Applied medical statistics

Applied Medical Statistics
Contents
Preface
Acknowledgments
About the Companion Website
1 What is Biostatistics
1.1 Overview
1.2 Some Statistical Terminology
1.2.1 Population and Sample
1.2.2 Homogeneity and Variation
1.2.3 Parameter and Statistic
1.2.4 Types of Data
1.2.5 Error
1.3 Workflow of Applied Statistics
1.4 Statistics and Its Related Disciplines
1.5 Statistical Thinking
1.6 Summary
1.7 Exercises
2 Descriptive Statistics
2.1 Frequency Tables and Graphs
2.1.1 Frequency Distribution of Numerical Data
2.1.2 Frequency Distribution of Categorical Data
2.2 Descriptive Statistics of Numerical Data
2.2.1 Measures of Central Tendency
2.2.2 Measures of Dispersion
2.3 Descriptive Statistics of Categorical Data
2.3.1 Relative Numbers
2.3.2 Standardization of Rates
2.4 Constructing Statistical Tables and Graphs
2.4.1 Statistical Tables
2.4.2 Statistical Graphs
2.5 Summary
2.6 Exercises
3 Fundamentals of Probability
3.1 Sample Space and Random Events
3.1.1 Definitions of Sample Space and Random Events
3.1.2 Operation of Events
3.2 Relative Frequency and Probability
3.2.1 Definition of Probability
3.2.2 Basic Properties of Probability
3.3 Conditional Probability and Independence of Events
3.3.1 Conditional Probability
3.3.2 Independence of Events
3.4 Multiplication Law of Probability
3.5 Addition Law of Probability
3.5.1 General Addition Law
3.5.2 Addition Law of Mutually Exclusive Events
3.6 Total Probability Formula and Bayes’ Rule
3.6.1 Total Probability Formula
3.6.2 Bayes’ Rule
3.7 Summary
3.8 Exercises
4 Discrete Random Variable
4.1 Concept of the Random Variable
4.2 Probability Distribution of the Discrete Random Variable
4.2.1 Probability Mass Function
4.2.2 Cumulative Distribution Function
4.2.3 Association Between the Probability Distribution and Relative Frequency Distribution
4.3 Numerical Characteristics
4.3.1 Expected Value
4.3.2 Variance and Standard Deviation
4.4 Commonly Used Discrete Probability Distributions
4.4.1 Binomial Distribution
4.4.2 Multinomial Distribution
4.4.3 Poisson Distribution
4.5 Summary
4.6 Exercises
5 Continuous Random Variable
5.1 Concept of Continuous Random Variable
5.2 Numerical Characteristics
5.3 Normal Distribution
5.3.1 Concept of the Normal Distribution
5.3.2 Standard Normal Distribution
5.3.3 Descriptive Methods for Assessing Normality
5.4 Application of the Normal Distribution
5.4.1 Normal Approximation to the Binomial Distribution
5.4.2 Normal Approximation to the Poisson Distribution
5.4.3 Determining the Medical Reference Interval
5.5 Summary
5.6 Exercises
6 Sampling Distribution and Parameter Estimation
6.1 Samples and Statistics
6.2 Sampling Distribution of a Statistic
6.2.1 Sampling Distribution of the Mean
6.2.2 Sampling Distribution of the Variance
6.2.3 Sampling Distribution of the Rate (Normal Approximation)
6.3 Estimation of One Population Parameter
6.3.1 Point Estimation and Its Quality Evaluation
6.3.2 Interval Estimation for the Mean
6.4 Estimation of Two Population Parameters
6.4.1 Estimation of the Difference in Means
6.4.1.1 Point Estimation
6.4.1.2 Interval Estimation
6.4.2 Estimation of the Ratio of Variances
6.4.2.1 Point Estimation
6.4.2.2 Interval Estimation
6.4.3 Estimation of the Difference Between Rates (Normal Approximation Method)
6.4.3.1 Point Estimation
6.4.3.2 Interval Estimation
6.5 Summary
6.6 Exercises
7 Hypothesis Testing for One Parameter
7.1 Overview
7.1.1 Concepts and Procedures
7.1.2 Type I and Type II Errors
7.1.3 One-sided and Two-sided Hypothesis
7.1.4 Association Between Hypothesis Testing and Interval Estimation
7.2 Hypothesis Testing for One Parameter
7.2.1 Hypothesis Tests for the Mean
7.2.1.1 Power of the Test
7.2.1.2 Sample Size Determination
7.2.2 Hypothesis Tests for the Rate (Normal Approximation Methods)
7.2.2.1 Power of the Test
7.2.2.2 Sample Size Determination
7.3 Further Considerations on Hypothesis Testing
7.3.1 About the Significance Level
7.3.2 Statistical Significance and Clinical Significance
7.4 Summary
7.5 Exercises
8 Hypothesis Testing for Two Population Parameters
8.1 Testing the Difference Between Two Population Means: Paired Samples
8.2 Testing the Difference Between Two Population Means: Independent Samples
8.2.1 t-Test for Means with Equal Variances
8.2.2 F-Test for the Equality of Two Variances
8.2.3 Approximation t-Test for Means with Unequal Variances
8.2.4 Z-Test for Means with Large-Sample Sizes
8.2.5 Power for Comparing Two Means
8.2.6 Sample Size Determination
8.3 Testing the Difference Between Two Population Rates (Normal Approximation Method)
8.3.1 Power for Comparing Two Rates
8.3.2 Sample Size Determination
8.4 Summary
8.5 Exercises
9 One-way Analysis of Variance
9.1 Overview
9.1.1 Concept of ANOVA
9.1.2 Data Layout and Modeling Assumption
9.2 Procedures of ANOVA
9.3 Multiple Comparisons of Means
9.3.1 Tukey’s Test
9.3.2 Dunnett’s Test
9.3.3 Least Significant Difference (LSD) Test
9.4 Checking ANOVA Assumptions
9.4.1 Check for Normality
9.4.2 Test for Homogeneity of Variances
9.4.2.1 Bartlett’s Test
9.4.2.2 Levene’s Test
9.5 Data Transformations
9.6 Summary
9.7 Exercises
10 Analysis of Variance in Different Experimental Designs
10.1 ANOVA for Randomized Block Design
10.1.1 Data Layout and Model Assumptions
10.1.2 Procedure of ANOVA
10.2 ANOVA for Two-factor Factorial Design
10.2.1 Concept of Factorial Design
10.2.2 Data Layout and Model Assumptions
10.2.3 Procedure of ANOVA
10.3 ANOVA for Repeated Measures Design
10.3.1 Characteristics of Repeated Measures Data
10.3.2 Data Layout and Model Assumptions
10.3.3 Procedure of ANOVA
10.3.4 Sphericity Test of Covariance Matrix
10.3.5 Multiple Comparisons of Means
10.4 ANOVA for 2 × 2 Crossover Design
10.4.1 Concept of a 2 × 2 Crossover Design
10.4.2 Data Layout and Model Assumptions
10.4.3 Procedure of ANOVA
10.5 Summary
10.6 Exercises
11 χ2 Test
11.1 Contingency Table
11.1.1 General Form of Contingency Table
11.1.2 Independence of Two Categorical Variables
11.1.3 Significance Testing Using the Contingency Table
11.2 χ2 Test for a 2 × 2 Contingency Table
11.2.1 Test of Independence
11.2.2 Yates’ Corrected χ2 test for a 2 × 2 Contingency Table
11.2.3 Paired Samples Design χ2 Test
11.2.4 Fisher’s Exact Tests for Completely Randomized Design
11.2.5 Exact McNemar’s Test for Paired Samples Design
11.3 χ2 Test for R × C Contingency Tables
11.3.1 Comparison of Multiple Independent Proportions
11.3.2 Multiple Comparisons of Proportions
11.4 χ2 Goodness-of-Fit Test
11.4.1 Normal Distribution Goodness-of-Fit Test
11.4.2 Poisson Distribution Goodness-of-Fit Test
11.5 Summary
11.6 Exercises
12 Nonparametric Tests Based on Rank
12.1 Concept of Order Statistics
12.2 Wilcoxon’s Signed-Rank Test for Paired Samples
12.3 Wilcoxon’s Rank-Sum Test for Two Independent Samples
12.4 Kruskal–Wallis Test for Multiple Independent Samples
12.4.1 Kruskal–Wallis Test
12.4.2 Multiple Comparisons
12.5 Friedman’s Test for Randomized Block Design
12.6 Further Considerations About Nonparametric Tests
12.7 Summary
12.8 Exercises
13 Simple Linear Regression
13.1 Concept of Simple Linear Regression
13.2 Establishment of Regression Model
13.2.1 Least Squares Estimation of a Regression Coefficient
13.2.2 Basic Properties of the Regression Model
13.2.3 Hypothesis Testing of Regression Model
13.3 Application of Regression Model
13.3.1 Confidence Interval Estimation of a Regression Coefficient
13.3.2 Confidence Band Estimation of Regression Model
13.3.3 Prediction Band Estimation of Individual Response Values
13.4 Evaluation of Model Fitting
13.4.1 Coefficient of Determination
13.4.2 Residual Analysis
13.5 Summary
13.6 Exercises
14 Simple Linear Correlation
14.1 Concept of Simple Linear Correlation
14.1.1 Definition of Correlation Coefficient
14.1.2 Interpretation of Correlation Coefficient
14.2 Hypothesis Testing of Correlation Coefficient
14.3 Confidence Interval Estimation for Correlation Coefficient
14.4 Spearman’s Rank Correlation
14.4.1 Concept of Spearman’s Rank Correlation Coefficient
14.4.2 Hypothesis Testing of Spearman’s Rank Correlation Coefficient
14.5 Summary
14.6 Exercises
15 Multiple Linear Regression
15.1 Multiple Linear Regression Model
15.1.1 Concept of the Multiple Linear Regression
15.1.2 Least Squares Estimation of Regression Coefficient
15.1.3 Properties of the Least Squares Estimators
15.1.4 Standardized Partial-Regression Coefficient
15.2 Hypothesis Testing
15.2.1 F-Test for Overall Regression Model
15.2.2 t-Test for Partial-Regression Coefficients
15.3 Evaluation of Model Fitting
15.3.1 Coefficient of Determination and Adjusted Coefficient of Determination
15.3.2 Residual Analysis and Outliers
15.4 Other Aspects of Regression
15.4.1 Multicollinearity
15.4.2 Selection of Independent Variables
15.4.3 Sample Size
15.5 Summary
15.6 Exercises
16 Logistic Regression
16.1 Logistic Regression Model
16.1.1 Linear Probability Model
16.1.2 Probability, Odds, and Logit Transformation
16.1.3 Definition of Logistic Regression
16.1.4 Inference for Logistic Regression
16.1.4.1 Estimation of Model Coefficient
16.1.4.2 Interpretation of Model Coefficient
16.1.4.3 Hypothesis Testing of Model Coefficient
16.1.4.4 Interval Estimation of Model Coefficient
16.1.5 Evaluation of Model Fitting
16.2 Conditional Logistic Regression Model
16.2.1 Characteristics of Conditional Logistic Regression Model
16.2.2 Estimation of Regression Coefficient
16.2.3 Hypothesis Testing of Regression Coefficient
16.3 Additional Remarks
16.3.1 Sample Size
16.3.2 Types of Independent Variables
16.3.3 Selection of Independent Variables
16.3.4 Missing Data
16.4 Summary
16.5 Exercises
17 Survival Analysis
17.1 Overview
17.1.1 Concept of Survival Analysis
17.1.2 Basic Functions of Survival Time
17.2 Description of the Survival Process
17.2.1 Product Limit Method
17.2.2 Life Table Method
17.3 Comparison of Survival Processes
17.3.1 Log-Rank Test
17.3.2 Other Methods for Comparing Survival Processes
17.4 Cox’s Proportional Hazards Model
17.4.1 Concept and Model Assumptions
17.4.2 Estimation of Model Coefficient
17.4.3 Hypothesis Testing of Model Coefficient
17.4.4 Evaluation of Model Fitting
17.5 Other Aspects of Cox’s Proportional Hazard Model
17.5.1 Hazard Index
17.5.2 Sample Size
17.6 Summary
17.7 Exercises
18 Evaluation of Diagnostic Tests
18.1 Basic Characteristics of Diagnostic Tests
18.1.1 Sensitivity and Specificity
18.1.2 Composite Measures of Sensitivity and Specificity
18.1.3 Predictive Values
18.1.4 Sensitivity and Specificity Comparison of Two Diagnostic Tests
18.2 Agreement Between Diagnostic Tests
18.2.1 Agreement of Categorical Data
18.2.2 Agreement of Numerical Data
18.3 Receiver Operating Characteristic Curve Analysis
18.3.1 Concept of an ROC Curve
18.3.2 Area Under the ROC Curve
18.3.3 Comparison of Areas Under ROC Curves
18.4 Summary
18.5 Exercises
19 Observational Study Design
19.1 Cross-Sectional Studies
19.1.1 Types of Cross-Sectional Studies
19.1.2 Probability Sampling Methods
19.1.3 Sample Size for Surveys
19.1.4 Cross-Sectional Studies for Clues of Etiology
19.2 Cohort Studies
19.2.1 Measures of Association in Cohort Studies
19.2.2 Sample Size for Cohort Studies
19.3 Case-Control Studies
19.3.1 Measures of Association in Case-Control Studies
19.3.2 Sample Size for Case-Control Studies
19.4 Summary
19.5 Exercises
20 Experimental Study Design
20.1 Overview
20.1.1 Basic Components of an Experimental Study
20.1.2 Principles of Experimental Study Design
20.1.3 Blinding Procedures in Clinical Trials
20.2 Completely Randomized Design
20.2.1 Concept of Completely Randomized Design
20.2.2 Sample Size for Completely Randomized Design
20.3 Randomized Block Design
20.3.1 Concepts of Randomized Block Design
20.3.2 Sample Size for Randomized Block Design
20.4 Factorial Design
20.5 Crossover Design
20.5.1 Concepts of Crossover Design
20.5.2 Sample Size for 2 × 2 Crossover Design
20.6 Summary
20.7 Exercises
Appendix
References
Index
EULA