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INTRODUCTORY
BIOSTATISTICS
INTRODUCTORY
BIOSTATISTICS
Copyright
CONTENTS
PREFACE
1 Descriptive Methods for Categorical Data
1.1 PROPORTIONS
1.1.1 Comparative Studies
1.1.2 Screening Tests
1.1.3 Displaying Proportions
1.2 RATES
1.2.1 Changes
1.2.2 Measures of Morbidity and Mortality
1.2.3 Standardization of Rates
1.3 RATIOS
1.3.1 Relative Risk
1.3.2 Odds and Odds Ratio
1.3.3 Generalized Odds for Ordered 2Dk Tables
1.3.4 Mantel ¨C Haenszel Method
1.3.5 Standardized Mortality Ratio
1.4 NOTES ON COMPUTATIONS
EXERCISES
2 Descriptive Methods for Continuous Data
2.1 TABULAR AND GRAPHICAL METHODS
2.1.1 One- Way Scatter Plots
2.1.2 Frequency Distribution
2.1.3 Histogram and the Frequency Polygon
2.1.4 Cumulative Frequency Graph and Percentiles
2.1.5 Stem- and- Leaf Diagrams
2.2 NUMERICAL METHODS
2.2.1 Mean
2.2.2 Other Measures of Location
2.2.3 Measures of Dispersion
2.2.4 Box Plots
2.3 SPECIAL CASE OF BINARY DATA
2.4 COEFFICIENTS OF CORRELATION
2.4.1 Pearson¡¯s Correlation Coe¡ë cient
2.4.2 Nonparametric Correlation Coe¡ë cients
2.5 NOTES ON COMPUTATIONS
EXERCISES
3 Probability and Probability Models
3.1 PROBABILITY
3.1.1 Certainty of Uncertainty
3.1.2 Probability
3.1.3 Statistical Relationship
3.1.4 Using Screening Tests
3.1.5 Measuring Agreement
3.2 NORMAL DISTRIBUTION
3.2.1 Shape of the Normal Curve
3.2.2 Areas under the Standard Normal Curve
3.2.3 Normal Distribution as a Probability Model
3.3 PROBABILITY MODELS FOR CONTINUOUS DATA
3.4 PROBABILITY MODELS FOR DISCRETE DATA
3.4.1 Binomial Distribution
3.4.2 Poisson Distribution
3.5 BRIEF NOTES ON THE FUNDAMENTALS
3.5.1 Mean and Variance
3.5.2 Pair- Matched Case ¨C Control Study
3.6 NOTES ON COMPUTATIONS
EXERCISES
4 Estimation of Parameters
4.1 BASIC CONCEPTS
4.1.1 Statistics as Variables
4.1.2 Sampling Distributions
4.1.3 Introduction to Con . dence Estimation
4.2 ESTIMATION OF MEANS
4.2.1 Con . dence Intervals for a Mean
4.2.2 Uses of Small Samples
4.2.3 Evaluation of Interventions
4.3 ESTIMATION OF PROPORTIONS
4.4 ESTIMATION OF ODDS RATIOS
4.5 ESTIMATION OF CORRELATION COEFFICIENTS
4.6 BRIEF NOTES ON THE FUNDAMENTALS
4.7 NOTES ON COMPUTATIONS
EXERCISES
5 Introduction to Statistical Tests of Signi.cance
5.1 BASIC CONCEPTS
5.1.1 Hypothesis Tests
5.1.2 Statistical Evidence
5.1.3 Errors
5.2 ANALOGIES
5.2.1 Trials by Jury
5.2.2 Medical Screening Tests
5.2.3 Common Expectations
5.3 SUMMARIES AND CONCLUSIONS
5.3.1 Rejection Region
5.3.2 p Values
5.3.3 Relationship to Con . dence Intervals
5.4 BRIEF NOTES ON THE FUNDAMENTALS
5.4.1 Type I and Type II Errors
5.4.2 More about Errors and p Values
EXERCISES
6 Comparison of Population Proportions
6.1 ONE- SAMPLE PROBLEM WITH BINARY DATA
6.2 ANALYSIS OF PAIR- MATCHED DATA
6.3 COMPARISON OF TWO PROPORTIONS
6.4 MANTEL ¨C HAENSZEL METHOD
6.5 INFERENCES FOR GENERAL TWO- WAY TABLES
6.6 FISHER¡¯S EXACT TEST
6.7 ORDERED 2Dk CONTINGENCY TABLES
6.8 NOTES ON COMPUTATIONS
EXERCISES
7 Comparison of Population Means
7.1 ONE- SAMPLE PROBLEM WITH CONTINUOUS DATA
7.2 ANALYSIS OF PAIR- MATCHED DATA
7.3 COMPARISON OF TWO MEANS
7.4 NONPARAMETRIC METHODS
7.4.1 Wilcoxon Rank- Sum Test
7.4.2 Wilcoxon Signed- Rank Test
7.5 ONE- WAY ANALYSIS OF VARIANCE
7.6 BRIEF NOTES ON THE FUNDAMENTALS
7.7 NOTES ON COMPUTATIONS
EXERCISES
8 Correlation and Regression
8.1 SIMPLE REGRESSION ANALYSIS
8.1.1 Simple Linear Regression Model
8.1.2 Scatter Diagram
8.1.3 Meaning of Regression Parameters
8.1.4 Estimation of Parameters
8.1.5 Testing for Independence
8.1.6 Analysis- of- Variance Approach
8.2 MULTIPLE REGRESSION ANALYSIS
8.2.1 Regression Model with Several Independent Variables
8.2.2 Meaning of Regression Parameters
8.2.3 E ¤ ect Modi . cations
8.2.4 Polynomial Regression
8.2.5 Estimation of Parameters
8.2.6 Analysis- of- Variance Approach
8.2.7 Testing Hypotheses in Multiple Linear Regression
8.3 NOTES ON COMPUTATIONS
EXERCISES
9 Logistic Regression
9.1 SIMPLE REGRESSION ANALYSIS
9.1.1 Simple Logistic Regression Model
9.1.2 Measure of Association
9.1.3 E ¤ ect of Measurement Scale
9.1.4 Tests of Association
9.1.5 Use of the Logistic Model for Di ¤ erent Designs
9.1.6 Overdispersion
9.2 MULTIPLE REGRESSION ANALYSIS
9.2.1 Logistic Regression Model with Several Covariates
9.2.2 E ¤ ect Modi . cations
9.2.3 Polynomial Regression
9.2.4 Testing Hypotheses in Multiple Logistic Regression
9.2.5 Receiver Operating Characteristic Curve
9.2.6 ROC Curve and Logistic Regression
9.3 BRIEF NOTES ON THE FUNDAMENTALS
EXERCISE
10 Methods for Count Data
10.1 POISSON DISTRIBUTION
10.2 TESTING GOODNESS OF FIT
10.3 POISSON REGRESSION MODEL
10.3.1 Simple Regression Analysis
10.3.2 Multiple Regression Analysis
10.3.3 Overdispersion
10.3.4 Stepwise Regression
EXERCISE
11 Analysis of Survival Data and Data from Matched Studies
11.1 SURVIVAL DATA
11.2 INTRODUCTORY SURVIVAL ANALYSES
11.2.1 Kaplan ¨C Meier Curve
11.2.2 Comparison of Survival Distributions
11.3 SIMPLE REGRESSION AND CORRELATION
11.3.1 Model and Approach
11.3.2 Measures of Association
11.3.3 Tests of Association
11.4 MULTIPLE REGRESSION AND CORRELATION
11.4.1 Proportional Hazards Model with Several Covariates
11.4.2 Testing Hypotheses in Multiple Regression
11.4.3 Time- Dependent Covariates and Applications
11.5 PAIR- MATCHED CASE ¨C CONTROL STUDIES
11.5.1 Model
11.5.2 Analysis
11.6 MULTIPLE MATCHING
11.6.1 Conditional Approach
11.6.2 Estimation of the Odds Ratio
11.6.3 Testing for Exposure E ¤ ect
11.7 CONDITIONAL LOGISTIC REGRESSION
11.7.1 Simple Regression Analysis
11.7.2 Multiple Regression Analysis
EXERCISES
12 Study Designs
12.1 TYPES OF STUDY DESIGNS
12.2 CLASSIFICATION OF CLINICAL TRIALS
12.3 DESIGNING PHASE I CANCER TRIALS
12.4 SAMPLE SIZE DETERMINATION FOR PHASE II TRIALS AND SURVEYS
12.5 SAMPLE SIZES FOR OTHER PHASE II TRIALS
12.5.1 Continuous Endpoints
12.5.2 Correlation Endpoints
12.6 ABOUT SIMON¡¯S TWO- STAGE PHASE II DESIGN
12.7 PHASE II DESIGNS FOR SELECTION
12.7.1 Continuous Endpoints
12.7.2 Binary Endpoints
12.8 TOXICITY MONITORING IN PHASE II TRIALS
12.9 SAMPLE SIZE DETERMINATION FOR PHASE III TRIALS
12.9.1 Comparison of Two Means
12.9.2 Comparison of Two Proportions
12.9.3 Survival Time as the Endpoint
12.10 SAMPLE SIZE DETERMINATION FOR CASE ¨C CONTROL STUDIES
12.10.1 Unmatched Designs for a Binary Exposure
12.10.2 Matched Designs for a Binary Exposure
12.10.3 Unmatched Designs for a Continuous Exposure
EXERCISES
BIBLIOGRAPHY
APPENDICES
APPENDIX A: TABLE OF RANDOM NUMBERS
APPENDIX B: AREA UNDER THE STANDARD NORMAL CURVE
APPENDIX C: PERCENTILES OF THE t DISTRIBUTION
APPENDIX D: PERCENTILES OF CHI- SQUARE DISTRIBUTIONS
APPENDIX E: PERCENTILES OF THE F DISTRIBUTION
Answers to Selected Exercises
INDEX
Nội dung
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