Introduction to Medical Statistics

In modern medical science, the use of statistical methods are ubiquitous, insofar as the research builds on quantitative methods. Whether the research question originates in the laboratory, the clinic, or epidemiologic registries, appropriate statistical methods are called for to collect, analyze and interpret the data. The ambition of the present book is to provide an introduction to basic statistical tools, so that it may be used as a companion in a first academic course on statistics for medical students.

The presentation should be as easy to follow as possible while maintaining a sufficient level of rigour. The book will not give insight into all the mathematical background needed to derive the stated results in a formal way, but rather focus on helping the understanding of the student. The exposition will be based on worked examples, with the focus on pedagogical analyses. Ideally, all examples should be taken from relevant and published medical studies, but this needs careful consideration of any copyrights involved. As a simple alternative, suitably simulated data can often be introduced instead.

Contents

A first list of topics to be covered includes:

• A very first example: Analysis of a single sample
• Types of data
• Random variation
• Descriptive statistics
  • Numerical measures
    • Central tendency
    • Variability
  • Graphical presentations
    • Stem-and-leaf
    • Histograms
    • Box-plots
    • Scatter plots
• Distributions
• The $z$-test and associated confidence interval
  • The standard form and its components
  • Definition of confidence interval
  • Hypothesis testing and the definition of a $p$-value
  • Why confidence intervals are usually to be preferred for $p$-values
• Comparison of two means
  • Small samples: $t$-test
• Comparison of two risks
  • Risk difference
  • Risk ratio
• Comparison of two odds
  • Odds ratio
• Comparison of two rates
• Linear regression
• Logistic regression
• Poisson regression
• Survival analysis regression (Cox regression)

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