MEDICAL STATISTICS FROM SCRATCH: AN INTRODUCTION FOR HEALTH PROFESSIONALS, 4THÁEDITION

Preface to the 4th Edition
Preface to the 3rd Edition xv
Preface to the 2nd Edition xvii
Preface to the 1st Edition xix
Introduction xxi
I Some Fundamental Stuff
1 First things first – the nature of data
Variables and data
The good, the bad, and the ugly – types of variables
Categorical data
Metric data
II Descriptive Statistics
2 Describing data with tables
Descriptive statistics. What can we do with raw data?
Frequency tables – nominal data
Frequency tables – ordinal data
Frequency tables – metric data
Cumulative frequency
Cross-tabulation – contingency tables
Ranking data
3 Every picture tells a story – describing data with charts
Picture it!
Charting nominal and ordinal data
Charting discrete metric data
Charting continuous metric data
Charting cumulative data
Charting time-based data – the time series chart
4 Describing data from its shape
The shape of things to come
Negative skew
Positive skew
Symmetric or mound-shaped distributions
Normal-ness – the Normal distribution
Bimodal distributions
Determining skew from a box plot
5 Measures of location – Numbers R Us
Numbers, percentages, and proportions
Summary measures of location
The mode
The median
The mean
Percentiles
6 Measures of spread – Numbers R Us (again)
The range
The interquartile range (IQR)
The boxplot (also known as the box and whisker plot)
Standard deviation
Standard deviation and the Normal distribution
Transforming data
7 Incidence, prevalence, and standardization
The incidence rate
The incidence rate ratio (IRR)
Prevalence
Some other useful (and common) rates
Age specific mortality rate
Standardisation – the standardised mortality rate
The direct method
The standard population
The indirect method
The standardised mortality ratio
III The Confounding Problem
8 Confounding – like the poor, (nearly) always with us
What is confounding?
Confounding by indication
Residual confounding
Detecting confounding
Dealing with confounding. If confounding is such a problem, what can we do about it?
IV Design and Data
9 Research design – Part I: Observational study designs
Hey ho! Hey ho! It’s off to work we go!
Types of study
Case reports and case series
Observational studies
From here to eternity – cohort studies
Confounding in cohort studies
Back to the future – case–control studies
Confounding in case–control studies
Comparing cohort and case–control designs
Ecological studies
The ecological fallacy
10 Research design – Part II: Getting stuck in – experimental studies
Clinical trials
Randomisation
Block randomisation
Stratification
Blinding
The cross-over randomised controlled trial
Selection of participants
Intention-to-treat analysis
11 Getting the participants for your study: ways of sampling
From populations to samples – statistical inference
The target and study populations, and the sample
Collecting the data – types of sample
The simple random sample
The systematic random sample
The stratified random sample
The cluster sample
Consecutive and convenience samples
How many participants should we have? Sample size
Inclusion and exclusion criteria
Getting the data
V Chance Would be a Fine Thing
12 The idea of probability
Calculating probability – proportional frequency
Two useful rules for simple probability
The multiplication rule for independent events
The addition rule for mutually exclusive events
Conditional and Bayesian statistics
Probability distributions
What is a probability distribution?
Discrete versus continuous probability distributions
The binomial probability distribution
The Poisson probability distribution
The Normal probability distribution
13 Risk and odds
Absolute risk and the absolute risk reduction
The risk ratio
The reduction in the risk ratio (or relative risk reduction) RRR
Reference value
Number needed to treat
What happens if the initial risk is small?
Confounding with the risk ratio
Odds
Why you can’t calculate risk in a case–control study
The odds ratio
Confounding with the odds ratio
Approximating the odds ratio with the risk ratio
VI The Informed Guess – An Introduction to Confidence Intervals
14 Estimating the value of a single population parameter – the idea of confidence intervals
Confidence interval estimation for a population mean
The standard error of the mean
How we use the standard error of the mean to calculate a confidence interval for a population mean
Confidence interval for a population proportion
Confidence interval for the median of a single population
15 Using confidence intervals to compare two population parameters
What’s the difference?
Comparing two independent population means
Assessing the confidence interval and the sample size
Comparing two paired population means
Within-subject and between-subject variation
Comparing two independent population proportions
Comparing two independent population medians – the Mann–Whitney rank sums method
Comparing two matched population medians – the Wilcoxon signed-ranks method
16 Confidence intervals for the ratio of two population parameters
Confidence interval for the ratio of two independent population means
Confidence interval for a population risk ratio
Confidence intervals for a population odds ratio
Confidence intervals for hazard ratios
VII Putting it to the Test
17 Testing hypotheses about the difference between two population parameters
Answering the question
The hypothesis
The null hypothesis
The hypothesis testing process
The p-value and the decision rule
A brief summary of a few of the most common tests
Using the p-value to compare the means of two independent populations
Interpreting computer hypothesis test results for the difference in two independent
population means – the two-sample t test
Output from Minitab – two-sample t test of difference in mean birthweights of babies
born to White mothers and to non-White mothers
Output from SPSS: two-sample t test of difference in mean birthweights of babies born to
White mothers and to non-White mothers
Comparing the means of two paired populations – the matched-pairs t test
Using p-values to compare the medians of two independent populations
The Mann–Whitney rank-sums test
How the Mann–Whitney test works
Correction for multiple comparisons
The Bonferroni correction
Interpreting computer output for the Mann–Whitney test
With Minitab
With SPSS
Comparing two matched medians – the Wilcoxon signed-ranks test
Confidence intervals versus hypothesis test
What could possibly go wrong?
Types of error – type I and type II errors
The power of a test
Maximising power – calculating sample size
Sample size when comparing the means of two independent populations
Sample size when comparing the proportions of two independent populations
18 The chi-squared (?2) test – what, why, and how?
Of all the tests in all the world – you had to walk into my hypothesis testing procedure
Using chi-squared to test for related-ness or the equality of proportions
Calculating the chi-squared statistic
Using the chi-squared test
Yate’s correction (continuity correction)
Fisher’s exact test
The chi-squared test with Minitab
The chi-squared test with SPSS
The chi-squared test for trend
SPSS output for chi-squared trend test
19 Testing hypotheses about the ratio of two population parameters
The chi-squared test with the risk ratio
The chi-squared test with odds ratios
The chi-squared test with hazard ratios
VIII Becoming Acquainted
20 Measuring the association between two variables
Plotting data
Association
The scatterplot
The correlation coefficient
Pearson’s correlation coefficient
Is the correlation coefficient significant in the population?
Spearman’s rank correlation coefficient
21 Measuring agreement
Spearman’s rank correlation coefficient
To agree or not to agree: that is the question
Cohen’s kappa (?)
Weighted kappa
Measuring the agreement between two metric continuous variables; Bland–Altman
IX Getting into a Relationship
22 Straight line models: linear regression
Weighted kappa
Relationship and association
Finding the equation of a straight line from a graph
A causal relationship – explaining variation
The linear regression model
Is the relationship linear?
Estimating the regression parameters – the method of ordinary least squares
Basic assumptions of the ordinary least squares procedure
Is the relationship statistically significant?
Estimating the regression parameters with SPSS and Minitab
Interpreting the regression coefficients
Goodness-of-fit, R2
Multiple linear regression
Adjusted goodness-of-fit: R2
Including nominal independent variables in the regression model: design variables and coding
Building your model. Which variables to include?
Automated variable selection methods
Manual variable selection methods
Adjustment and confounding
An example from practice
Diagnostics – checking the basic assumptions of the multiple linear regression model
Analysis of variance
23 Curvy models: Logistic regression
The binary outcome variable
Finding an appropriate model
The logistic regression model
Estimating the parameter values
Interpreting the regression coefficients
Is the model significant in the population?
Getting the odds ratio directly from the regression results
Is the odds ratio significant?
The multiple logistic regression model
Building the model – variable selection
Goodness-of-fit
Pearson's chi-squared; the Deviance statistic; the Hosmer–Lemeshow statistic
24 Counting models: Poisson regression
Poisson regression and the Poisson regression model
Interpreting the regression coefficients
When the outcome is a count
When the outcome is a rate
Building the model – variable selection
Goodness-of-fit
The zero-inflated Poisson regression model
Negative binomial regression
Zero-inflated negative binomial regression
X Four More Chapters
25 Measuring survival
Censored data
Calculating survival probabilities and the proportion surviving: the Kaplan–Meier table
The Kaplan–Meier curve
Determining median survival time
Comparing survival with two groups
The log-rank test
The hazard ratio
The proportional hazards (Cox’s) regression model
The proportional hazards (Cox’s) regression model – the detail
Checking the proportional hazards assumption
26 Systematic review and meta-analysis
Introduction
Systematic review – what it is
The forest plot – what does it show?
Publication and other biases
The funnel plot
Graphical interpretation of funnel plot for asymmetry
Significance test for asymmetry in funnel plot – Begg's and Egger's tests
Combining the studies: meta-analysis
The problem of heterogeneity
Testing for heterogeneity – Cochrane's Q test; the I2 test
27 Diagnostic testing
Sensitivity, specificity
Positive predictive value (PPV)
Negative predictive value (NPV)
The sensitivity versus specificity trade-off
Using the ROC curve to find the optimum trade-off value (or cut-off)
28 Missing data
The missing data problem
Types of missingness: MCAR, MAR, MNAR
The consequences of missing data
Methods for dealing with missing data
List-wise deletion (or complete case analysis)
Pair-wise deletion (or available case analysis)
Simple imputation
Replacement by the mean
Last observation carried forward (LOCF)
Regression-based imputation
Multiple imputation (MI)
Other methods: FIML, EM, MissForest, Nearest Neighbour
Appendix: Table of random numbers
References
Solutions to Exercises
Index

Correctly understanding and using medical statistics is a key skill for all medical students and health professionals.
In an informal and friendly style, Medical Statistics from Scratch provides a practical foundation for everyone whose first interest is probably not medical statistics. Keeping the level of mathematics to a minimum, it clearly illustrates statistical concepts and practice with numerous real-world examples and cases drawn from current medical literature.
Medical Statistics from Scratch is an ideal learning partner for all medical students and health professionals needing an accessible introduction, or a friendly refresher, to the fundamentals of medical statistics.

Author
• DAVID BOWERS, Leeds Institute of Health Sciences, School of Medicine, University of Leeds, Leeds, UK