Statistical Methodologies with Medical Applications

This book presents the methodology and applications of a range of important topics in statistics, and is designed for graduate students in Statistics and Biostatistics and for medical researchers. Illustrations and more than ninety exercises with solutions are presented. They are constructed from the research findings of the medical journals, summary reports of the Centre for Disease Control (CDC) and the World Health Organization (WHO), and practical situations. The illustrations and exercises are related to topics such as immunization, obesity, hypertension, lipid levels, diet and exercise, harmful effects of smoking and air pollution, and the benefits of gluten free diet. This book can be recommended for a one or two semester graduate level course for students studying Statistics, Biostatistics, Epidemiology and Health Sciences. It will also be useful as a companion for medical researchers and research oriented physicians.

Auteur
SRS Rao Poduri, Professor of Statistics, University of Rochester. Since receiving his?Ph.D degree in Statistics in 1965 from Harvard University under the supervision of the eminent professor William G. Cochran, Professor Poduri has?been teaching courses in five or six major areas of statistics to graduate and undergraduate students at the University of Rochester.

Résumé

This book presents the methodology and applications of a range of important topics in statistics, and is designed for graduate students in Statistics and Biostatistics and for medical researchers. Illustrations and more than ninety exercises with solutions are presented. They are constructed from the research findings of the medical journals, summary reports of the Centre for Disease Control (CDC) and the World Health Organization (WHO), and practical situations. The illustrations and exercises are related to topics such as immunization, obesity, hypertension, lipid levels, diet and exercise, harmful effects of smoking and air pollution, and the benefits of gluten free diet.
This book can be recommended for a one or two semester graduate level course for students studying Statistics, Biostatistics, Epidemiology and Health Sciences. It will also be useful as a companion for medical researchers and research oriented physicians.

Contenu

Topics for illustrations, examples and exercises xv

Preface xvii

List of abbreviations xix

1 Statistical measures 1

1.1 Introduction 1

1.2 Mean, mode and median 2

1.3 Variance and standard deviation 3

1.4 Quartiles, deciles and percentiles 4

1.5 Skewness and kurtosis 5

1.6 Frequency distributions 6

1.7 Covariance and correlation 7

1.8 Joint frequency distribution 9

1.9 Linear transformation of the observations 10

1.10 Linear combinations of two sets of observations 10

Exercises 11

2 Probability, random variable, expected value and variance 14

2.1 Introduction 14

2.2 Events and probabilities 14

2.3 Mutually exclusive events 15

2.4 Independent and dependent events 15

2.5 Addition of probabilities 16

2.6 Bayes' theorem 16

2.7 Random variables and probability distributions 17

2.8 Expected value, variance and standard deviation 17

2.9 Moments of a distribution 18

Exercises 18

3 Odds ratios, relative risk, sensitivity, specificity and the ROC curve 19

3.1 Introduction 19

3.2 Odds ratio 19

3.3 Relative risk 20

3.4 Sensitivity and specificity 21

3.5 The receiver operating characteristic (ROC) curve 22

Exercises 22

4 Probability distributions, expectations, variances and correlation 24

4.1 Introduction 24

4.2 Probability distribution of a discrete random variable 25

4.3 Discrete distributions 25

4.4 Continuous distributions 29

4.5 Joint distribution of two discrete random variables 34

4.6 Bivariate normal distribution 37

Exercises 38

5 Means, standard errors and confidence limits 40

5.1 Introduction 40

5.2 Expectation, variance and standard error (S.E.) of the sample mean 41

5.3 Estimation of the variance and standard error 42

5.4 Confidence limits for the mean 43

5.5 Estimator and confidence limits for the difference of two means 44

5.6 Approximate confidence limits for the difference of two means 46

5.7 Matched samples and paired comparisons 47

5.8 Confidence limits for the variance 48

5.9 Confidence limits for the ratio of two variances 49

5.10 Least squares and maximum likelihood methods of estimation 49

Exercises 51

6 Proportions, odds ratios and relative risks: Estimation and confidence limits 54

6.1 Introduction 54

6.2 A single proportion 54

6.3 Confidence limits for the proportion 55

6.4 Difference of two proportions or percentages 56

6.5 Combining proportions from independent samples 56

6.6 More than two classes or categories 57

6.7 Odds ratio 58

6.8 Relative risk 59

Exercises 59

7 Tests of hypotheses: Means and variances 62

7.1 Introduction 62

7.2 Principle steps for the tests of a hypothesis 63

7.3 Right-sided alternative, test statistic and critical region 65

7.4 Left-sided alternative and the critical region 69

7.5 Two-sided alternative, critical region and the p-value 72

7.6 Difference between two means: Variances known 75

7.7 Matched samples and paired comparison 77

7.8 Test for the variance 77

7.9 Test for the equality of two variances 78

7.10 Homogeneity of variances 79

Exercises 80

8 Tests of hypotheses: Proportions and percentages 82

8.1 A single proportion 82

8.2 Right-sided alternative 82

8.3 Left-sided alternative 85

8.4 Two-sided alternative 87

8.5 Difference of two proportions 90

8.6 Specified difference of two proportions 95

8.7 Equality of two or more proportions 95 8.8 A common prop...