Statistical Methodologies with Medical Applications

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 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. Content: Topics for illustrations, examples and exercises xvPreface xviiList of abbreviations xix1 Statistical measures 11.1 Introduction 11.2 Mean, mode and median 21.3 Variance and standard deviation 31.4 Quartiles, deciles and percentiles 41.5 Skewness and kurtosis 51.6 Frequency distributions 61.7 Covariance and correlation 71.8 Joint frequency distribution 91.9 Linear transformation of the observations 101.10 Linear combinations of two sets of observations 10Exercises 112 Probability, random variable, expected value and variance 142.1 Introduction 142.2 Events and probabilities 142.3 Mutually exclusive events 152.4 Independent and dependent events 152.5 Addition of probabilities 162.6 Bayes' theorem 162.7 Random variables and probability distributions 172.8 Expected value, variance and standard deviation 172.9 Moments of a distribution 18Exercises 183 Odds ratios, relative risk, sensitivity, specificity and the ROC curve 193.1 Introduction 193.2 Odds ratio 193.3 Relative risk 203.4 Sensitivity and specificity 213.5 The receiver operating characteristic (ROC) curve 22Exercises 224 Probability distributions, expectations, variances and correlation 244.1 Introduction 244.2 Probability distribution of a discrete random variable 254.3 Discrete distributions 254.4 Continuous distributions 294.5 Joint distribution of two discrete random variables 344.6 Bivariate normal distribution 37Exercises 385 Means, standard errors and confidence limits 405.1 Introduction 405.2 Expectation, variance and standard error (S.E.) of the sample mean 415.3 Estimation of the variance and standard error 425.4 Confidence limits for the mean 435.5 Estimator and confidence limits for the difference of two means 445.6 Approximate confidence limits for the difference of two means 465.7 Matched samples and paired comparisons 475.8 Confidence limits for the variance 485.9 Confidence limits for the ratio of two variances 495.10 Least squares and maximum likelihood methods of estimation 49Exercises 516 Proportions, odds ratios and relative risks: Estimation and confidence limits 546.1 Introduction 546.2 A single proportion 546.3 Confidence limits for the proportion 556.4 Difference of two proportions or percentages 566.5 Combining proportions from independent samples 566.6 More than two classes or categories 576.7 Odds ratio 586.8 Relative risk 59Exercises 597 Tests of hypotheses: Means and variances 627.1 Introduction 627.2 Principle steps for the tests of a hypothesis 637.3 Right-sided alternative, test statistic and critical region 657.4 Left-sided alternative and the critical region 697.5 Two-sided alternative, critical region and the p-value 727.6 Difference between two means: Variances known 757.7 Matched samples and paired comparison 777.8 Test for the variance 777.9 Test for the equality of two variances 787.10 Homogeneity of variances 79Exercises 808 Tests of hypotheses: Proportions and percentages 828.1 A single proportion 828.2 Right-sided alternative 828.3 Left-sided alternative 858.4 Two-sided alternative 878.5 Difference of two proportions 908.6 Specified difference of two proportions 958.7 Equality of two or more proportions 958.8 A common proportion 96Exercises 979 The Chisquare statistic 999.1 Introduction 999.2 The test statistic 999.3 Test of goodness of fit 1019.4 Test of independence: (r x c) classification 1019.5 Test of independence: (2x2) classification 104Exercises 10710 Regression and correlation 11010.1 Introduction 11010.2 The regression model: One independent variable 11010.3 Regression on two independent variables 11810.4 Multiple regression: The least squares estimation 12410.5 Indicator variables 13210.6 Regression through the origin 13510.7 Estimation of trends 13610.8 Logistic regression and the odds ratio 13810.9 Weighted Least Squares (WLS) estimator 14110.10 Correlation 14210.11 Further topics in regression 144Exercises 14811 Analysis of variance and covariance: Designs of experiments 15211.1 Introduction 15211.2 One-way classification: Balanced design 15311.3 One-way random effects model: Balanced design 15511.4 Inference for the variance components and the mean 15511.5 One-way classification: Unbalanced design and fixed effects 15711.6 Unbalanced one-way classification: Random effects 15911.7 Intraclass correlation 16011.8 Analysis of covariance: The balanced design 16111.9 Analysis of covariance: Unbalanced design 16511.10 Randomized blocks 16811.11 Repeated measures design 17011.12 Latin squares 17211.13 Cross-over design 17411.14 Two-way cross-classification 17511.15 Missing observations in the designs of experiments 184Exercises 18612 Meta-analysis 19012.1 Introduction 19012.2 Illustrations of large-scale studies 19012.3 Fixed effects model for combining the estimates 19112.4 Random effects model for combining the estimates 19312.5 Alternative estimators for 2 19412.6 Tests of hypotheses and confidence limits for the variance components 194Exercises 19513 Survival analysis 19713.1 Introduction 19713.2 Survival and hazard functions 19813.3 Kaplan-Meir product-limit estimator 19813.4 Standard error of S(tm) and confidence limits for S(tm) 19913.5 Confidence limits for S(tm) with the right-censored observations 19913.6 Log-Rank test for the equality of two survival distributions 20113.7 Cox's proportional hazard model 202Exercises 20314 Nonparametric statistics 20514.1 Introduction 20514.2 Spearman's rank correlation coefficient 20514.3 The Sign test 20614.4 Wilcoxon (1945) Matched-pairs Signed-ranks test 20814.5 Wilcoxon's test for the equality of the distributions of two non-normal populations with unpaired sample observations 20914.6 McNemer's (1955) matched pair test for two proportions 21014.7 Cochran's (1950) Q-test for the difference of three or more matched proportions 21114.8 Kruskal-Wallis one-way ANOVA test by ranks 212Exercises 21315 Further topics 21515.1 Introduction 21515.2 Bonferroni inequality and the Joint Confidence Region 21515.3 Least significant difference (LSD) for a pair of treatment effects 21715.4 Tukey's studentized range test 21715.5 Scheffe's simultaneous confidence intervals 21815.6 Bootstrap confidence intervals 21915.7 Transformations for the ANOVA 220Exercises 221Solutions to exercises 222Appendix tables 249References 261Index 264