Epidemiology with R

Cover
Epidemiology with R
Copyright
Contents
Preface
	What this book is not
Acknowledgements
List of Figures
Introduction
	What you should do
	Code chunks
	Graphs in this book
	Practicing R
Chapter 1: Using R
	1.1 Installing and using R
	1.2 Documenting your code and results
		1.2.1 R markdown
		1.2.2 Sweave / knitr
		1.2.3 Coding style in R
		1.2.4 R lingo
	1.3 Simple usage of R
		1.3.1 Using R as a calculator
		1.3.2 A functional language
			Probability functions
			Objects and functions
			What makes R different: functions
		1.3.3 Sequences
		1.3.4 The births data
		1.3.5 Referencing parts of a data frame
		1.3.6 Summaries
		1.3.7 Generating new variables
		1.3.8 Logical variables
		1.3.9 Turning a variable into a factor
			Manipulating factor levels
			Grouping values of a quantitative variable
		1.3.10 Tables
			Tables of means and other things
		1.3.11 Reading data
		1.3.12 Saving data
			Saving the work space
			Saving R objects in a file
		1.3.13 The search path
			Attaching a data frame
			Using with
	1.4 Graphics
		1.4.1 ggplot2
		1.4.2 Base graphics
		1.4.3 Simple base graphs
			Plot on the screen
			Colours
			Adding to a plot
			Using indexing for plot elements
			Interacting with a plot
			Saving graphs for use in other documents
			Same graph on multiple devices
			The par() command
	1.5 Frequency data
		1.5.1 Graphical overview
		1.5.2 Ad hoc analyses of admissions
	1.6 Tables and arrays for results
	1.7 Dates in R
	1.8 Numerical accuracy
		1.8.1 Accuracy of matching variables
	1.9 tidyverse and data.table
Chapter 2: Measures of disease occurrence
	2.1 Prevalence
	2.2 Mortality rate
	2.3 Incidence rate
	2.4 Standardized mortality ratio
	2.5 Survival
		2.5.1 Cumulative risk
		2.5.2 Competing risks
		2.5.3 Sojourn time
Chapter 3: Prevalence data—models, likelihood, and binomial regression
	3.1 Likelihood
		3.1.1 A single probability
		3.1.2 Simple confidence interval
		3.1.3 Confidence intervals in general
		3.1.4 The normal distribution
		3.1.5 Simple confidence intervals from models
		3.1.6 Tests and p-values
	3.2 Prevalence by age
	3.3 Comparing different models for the same data
		3.3.1 Likelihood-ratio test
		3.3.2 Deviance
		3.3.3 Deviance and goodness of fit
		3.3.4 AIC and BIC
Chapter 4: Regression models
	4.1 Types of models
	4.2 Normal linear regression model
	4.3 Simple linear regression
	4.4 Multiple regression
		4.4.1 Estimation in the normal linear regression model
		4.4.2 R-squared
		4.4.3 Multiple regression
		4.4.4 Standardized variables
		4.4.5 Predictions from the normal regression model
	4.5 Model formulae in R
	4.6 Regression models and generalized linear models
		4.6.1 Categorical effects
		4.6.2 Linear and categorical effects
		4.6.3 ANOVA–ANCOVA
		4.6.4 Categorical-linear interaction
			Special interaction?
		4.6.5 Categorical by categorical interaction
	4.7 Collinearity and aliasing
	4.8 Logarithmic transformations
		4.8.1 Logarithms
		4.8.2 Log transform of the response variable
		4.8.3 Coefficient of variation
		4.8.4 Log transform of an explanatory variable
		4.8.5 Log transform of both the response and explanatory variables
Chapter 5: Analysis of follow-up data
	5.1 Basic data structure
	5.2 Probability model
		5.2.1 Data
		5.2.2 Likelihood for a rate
		5.2.3 Estimates of rates and rate ratios
	5.3 Representation of follow-up data
		5.3.1 Lexis object for follow-up data
			Scaling of Lexis diagrams
	5.4 Splitting the follow-up time along a time-scale
	5.5 Smooth age-effects for rates
		5.5.1 Disaggregated data
		5.5.2 Including sex in the model
	5.6 SMR
		5.6.1 Modelling the SMR
	5.7 Time-dependent variables
		5.7.1 Cutting time at a specific date
			The precursor states
		5.7.2 Modelling time-dependent variables
			Survival?
		5.7.3 Clinical measurements in cohort studies
			Analysis using clinical measurements
Chapter 6: Parametrization and prediction of rates
	6.1 Predictions and contrasts
	6.2 Prediction of a single rate
	6.3 Categorical variables
		6.3.1 Groups and rate ratios
			Comparing all groups
	6.4 Modelling the effect of quantitative variables
		6.4.1 Categorizing quantitative variables: don’t
		6.4.2 Linear effect
			Predicting the rates
		6.4.3 Polynomial effects
		6.4.4 Other types of non-linear effects
			Natural splines
			Penalized splines
	6.5 Two quantitative predictors
		6.5.1 Age and period
		6.5.2 Age and cohort
		6.5.3 Contours of joint effects
			Image plot / heatmap
	6.6 Quantitative interactions
		6.6.1 Age–period interaction
			Age-specific rates at different dates (periods)
			Period-specific rates at different ages
		6.6.2 Age and cohort interaction
		6.6.3 Parametric interaction models
		6.6.4 Varying coefficients models for interaction
		6.6.5 Summary of quantitative interactions
Chapter 7: Case-control and case-cohort studies
	7.1 Follow-up and case-control studies
		7.1.1 Probabilities and odds in case-control studies
		7.1.2 The sampling fractions
		7.1.3 A simple example
	7.2 Statistical model for the odds ratio
		7.2.1 Analysis by logistic regression
	7.3 Odds ratio and rate ratio
		7.3.1 Incidence density sampling
	7.4 Confounding and stratified sampling
		7.4.1 Stratified sampling
	7.5 Individually matched studies
		7.5.1 An example
		7.5.2 When conditional analysis is not needed
	7.6 Nested case-control studies
		7.6.1 Register-based case-control studies
	7.7 Case-cohort studies
Chapter 8: Survival analysis
	8.1 Introduction
	8.2 Life table estimator of survival function
	8.3 Kaplan--Meier estimator of survival
		8.3.1 Survival in two groups
	8.4 The Cox model
		8.4.1 Mean survival or survival at mean?
	8.5 The time-scale
	8.6 Relation between Cox and Poisson models
		8.6.1 Simple parametric mortality functions
			Baseline mortality rate
			Survival curves
		8.6.2 Proportional hazards?
		8.6.3 The Cox model as a Poisson model
	8.7 Time-dependent covariates
	8.8 Competing risks
	8.9 Modelling cause specific rates
		8.9.1 Limitations
	8.10 The Fine--Gray approach to competing risks
	8.11 Time-dependent variables and competing risks
Chapter 9: Do not group quantitative variables
	9.1 Problems Caused by Categorizing Continuous Variables
References
Index