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