Statistics as a Resource in Medical Research


María Teresa Gómez García – Obstetrics and Gynecology Department, University and Hospital Complex of Albacete, Medical Science Department, School of Medicine of Albacete, Universidad de Castilla la Mancha, Albacete, Spain
María Del Mar Pérez Haro – Obstetrics and Gynecology Department, Hospital of Almansa, Albacete, Spain
María De Los Llanos Perez Haro – Urology Department, Hospital Universitario Central de Asturias, Oviedo, Spain
María José Pérez Haro – Statistical Analyst, Researcher, Senior Advisor, Biostatech, Santiago de Compostela, Galicia, Spain

Series: Mathematics Research Developments
BISAC: MAT029000; MED090000; MED000000

This book aims to provide a comprehensive and effective overview of the practical applications of statistics in the realm of healthcare. The primary goal of this book is to furnish readers, particularly medical researchers, and practitioners, with a deep understanding of statistical methods that find utility in healthcare scenarios. The document achieves this by meticulously detailing various statistical techniques and bolstering comprehension through illustrative case studies.

These case studies serve as a critical component, allowing readers to delve into the intricacies of each applied technique. The analyses not only elucidate the appropriateness of the methodology but also elucidate the interpretation of results and the soundness of conclusions drawn. To enhance learning, the book presents practical activities that challenge learners to tackle related situations, along with solutions that utilize the powerful and free software, RStudio. The book thoughtfully provides explanations on employing this software and includes the requisite code for resolving each practical scenario.

Intended for those who possess a foundational understanding of statistics but seek a deeper grasp of its application in healthcare, the book fills a crucial knowledge gap. While targeted primarily at medical researchers and practitioners, its content and methodologies hold relevance for undergraduates, graduates, and professionals in health sciences.

The book commences with a historical overview of statistical methods in public health research and introduces readers to R, an open-source programming language and statistical computing environment. Subsequent chapters explore the design and interpretation of clinical trials, touching on their advantages, limitations, and even delving into Bayesian methods. The discussion extends to the observation and description of specific events in a population using numeric and graphic methods in the context of descriptive statistics.

The book also delves into inferential statistics, the assessment of risk, and the identification of prognostic factors, all vital components of modern patient management and decision-making. Epidemiological tools, including spatial data analysis, are expounded upon in the context of health practice. Additionally, survival analysis, a pertinent methodology for investigating event occurrences, is thoroughly examined.

Readers are guided through key concepts and practical applications of survival analysis methods in a dedicated chapter. The document culminates with a comprehensive bibliography and a compilation of referenced articles.

Table of Contents

About the Authors 
Chapter 1. Historical Revision of the Evolution of Statistical Methods in Public Health Research: Introduction to RStudio 
1.1. Historical Revision 
1.2. Introduction to RStudio 
1.2.1. Vectors 
1.2.2. Factors 
1.2.3. Matrices 
1.2.4. Lists 
1.2.5. Working with Data Objects 
1.2.6. Calculations with Vectors and Functions 
1.2.7. General Functions 
1.2.8. Building Functions 
1.2.9. Entering Data 
1.2.10. Generating Special Data 
1.2.11. Graphs with R 
1.2.12. Solutions to the Exercises Proposed throughout This Chapter 
1.2.13. Renaming the Elements of a Vector 
1.2.14. Matrices in R 
1.2.15. Simulation 
1.2.16. Simulating the Rolling of a Die 
1.2.17. Simulating Bernoulli’s Experiments 
1.2.18. Probability and Density Functions 
1.2.19. Simulating a Normal Distribution 
1.2.20. Answers to the Previous Questions 
1.2.21. The Power of a Test 
1.2.22. Working with Data Sets 
1.2.23. Renaming Variables with the ‘Rename()’ Function 
1.2.24. Importing Data 
Chapter 2. Design and Interpretation of Clinical Studies 
2.1. Observational Studies 
2.1.1. Abstract 
2.1.2. Abstract 
2.1.3. Descriptive (or Non-Analytical) Studies 
2.1.4. Analytic Studies 
2.1.5. Cohort Studies versus Case Control Studies (Table 7) 
2.2. Experimental Studies 
2.2.1. Types of Interventional Studies 
2.2.2. Relevant Features to Consider in Experimental Studies 
2.3. Systematic Reviews 
2.4. Meta-Analysis 
2.4.1. About Heterogeneity 
2.4.2. About the Election of the Model 
2.4.3. Meta-Analysis with RStudio 
2.5. Retrospective Studies 
2.6. Screening Studies 
2.7. Solutions of the Proposed Exercises 
Chapter 3. Descriptive Statistics 
3.1. Aims and Methods in Descriptive Statistics 
3.2. Measures of Central Tendency 
3.2.1. Absolute Frequency (ni) 
3.2.2. Relative Frequency (fi) 
3.2.3. Cumulative Absolute Frequency (Ni) 
3.2.4. Cumulative Relative Frequency (Fi) 
3.2.5. Gathering Data 
3.2.6. Measures of Central Tendency 
3.3. Measures of Spread 
3.3.1. Range 
3.4. Measures of Location 
3.5. Skewness and Kurtosis 
3.5.1. Skewness 
3.5.2. Lack of Symmetry and Measures of Spread 
3.5.3. Kurtosis 
3.6. Descriptive Statistics with RStudio 
3.6.1. The ‘EDA()’ Function 
3.6.2. Using Commands 
3.7. Exercises and Solutions 
Chapter 4. Descriptive Statistics: Plots and Graphs 
4.1. Pie Chart 
4.1.1. Pie Charts with RStudio 
4.2. Dot Chart 
4.3. Bar Chart 
4.4. Histograms 
4.5. Box Plots 
4.5.1. Box Plots with RStudio 
4.5.2. Box Plots with ‘ggplot()’ 
4.6. Time Series Plots 
4.6.1. Basic Elements in Time Series 
4.7. Stem and Leaves Plots 
4.8. Violin Plots 
4.8.1. Violin Plot with ggplot2 
4.9. Kaplan-Meier Curves 
4.10. Forest Plots 
4.11. Spider Depictions 
4.12. Swimmer Depictions 
4.13. Waterfall Depictions 
4.13.1. Waterfall Plots with ggplot2 
Chapter 5. Inferential Statistics 
5.1. Probability and Random Variables 
5.1.1. Probability 
5.1.2. Random Variables: Concepts and Types 
5.1.3. Probability Density Function and Cumulative Distribution Function 
5.1.4. Cumulative Distribution Function 
5.1.5. Parameters of Central Tendency and Spread 
5.2. Distributions: Discrete and Continuous Distributions 
5.2.1. Discrete Distributions 
5.3. Continuous Distributions 
5.3.1. The Uniform Continuous Distribution (Figure 267) 
5.3.2. Properties of the Normal Curve 
5.3.3. Exponential Distribution (Figure 277) 
5.4. Sampling 
5.4.1. Features That Sample Statistics Must Fulfil 
5.4.2. Central Limit Theorem 
5.4.3. Confidence Intervals 
5.5. Hypothesis Testing 
5.5.1. Type I and Type II Errors 
5.5.2. Briefly (Table 52) 
5.5.3. Test Statistic and p-Value 
5.5.4. Steps for Hypothesis Testing 
5.5.5. The Most Important Hypothesis Tests (Table 54) 
5.5.6. Statistical Significance versus Clinical Significance 
5.6. Non-Parametric Methods 
5.6.1. Parametric versus Non-Parametric Tests (See Table 58) 
5.6.2. Non-Parametric Tests: The Wilcoxon Rank-Sum Test; The Wilcoxon Signed Rank Test 
5.7. Contingency Tables 
5.7.1. The Chi-Squared Test for Independence 
5.7.2. The Fisher’s Exact Test 
5.7.3. The Chi-Squared Goodness-Of-Fit Test 
5.8. Analysis of Variance 
5.8.1. ANalysis of VAriance (ANOVA) 
5.9. Linear Regression 
5.9.1. The Simple Linear Regression Model 
5.9.2. The Method of the Least Squares 
5.9.3. Prediction 
5.9.4. Graphical Representation: The Scatterplot 
5.9.5. Conditions for the Least Squares Line 
5.9.6. Correlation Analysis: Correlation Coefficient and Determination Coefficient 
5.9.7. Hypothesis Tests in Simple Linear Regression 
5.10. Bayesian Approach 
5.10.1. Conditional Probability 
5.10.2. Mutually-Exclusive and Exhaustive Events 
5.10.3. The Law of Total Probability 
5.10.4. Bayes’ Theorem 
5.10.5. Bayesian Approach in Diagnostic Test 
5.10.6. The Beta Distribution (Figure 342) 
5.10.7. Bayesian Methods with RStudio 
5.10.8. Bayesian Methods in Linear Regression 
5.11. Solutions of the Exercises 
5.11.1. Cumulative Distribution Function (See Table 76 and Figure 347) 
Chapter 6. Statistical Assessment of Risks 
6.1. Absolute and Relative Measures of Effect 
6.1.1. Basic Concepts 
6.1.2. Risk Ratio versus Odds Ratio 
6.1.3. Hazard Ratios 
6.1.4. Endpoints 
6.2. Regression Models 
6.2.1. Odds Ratio Generated by Logistic Regression 
6.2.2. Hazard Ratio Generated by Cox Proportional Hazard Regression Models 
6.3. Binary Data and ROC Curves 
6.3.1. Methods for Selecting the Best Cut-off Point in a ROC Curve 
Chapter 7. Epidemiologic Tools for Health PractisePractice 
7.1. Basic Epidemiological Concepts 
7.1.1. Types of Statistical Models and Basic Concepts in Epidemiology 
7.1.2. Basic Concepts 
7.2. Mathematical Modelling Basics in Infectious Disease 
7.2.1. A Simulation of the SIR Model with R 
7.3. Spatial Data Analysis 
Chapter 8. Survival Analysis 
8.1. Censoring 
8.2. Some Distributions of Failure Time 
8.2.1. Distributions of Failure Times 
8.3. Regression Models in Survival Analysis 
8.4. Survival Function 
8.4.1. Kaplan-Meier Estimator 
Chapter 9. References and Bibliography 
Chapter 1 
Chapter 2 
Chapter 3 
Chapter 4 
Chapter 5 
Chapter 6 
Chapter 7 
Chapter 8 

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