sided Hypothesis 1527.1.4 Association Between Hypothesis Testing and Interval Estimation 1537.2 Hypothesis Testing for One Parameter 1557.2.1 Hypothesis Tests for the Mean 1557.2.1.1 Power of the Test 1567.2.1.2 Sample Size Determination 1607.2.2 Hypothesis Tests for the Rate (Normal Approximation Methods) 1627.2.2.1 Power of the Test 1637.2.2.2 Sample Size Determination 1647.3 Further Considerations on Hypothesis Testing 1647.3.1 About the Significance Level 1647.3.2 Statistical Significance and Clinical Significance 1657.4 Summary 1657.5 Exercises 1668 Hypothesis Testing for Two Population Parameters 1698.1 Testing the Difference Between Two Population Means: Paired Samples 1708.2 Testing the Difference Between Two Population Means: Independent Samples 1738.2.1 t-Test for Means with Equal Variances 1738.2.2 F-Test for the Equality of Two Variances 1768.2.3 Approximation t-Test for Means with Unequal Variances 1788.2.4 Z-Test for Means with Large-Sample Sizes 1818.2.5 Power for Comparing Two Means 1828.2.6 Sample Size Determination 1838.3 Testing the Difference Between Two Population Rates (Normal Approximation Method) 1858.3.1 Power for Comparing Two Rates 1868.3.2 Sample Size Determination 1878.4 Summary 1888.5 Exercises 1899 One-way Analysis of Variance 1939.1 Overview 1939.1.1 Concept of ANOVA 1949.1.2 Data Layout and Modeling Assumption 1959.2 Procedures of ANOVA 1969.3 Multiple Comparisons of Means 2049.3.1 Tukey's Test 2049.3.2 Dunnett's Test 2069.3.3 Least Significant Difference (LSD) Test 2099.4 Checking ANOVA Assumptions 2119.4.1 Check for Normality 2119.4.2 Test for Homogeneity of Variances 2139.4.2.1 Bartlett's Test 2139.4.2.2 Levene's Test 2159.5 Data Transformations 2179.6 Summary 2189.7 Exercises 21810 Analysis of Variance in Different Experimental Designs 22110.1 ANOVA for Randomized Block Design 22110.1.1 Data Layout and Model Assumptions 22310.1.2 Procedure of ANOVA 22410.2 ANOVA for Two-factor Factorial Design 22910.2.1 Concept of Factorial Design 23010.2.2 Data Layout and Model Assumptions 23310.2.3 Procedure of ANOVA 23410.3 ANOVA for Repeated Measures Design 24010.3.1 Characteristics of Repeated Measures Data 24010.3.2 Data Layout and Model Assumptions 24210.3.3 Procedure of ANOVA 24310.3.4 Sphericity Test of Covariance Matrix 24510.3.5 Multiple Comparisons of Means 24810.4 ANOVA for 2 × 2 Crossover Design 25110.4.1 Concept of a 2 × 2 Crossover Design 25110.4.2 Data Layout and Model Assumptions 25210.4.3 Procedure of ANOVA 25410.5 Summary 25610.6 Exercises 25711 chi² Test 26111.1 Contingency Table 26211.1.1 General Form of Contingency Table 26311.1.2 Independence of Two Categorical Variables 26411.1.3 Significance Testing Using the Contingency Table 26511.2 chi² Test for a 2 × 2 Contingency Table 26611.2.1 Test of Independence 26611.2.2 Yates' Corrected chi² test for a 2 × 2 Contingency Table 26911.2.3 Paired Samples Design chi² Test 26911.2.4 Fisher's Exact Tests for Completely Randomized Design 27211.2.5 Exact McNemar's Test for Paired Samples Design 27511.3 chi² Test for R × C Contingency Tables 27611.3.1 Comparison of Multiple Independent Proportions 27611.3.2 Multiple Comparisons of Proportions 27811.4 chi² Goodness-of-Fit Test 28011.4.1 Normal Distribution Goodness-of-Fit Test 28111.4.2 Poisson Distribution Goodness-of-Fit Test 28311.5 Summary 28411.6 Exercises 28512 Nonparametric Tests Based on Rank 28912.1 Concept of Order Statistics 28912.2 Wilcoxon's Signed-Rank Test for Paired Samples 29012.3 Wilcoxon's Rank-Sum Test for Two Independent Samples 29512.4 Kruskal-Wallis Test for Multiple Independent Samples 29912.4.1 Kruskal-Wallis Test 29912.4.2 Multiple Comparisons 30112.5 Friedman's Test for Randomized Block Design 30312.6 Further Considerations About Nonparametric Tests 30612.7 Summary 30612.8 Exercises 30613 Simple Linear Regression 31113.1 Concept of Simple Linear Regression 31113.2 Establishment of Regression Model 31413.2.1 Least Squares Estimation of a Regression Coefficient 31413.2.2 Basic Properties of the Regression Model 31613.2.3 Hypothesis Testing of Regression Model 31713.3 Application of Regression Model 32113.3.1 Confidence Interval Estimation of a Regression Coefficient 32113.3.2 Confidence Band Estimation of Regression Model 32213.3.3 Prediction Band Estimation of Individual Response Values 32313.4 Evaluation of Model Fitting 32513.4.1 Coefficient of Determination 32513.4.2 Residual Analysis 32613.5 Summary 32713.6 Exercises 32814 Simple Linear Correlation 33114.1 Concept of Simple Linear Correlation 33114.1.1 Definition of Correlation Coefficient 33114.1.2 Interpretation of Correlation Coefficient 33414.2 Hypothesis Testing of Correlation Coefficient 33614.3 Confidence Interval Estimation for Correlation Coefficient 33814.4 Spearman's Rank Correlation 34014.4.1 Concept of Spearman's Rank Correlation Coefficient 34014.4.2 Hypothesis Testing of Spearman's Rank Correlation Coefficient 34214.5 Summary 34214.6 Exercises 34315 Multiple Linear Regression 34515.1 Multiple Linear Regression Model 34615.1.1 Concept of the Multiple Linear Regression 34615.1.2 Least Squares Estimation of Regression Coefficient 34915.1.3 Properties of the Least Squares Estimators 35115.1.4 Standardized Partial-Regression Coefficient 35115.2 Hypothesis Testing 35215.2.1 F-Test for Overall Regression Model 35215.2.2 t-Test for Partial-Regression Coefficients 35415.3 Evaluation of Model Fitting 35615.3.1 Coefficient of Determination and Adjusted Coefficient of Determination 35615.3.2 Residual Analysis and Outliers 35715.4 Other Aspects of Regression 35915.4.1 Multicollinearity 35915.4.2 Selection of Independent Variables 36115.4.3 Sample Size 36415.5 Summary 36415.6 Exercises 36416 Logistic Regression 36916.1 Logistic Regression Model 37016.1.1 Linear Probability Model 37116.1.2 Probability, Odds, and Logit Transformation 37116.1.3 Definition of Logistic Regression 37316.1.4 Inference for Logistic Regression 37516.1.4.1 Estimation of Model Coefficient 37516.1.4.2 Interpretation of Model Coefficient 37816.1.4.3 Hypothesis Testing of Model Coefficient 38016.1.4.4 Interval Estimation of Model Coefficient 38216.1.5 Evaluation of Model Fitting 38516.2 Conditional Logistic Regression Model 38816.2.1 Characteristics of Conditional Logistic Regression Model 39016.2.2 Estimation of Regression Coefficient 39016.2.3 Hypothesis Testing of Regression Coefficient 39316.3 Additional Remarks 39416.3.1 Sample Size 39416.3.2 Types of Independent Variables 39416.3.3 Selection of Independent Variables 39516.3.4 Missing Data 39516.4 Summary 39516.5 Exercises 39617 Survival Analysis 39917.1 Overview 40017.1.1 Concept of Survival Analysis 40017.1.2 Basic Functions of Survival Time 40217.2 Description of the Survival Process 40517.2.1 Product Limit Method 40517.2.2 Life Table Method 40817.3 Comparison of Survival Processes 41017.3.1 Log-Rank Test 41017.3.2 Other Methods for Comparing Survival Processes 41317.4 Cox's Proportional Hazards Model 41417.4.1 Concept and Model Assumptions 41517.4.2 Estimation of Model Coefficient 41717.4.3 Hypothesis Testing of Model Coefficient 41917.4.4 Evaluation of Model Fitting 42017.5 Other Aspects of Cox's Proportional Hazard Model 42117.5.1 Hazard Index 42117.5.2 Sample Size 42117.6 Summary 42217.7 Exercises 42318 Evaluation of Diagnostic Tests 43118.1 Basic Characteristics of Diagnostic Tests 43118.1.1 Sensitivity and Specificity 43318.1.2 Composite Measures of Sensitivity and Specificity 43518.1.3 Predictive Values 43818.1.4 Sensitivity and Specificity Comparison of Two Diagnostic Tests 44018.2 Agreement Between Diagnostic Tests 44318.2.1 Agreement of Categorical Data 44418.2.2 Agreement of Numerical Data 44718.3 Receiver Operating Characteristic Curve Analysis 44818.3.1 Concept of an ROC Curve 44918.3.2 Area Under the ROC Curve 45018.3.3 Comparison of Areas Under ROC Curves 45318.4 Summary 45618.5 Exercises 45719 Observational Study Design 46119.1 Cross-Sectional Studies 46219.1.1 Types of Cross-Sectional Studies 46219.1.2 Probability Sampling Methods 46219.1.3 Sample Size for Surveys 46619.1.4 Cross-Sectional Studies for Clues of Etiology 46819.2 Cohort Studies 46919.2.1 Measures of Association in Cohort Studies 46919.2.2 Sample Size for Cohort Studies 47019.3 Case-Control Studies 47219.3.1 Measures of Association in Case-Control Studies 47219.3.2 Sample Size for Case-Control Studies 47319.4 Summary 47419.5 Exercises 47520 Experimental Study Design 47720.1 Overview 47820.1.1 Basic Components of an Experimental Study 47820.1.2 Principles of Experimental Study Design 48020.1.3 Blinding Procedures in Clinical Trials 48220.2 Completely Randomized Design 48320.2.1 Concept of Completely Randomized Design 48320.2.2 Sample Size for Completely Randomized Design 48520.3 Randomized Block Design 48620.3.1 Concepts of Randomized Block Design 48620.3.2 Sample Size for Randomized Block Design 48820.4 Factorial Design 48920.5 Crossover Design 49120.5.1 Concepts of Crossover Design 49120.5.2 Sample Size for 2 × 2 Crossover Design 49220.6 Summary 49320.7 Exercises 493Appendix 495References 549Index 557

O autorze

Jingmei Jiang, PhD, is Professor of Biostatistics, as well as a Doctoral Tutor in the Institute of Basic Medical Sciences (IBMS) of the Chinese Academy of Medical Sciences (CAMS) and School of Basic Medicine of Peking Union Medical College (PUMC). She has edited or co-edited seven academic monographs on biostatistics, and is also an editorial board member of several international journals. She is undertaking several research projects at the National Natural Science Foundation of China and other agencies.