# Statistical Methodologies with Medical Applications

## Rao, P.

1ª Edición Diciembre 2016

Inglés

Tapa dura

288 pags

500 gr

17 x 24 x cm

### ISBN 9781119258490

### Editorial WILEY

## LIBRO IMPRESO

## LIBRO ELECTRÓNICO

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### Description

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 HealthOrganization (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 airpollution, 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 medicalresearchers and research oriented physicians.

### Table of Contents

1 Statistical Measures

- 1.1 Introduction
- 1.2 Mean, Mode and Median
- 1.3 Variance and Standard Deviation
- 1.4 Quartiles, Deciles and Percentiles
- 1.5 Skewness and Kurtosis
- 1.6 Frequency Distributions
- 1.7 Covariance and Correlation
- 1.8 Joint Frequency Distribution
- 1.9 Linear transformation of the observations
- 1.10 Linear combinations of two sets of observations
- Exercises

2 Probability, Random Variable, Expected value and Variance

- 2.1 Introduction
- 2.2 Events and Probabilities
- 2.3 Mutually exclusive events
- 2.4 Independent and dependent events
- 2.5 Addition of probabilities
- 2.6 Bayes' theorem
- 2.7 Random variables and Probability Distributions
- 2.8 Expected Value, Variance and Standard Deviation
- 2.9 Moments of a distribution
- Exercises

3 Odds Ratios, Relative Risk, Sensitivity and Specificity and the ROC Curve

- 3.1 Introduction
- 3.2 Odds Ratio
- 3.3 Relative Risk
- 3.4 Sensitivity and Specificity
- 3.5 The receiving Operating Characteristic (ROC) Curve
- Exercises

4 Probability distributions

- 4.1 Introduction
- 4.2 Probability distribution of a discrete random variable
- 4.3 Discrete distributions
- 4.3.1 Uniform distribution
- 4.3.2 Binomial distribution
- 4.3.3 Multinomial distribution
- 4.3.4 Poisson distribution
- 4.3.5 Hypergeometric distribution
- 4.4 Continuous distributions
- 4.4.1 Uniform distribution for the continuous variable
- 4.4.2 Normal distribution
- 4.4.3 Normal approximation to the binomial distribution
- 4.4.4 Gamma distribution
- 4.4.5 Exponential distribution
- 4.4.6 Chisquare distribution
- 4.4.7 Weibull distribution
- 4.4.8 Student's - t and F-distributions
- 4.5 Joint distribution of two discrete random variables
- 4.5.1 Conditional distributions, means and variances
- 4.5.2 Unconditional expectations and variances
- 4.6 Bivariate normal distribution
- Exercises
- Appendix A4

5 Means, Standard Errors and Confidence Limits

- 5.1 Introduction
- 5.2 Expectation, Variance and Standard Error (S.E.) of the sample mean
- 5.3 Estimation of the Variance and Standard Error
- 5.4 Confidence Limits for the mean
- 5.5 Estimator and Confidence Limits for the difference of two means
- 5.6 Approximate confidence limits for the difference of two means
- 5.6.1 Large samples.
- 5.6.2 Welch - Aspin approximation.
- 5.6.3 Cochran's approximation.
- 5.7 Matched samples and paired comparisons
- 5.8 Confidence limits for the variance
- 5.9 Confidence limits for the ratio of two variances
- 5.10 Least Squares and Maximum Likelihood methods of estimation
- Exercises
- Appendix A5
- A5.1 Tschebycheff’s inequality
- A5.2 Mean Square Error

6 Proportions, Odds Ratios and Relative Risks: Estimation and Confidence Limits

- 6.1 Introduction
- 6.2 A single proportion
- 6.3 Confidence limits for the proportion
- 6.4 Difference of two proportions or percentages
- 6.5 Combining proportions from independent samples
- 6.6 More than two classes or categories
- 6.7 Odds ratio
- 6.8 Relative risk
- Exercises
- Appendix A6

7 Tests of Hypotheses: Means and Variances

- 7.1 Introduction
- 7.2 Principle steps for the tests of a hypothesis
- 7.2.1 Null and alternate hypotheses
- 7.2.2 Decision rule, test statistic and Type I & II errors
- 7.2.3 Significance level and Critical region
- 7.2.4 The p-value
- 7.2.5 Power of the test and the sample size
- 7.3 Right - sided alternative, test statistic and Critical Region
- 7.3.1 The p-value
- 7.3.2 Power of the test
- 7.3.3 Sample size for specified power
- 7.3.4 Right-sided alternative and estimated variance
- 7.3.5 Power of the test with estimated variance
- 7.4 Left-sided alternative and the Critical Region
- 7.4.1 The p-value
- 7.4.2 Power of the test
- 7.4.3 Sample size for specified power
- 7.4.4 Left-sided alternative with estimated variance
- 7.5 Two-sided alternative: Critical Region and the p-value
- 7.5.1 Power of the test
- 7.5.2 Sample size for specified power
- 7.5.3 Two-sided alternative and estimated variance
- 7.6 Difference between two means: variances known
- 7.6.1 Difference between two means: variances estimated
- 7.7 Matched samples and paired comparisons
- 7.8 Test for the variance
- 7.9 Test for the equality of two variances
- 7.10 Homogeneity of variances
- Exercises

8 Tests of hypotheses: Proportions and Percentages

- 8.1 A single proportion
- 8.2 Right-sided alternative
- 8.2.1 Critical Region
- 8.2.2 The p-value
- 8.2.3 Power of the test
- 8.2.4 Sample size for specified power
- 8.3 Left-sided alternative
- 8.3.1 Critical region
- 8.3.2 The p-value
- 8.3.3 Power of the test
- 8.3.4 Sample size for specified power
- 8.4 Two-sided alternative
- 8.4.1 Critical Region
- 8.4.2 The p-value
- 8.4.3 Power of the test
- 8.4.4 Sample size for specified power
- 8.5 Difference of two proportions
- 8.5.1 Right-side alternative: Critical Region and p-value
- 8.5.2 Right-sided alternative: Power and sample size
- 8.5.3 Left-sided alternative: Critical Region and p-value
- 8.5.4 Left-sided alternative: Power and sample size
- 8.5.5 Two-sided alternative: Critical Region and p-value
- 8.5.6 Power and sample size
- 8.6 Specified difference of two proportions
- 8.7 Equality of two or more proportions
- 8.8 A common proportion
- Exercises

9 The Chisquare Statistic

- 9.1 Introduction
- 9.2 The test statistic
- 9.2.1 A single proportion
- 9.2.2 Specified proportions
- 9.3 Test of goodness of fit
- 9.4 Test of independence: (r x c) classification
- 9.5 Test of independence: (2 x 2) classification
- 9.5.1 Fisher’s Exact Test of Independence
- 9.5.2 Mantel-Hanszel test statistic
- Exercises
- Appendix A9
- A9.1 Derivation of (9.4a)
- A9.2 Equality of the proportions

10 Regression and Correlation

- 10.1 Introduction
- 10.2 The Regression model: one independent variable
- 10.2.1 Least Squares Estimation of the regression
- 10.2.2 Properties of the estimators
- 10.2.3 ANOVA (Analysis of Variance) for the Significance of the regression
- 10.2.4 Tests of hypotheses, Confidence limits and Prediction intervals
- 10.3 Regression on two independent variables
- 10.3.1 Properties of the estimators
- 10.3.2 ANOVA for the Significance of the regression
- 10.3.3 Tests of hypotheses, Confidence limits and Prediction intervals
- 10.4 Multiple regressions: The Least Squares Estimation
- 10.4.1 ANOVA for the Significance of the regression
- 10.4.2 Tests of hypotheses, Confidence limits and Prediction intervals
- 10.4.3 Multiple Correlation, Adjusted R2 and Partial Correlation
- 10.4.4 Effect of including two or more independent variables and the Partial F- test
- 10.4.5 Equality of two or more series of regressions
- 10.5 Indicator variables
- 10.5.1 Separate regressions
- 10.5.2 Regressions with equal slopes
- 10.5.3 Regressions with the same intercepts
- 10.6 Regression through the origin
- 10.7 Estimation of trends
- 10.8 Logistic regression and the Odds Ratio
- 10.8.1 A single continuous predictor
- 10.8.2 Two continuous predictors
- 10.8.3 A single dichotomous predictor
- 10.9 Weighted Least Squares (WLS) Estimator
- 10.10 Correlation
- 10.10.1 Test of hypothesis that two random variables are uncorrelated
- 10.10.2 Test of hypothesis that the correlation coefficient takes a specified value
- 10.10.3 Confidence limits for the correlation coefficient
- 10.11 Further topics in regression
- 10.11.1 Linearity of the regression model.
- 10.11.2 The assumption that , same at each Xi .
- 10.11.3 Missing observations.
- 10.11.4 Transformation of the regression model
- 10.11.5 Errors of measurements of (Xi, Yi).
- Exercises
- Appendix A10
- A 10.1 Square of the Correlation of Yi and
- A10.2 Multiple Regression
- A10.3 Expression for SSR in (10.3.8)

11 Analysis of Variance and Covariance

- 11.1 Introduction
- 11.2 One-way Classification: Balanced design
- 11.3 One-way random effects model: balanced design
- 11.4 Inference for the variance components and the mean
- 11.5 One-way Classification: Unbalanced Design; fixed effects
- 11.6 Unbalanced one-way classification: Random effects
- 11.7 Intraclass correlation
- 11.8 Analysis of Covariance: The balanced design
- 11.8.1 The model and the Least Squares Estimation
- 11.8.2 Tests of hypotheses for the slope coefficient and equality of the means
- 11.8.3 Confidence limits for the adjusted means and their differences
- 11.9 Analysis of Covariance: Unbalanced design
- 11.9.1 Confidence limits for the adjusted means and the differences of the treatment effects
- 11.10 Randomized Blocks
- 11.10.1 Randomized blocks: Random and Mixed effects models
- 11.11 Repeated measures design
- 11.12 Latin Squares
- 11.12.1 The model and analysis
- 11.13 Crossover design
- 11.14 Two-way Cross-classification
- 11.14.1 Additive model: balanced design
- 11.14.2 Two-way Cross-classification with interaction: balanced design
- 11.14.3 Two-way Cross-classification: Unbalanced additive model
- 11.14.4 Unbalanced Cross-classification with interaction
- 11.14.5 Multiplicative interaction and Tukey's test for nonadditivity
- 11.15 Missing observations in the Designs of Experiments
- Exercises
- Appendix A11
- A11.1 Variance of in (11.25) from Rao (1977, p.20)
- A11.2 Total Sum of squares (SS) and Sum of Products (SP) can be decomposed into the Within and Between SS and SP as follows

12 Meta – analysis

- 12.1 Introduction
- 12.2 Illustrations of large scale studies
- 12.3 Fixed effects models for combining the estimates
- 12.4 Random effects models for combining the estimates
- 12.5 Alternative estimatior for
- 12.6 Tests of hypotheses and confidence limits for the variance components
- Exercises

13 Survival Analysis

- 13.1 Introduction
- 13.2 Survival and hazard functions
- 13.3 Kaplan-Meir Product-Limit Estimator
- 13.4 Standard errors of and confidence limits for
- 13.5 Confidence limits for with right-censored observations
- 13.6 Log-Rank test for the equality of two survival distributions
- 13.7 Cox's Proportional Hazard Model
- Exercises
- Appendix A13

14 Nonparametric Statistics

- 14.1 Introduction
- 14.2 Spearman's Rank Correlation Coefficient
- 14.3 The Sign test
- 14.4 Wilcoxon (1945) Matched-pairs Signed-ranks test
- 14.5 Wilcoxon test for the equality of the distributions two non-normal populations with unpaired sample observations.
- 14.6 McNemer's (1955) matched pairs test for two proportions
- 14.7 Cochran's (1950) Q- test for the difference of three or more matched proportions
- 14.8 Kruskal-Wallis One-way ANOVA test by ranks
- Exercises

15 Further Topics

- 15.1 Introduction
- 15.2 Bonferroni inequality and the joint Confidence Region
- 15.3 Least significant difference (LSD) for a pair of treatment effects
- 15.4 Tukey's Studentized range test
- 15.5 Scheffe's Simultaneous Confidence intervals
- 15.6 Bootstrap Confidence intervals
- 15.7 Transformations for the ANOVA
- Exercises
- Appendix A15
- A15.1 Variance stabilizing transformation

Solutions to Exercises

References

Appendix Tables

Index

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