1 Fundamental issues

1.1 What is epidemiology?

1.2 Case studies: The work of Doll and Hill

1.3 Populations and samples

1.3.1 Populations

1.3.2 Samples

1.4 Measuring disease

1.4.1 Incidence and prevalence

1.5 Measuring the risk factor

1.6 Causality

1.6.1 Association

1.6.2 Problems with establishing causality

1.6.3 Principles of causality

1.7 Studies using routine data

1.7.1 Ecological data

1.7.2 National sources of data on disease

1.7.3 National sources of data on risk factors

1.7.4 International data

1.8 Study design

1.8.1 Intervention studies

1.8.2 Observational studies

1.9 Data analysis

Exercises

2 Basic analytical procedures

2.1 Introduction

2.1.1 Inferential procedures

2.2 Case study

2.2.1 The Scottish Heart Health Study

2.3 Types of variables

2.3.1 Qualitative variables

2.3.2 Quantitative variables

2.3.3 The hierarchy of type

2.4 Tables and charts

2.4.1 Tables in reports

2.4.2 Diagrams in reports

2.5 Inferential techniques for categorical variables

2.5.1 Contingency tables

2.5.2 Binary variables: proportions and percentages

2.5.3 Comparing two proportions or percentages

2.6 Descriptive Techniques for quantitative variables

2.6.1 The five-number summary

2.6.2 Quantiles

2.6.3 The two-number summary

2.6.4 Other summary statistics of spread

2.6.5 Assessing symmetry

2.6.6 Investigating shape

2.7 Inferences about means

2.7.1 Checking normality

2.7.2 Inferences for a single mean

2.7.3 Comparing two means

2.7.4 Paired data

2.8 Inferential techniques for non-normal data

2.8.1 Transformations

2.8.2 Nonparametric tests

2.8.3 Confidence intervals for medians

2.9 Measuring agreement

2.9.1 Quantitative variables

2.9.2 Categorical variables

2.9.3 Ordered categorical variables

2.9.4 Internal consistency

2.10 Assessing diagnostic tests

2.10.1 Accounting for sensitivity and specificity

Exercises

3 Assessing risk factors

3.1 Risk and relative risk

3.2 Odds and odds ratio

3.3 Relative risk or odds ratio?

3.4 Prevalence studies

3.5 Testing association

3.5.1 Equivalent tests

3.5.2 One-sided tests

3.5.3 Continuity corrections

3.5.4 Fisher's exact test

3.5.5 Limitations of tests

3.6 Risk factors measured at several levels

3.6.1 Continuous risk factors

3.6.2 A test for linear trend

3.6.3 A test for nonlinearity

3.7 Attributable risk

3.8 Rate and relative rate

3.8.1 The general epidemiological rate

3.9 Measures of difference

3.10 EPITAB commands in Stata

Exercises

4 Confounding and interaction

4.1 Introduction

4.2 The concept of confounding

4.3 Identification of confounders

4.3.1 A strategy for selection

4.4 Assessing confounding

4.4.1 Using estimation

4.4.2 Using hypothesis tests

4.4.3 Dealing with several confounding variables

4.5 Standardisation

4.5.1 Direct standardisation of event rates

4.5.2 Indirect standardisation of event rates

4.5.3 Standardisation of risks

4.6 Mantel–Haenszel methods

4.6.1 The Mantel–Haenszel relative risk

4.6.2 The Cochran–Mantel–Haenszel test

4.6.3 Further comments

4.7 The concept of interaction

4.8 Testing for interaction

4.8.1 Using the relative risk

4.8.2 Using the odds ratio

4.8.3 Using the risk difference

4.8.4 Which type of interaction to use?

4.8.5 Which interactions to test?

4.9 Dealing with interaction

4.10 EPITAB commands in Stata

Exercises

5 Cohort studies

5.1 Design considerations

5.1.1 Advantages

5.1.2 Disadvantages

5.1.3 Alternative designs with economic advantages

5.1.4 Studies with a single baseline sample

5.2 Analytical considerations

5.2.1 Concurrent follow-up

5.2.2 Moving baseline dates

5.2.3 Varying follow-up durations

5.2.4 Withdrawals

5.3 Cohort life tables

5.3.1 Allowing for sampling variation

5.3.2 Allowing for censoring

5.3.3 Comparison of two life tables

5.3.4 Limitations

5.4 Kaplan-Meier estimation

5.4.1 An empirical comparison

5.5 Comparison of two sets of survival probabilities

5.5.1 Mantel–Haenszel methods

5.5.2 The log-rank test

5.5.3 Weighted log-rank tests

5.5.4 Allowing for confounding variables

5.5.5 Comparing three of more groups

5.6 Competing risk

5.7 The person-years method

5.7.1 Age-specific rates

5.7.2 Summarisation of rates

5.7.3 Comparison of two SERs

5.7.4 Mantel–Haenszel methods

5.7.5 Further comments

5.8 Period-cohort analysis

5.8.1 Period-specific rates

Exercises

6 Case–control studies

6.1 Basic design concepts

6.1.1 Advantages

6.1.2 Disadvantages

6.2 Basic methods of analysis

6.2.1 Dichotomous exposure

6.2.2 Polytomous exposure

6.2.3 Confounding and interaction

6.2.4 Attributable risk

6.3 Selection of cases

6.3.1 Definition

6.3.2 Inclusion and exclusion criteria

6.3.3 Incident or prevalent?

6.3.4 Source

6.3.5 Consideration of bias

6.4 Selection of controls

6.4.1 General principles

6.4.2 Hospital controls

6.4.3 Community controls

6.4.4 Other sources

6.4.5 How many?

6.5 Matching

6.5.1 Advantages

6.5.2 Disadvantages

6.5.3 One-to-many matching

6.5.4 Matching in other study designs

6.6 The analysis of matched studies

6.6.1 1 : 1 Matching

6.6.2 1 : *c* Matching

6.6.3 1 : Variable matching

6.6.4 Many : many matching

6.6.5 A modelling approach

6.7 Nested case–control studies

6.7.1 Matched studies

6.7.2 Counter-matched studies

6.8 Case-cohort studies

6.9 Case-crossover studies

Exercises

7 Intervention studies

7.1 Introduction

7.1.1 Advantages

7.1.2 Disadvantages

7.2 Ethical considerations

7.2.1 The protocol

7.3 Avoidance of bias

7.3.1 Use of a control group

7.3.2 Blindness

7.3.3 Randomisation

7.3.4 Consent before randomisation

7.3.5 Analysis by intention-to-treat

7.4 Parallel group studies

7.4.1 Number needed to treat

7.4.2 Cluster randomised trials

7.4.3 Stepped wedge trials

7.4.4 Non-inferiority trials

7.5 Cross-over studies

7.5.1 Graphical analysis

7.5.2 Comparing means

7.5.3 Analysing preferences

7.5.4 Analysing binary data

7.6 Sequential studies

7.6.1 The Haybittle-Peto stopping rule

7.6.2 Adaptive designs

7.7 Allocation to treatment group

7.7.1 Global randomisation

7.7.2 Stratified randomization

7.7.3 Implementation

7.8 Trials as cohorts

Exercises

8 Sample size determination

8.1 Introduction

8.2 Power

8.2.1 Choice of alternative hypothesis

8.3 Testing a mean value

8.3.1 Common choices for power and significance level

8.3.2 Using a table of sample sizes

8.3.3 The minimum detectable difference

8.3.4 The assumption of known standard deviation

8.4 Testing a difference between means

8.4.1 Using a table of sample sizes

8.4.2 Power and minimum detectable difference

8.4.3 Optimum distribution of the sample

8.4.4 Paired data

8.5 Testing a proportion

8.5.1 Using a table of sample sizes

8.6 Testing a relative risk

8.6.1 Using a table of sample sizes

8.6.2 Power and minimum detectable relative risk

8.7 Case–control studies

8.7.1 Using a table of sample sizes

8.7.2 Power and minimum detectable relative risk

8.7.3 Comparison with cohort studies

8.7.4 Matched studies

8.8 Complex sampling designs

8.9 Concluding remarks

Exercises

9 Modelling quantitative outcome variables

9.1 Statistical models

9.2 One categorical explanatory variable

9.2.1 The hypotheses to be tested

9.2.2 Construction of the ANOVA table

9.2.3 How the ANOVA table is used

9.2.4 Estimation of group means

9.2.5 Comparison of group means

9.2.6 Fitted values

9.2.7 Using computer packages

9.3 One quantitative explanatory variable

9.3.1 Simple linear regression

9.3.2 Correlation

9.3.3 Nonlinear regression

9.4 Two categorical explanatory variables

9.4.1 Model specification

9.4.2 Model fitting

9.4.3 Balanced data

9.4.4 Unbalanced data

9.4.5 Fitted values

9.4.6 Least squares means

9.4.7 Interaction

9.5 Model building

9.6 General linear models

9.7 Several explanatory variables

9.7.1 Information criteria

9.7.2 Boosted regression

9.8 Model checking

9.9 Confounding

9.9.1 Adjustment using residuals

9.10 Splines

9.10.1 Choice of knots

9.10.2 Other types of splines

9.11 Panel data

9.12 Non-normal alternatives

Exercises

10 Modelling binary outcome data

10.1 Introduction

10.2 Problems with standard regression models

10.2.1 The r-x relationship may well not be linear

10.2.2 Predicted values of the risk may be outside the valid range

10.2.3 The error distribution is not normal

10.3 Logistic regression

10.4 Interpretation of logistic regression coefficients

10.4.1 Binary risk factors

10.4.2 Quantitative risk factors

10.4.3 Categorical risk factors

10.4.4 Ordinal risk factors

10.4.5 Floating absolute risks

10.5 Generic data

10.6 Multiple logistic regression models

10.7 Tests of hypotheses

10.7.1 Goodness of fit for grouped data

10.7.2 Goodness of fit for generic data

10.7.3 Effect of a risk factor

10.7.4 Information criteria

10.7.5 Tests for linearity and nonlinearity

10.7.6 Tests based upon estimates and their standard errors

10.7.7 Problems with missing values

10.8 Confounding

10.9 Interaction

10.9.1 Between two categorical variables

10.9.2 Between a quantitative and categorical variable

10.9.3 Between two quantitative variables

10.10 Dealing with a quantitative explanatory variable

10.10.1 Linear form

10.10.2 Categorical form

10.10.3 Linear spline form

10.10.4 Generalisations

10.11 Model checking

10.11.1 Residuals

10.11.2 Influential observations

10.12 Measurement error

10.12.1 Regression to the mean

10.12.2 Correcting for regression dilution

10.13 Case–control studies

10.13.1 Unmatched studies

10.13.2 Matched studies

10.14 Outcomes with several levels

10.14.1 The proportional odds assumption

10.14.2 The proportional odds model

10.14.3 Multinomial regression

10.15 Longitudinal data

10.16 Binomial regression

10.16.1 Adjusted risks

10.16.2 Risk differences

10.16.3 Problems with binomial models

10.17 Propensity scoring

10.17.1 Pair-matched propensity scores

10.17.2 Stratified propensity scores

10.17.3 Weighting by the inverse propensity score

10.17.4 Adjusting for the propensity score

10.17.5 Deriving the propensity score

10.17.6 Propensity score outliers

10.17.7 Conduct of the matched design

10.17.8 Analysis of the matched design

10.17.9 Case studies

10.17.10 Interpretation of effects

10.17.11 Problems with estimating uncertainty

10.17.12 Propensity scores in practice

Exercises

11 Modelling follow-up data

11.1 Introduction

11.1.1 Models for survival data

11.2 Basic functions of survival time

11.2.1 The survival function

11.2.2 The hazard function

11.3 Estimating the hazard function

11.3.1 Kaplan–Meier estimation

11.3.2 Person-time estimation

11.3.3 Actuarial estimation

11.3.4 The cumulative hazard

11.4 Probability models

11.4.1 The probability density and cumulative distribution functions

11.4.2 Choosing a model

11.4.3 The exponential distribution

11.4.4 The Weibull distribution

11.4.5 Other probability models

11.5 Proportional hazards regression models

11.5.1 Comparing two groups

11.5.2 Comparing several groups

11.5.3 Modelling with a quantitative variable

11.5.4 Modelling with several variables

11.5.5 Left-censoring

11.6 The Cox proportional hazards model

11.6.1 Time-dependent covariates

11.6.2 Recurrent events

11.7 The Weibull proportional hazards model

11.8 Model checking

11.8.1 Log cumulative hazard plots

11.8.2 An objective test of proportional hazards for the Cox model

11.8.3 An objective test of proportional hazards for the Weibull model

11.8.4 Residuals and influence

11.8.5 Nonproportional hazards

11.9 Competing risk

11.9.1 Joint modeling of longitudinal and survival data

11.10 Poisson regression

11.10.1 Simple regression

11.10.2 Multiple regression

11.10.3 Comparison of standardised event ratios

11.10.4 Routine or registration data

11.10.5 Generic data

11.10.6 Model checking

11.11 Pooled logistic regression

Exercises

12 Meta-analysis

12.1 Reviewing evidence

12.1.1 The Cochrane collaboration

12.2 Systematic review

12.2.1 Designing a systematic review

12.2.2 Study quality

12.3 A General approach to pooling

12.3.1 Inverse variance weighting

12.3.2 Fixed effect and random effects

12.3.3 Quantifying heterogeneity

12.3.4 Estimating the between-study variance

12.3.5 Calculating inverse variance weights

12.3.6 Calculating standard errors from confidence intervals

12.3.7 Case studies

12.3.8 Pooling risk differences

12.3.9 Pooling differences in mean values

12.3.10 Other quantities

12.3.11 Pooling mixed quantities

12.3.12 Dose-response meta-analysis

12.4 Investigating heterogeneity

12.4.1 Forest plots

12.4.2 Influence plots

12.4.3 Sensitivity analyses

12.4.4 Meta-regression

12.5 Pooling tabular data

12.5.1 Inverse variance weighting

12.5.2 Mantel–Haenszel methods

12.5.3 The Peto method

12.5.4 Dealing with zeros

12.5.5 Advantages and disadvantages of using tabular data

12.6 Individual participant data

12.7 Dealing with aspects of study quality

12.8 Publication bias

12.8.1 The funnel plot

12.8.2 Consequences of publication bias

12.8.3 Correcting for publication bias

12.8.4 Other causes of asymmetry in funnel plots

12.9 Advantages and limitations of meta-analysis

Exercises

13 Risk scores And clinical decision rules

13.1 Introduction

13.1.1 Individual and population level interventions

13.1.2 Scope of this chapter

13.2 Association and prognosis

13.2.1 The concept of discrimination

13.2.2 Risk factor thresholds

13.2.3 Risk thresholds

13.2.4 Odds ratios and discrimination

13.3 Risk scores from statistical models

13.3.1 Logistic regression

13.3.2 Multiple variable risk scores

13.3.3 Cox regression

13.3.4 Risk thresholds

13.3.5 Multiple thresholds

13.4 Quantifying discrimination

13.4.1 The area under the curve

13.4.2 Comparing AUCs

13.4.3 Survival data

13.4.4 The standardised mean effect size

13.4.5 Other measures of discrimination

13.5 Calibration

13.5.1 Overall calibration

13.5.2 Mean calibration

13.5.3 Grouped calibration

13.5.4 Calibration plots

13.6 Recalibration

13.6.1 Recalibration of the mean

13.6.2 Recalibration of scores in a fixed cohort

13.6.3 Recalibration of parameters from a Cox model

13.6.4 Recalibration and discrimination

13.7 The accuracy of predictions

13.7.1 The Brier score

13.7.2 Comparison of Brier scores

13.8 Assessing an extraneous prognostic variable

13.9 Reclassification

13.9.1 The integrated discrimination improvement from a fixed cohort

13.9.2 The net reclassification improvement from a fixed cohort

13.9.3 The integrated discrimination improvement from a variable cohort

13.9.4 The net reclassification improvement from a variable cohort

13.9.5 Software

13.10 Validation

13.11 Presentation of risk scores

13.11.1 Point scoring

13.12 Impact Studies

Exercises

14 Computer-intensive methods

14.1 Rationale

14.2 The bootstrap

14.2.1 Bootstrap distributions

14.3 Bootstrap confidence intervals

14.3.1 Bootstrap normal intervals

14.3.2 Bootstrap percentile intervals

14.3.3 Bootstrap bias-corrected intervals

14.3.4 Bootstrap bias-corrected and accelerated intervals

14.3.5 Overview of the worked example

14.3.6 Choice of bootstrap interval

14.4 Practical issues when bootstrapping

14.4.1 Software

14.4.2 How many replications should be used?

14.4.3 Sensible strategies

14.5 Further examples of bootstrapping

14.5.1 Complex bootstrap samples

14.6 Bootstrap hypothesis testing

14.7 Limitations of bootstrapping

14.8 Permutation tests

14.8.1 Monte Carlo permutation tests

14.8.2 Limitations

14.9 Missing values

14.9.1 Dealing with missing values

14.9.2 Types of missingness

14.9.3 Complete case analyses

14.10 Naive imputation methods

14.10.1 Mean imputation

14.10.2 Conditional mean and regression imputation

14.10.3 Hot deck imputation and predictive mean matching

14.10.4 Longitudinal data

14.11 Univariate multiple imputation

14.11.1 Multiple imputation by regression

14.11.2 The three-step process in MI

14.11.3 Imputer's and analyst's models

14.11.4 Rubin's equations

14.11.5 Imputation diagnostics

14.11.6 Skewed continuous data

14.11.7 Other types of variables

14.11.8 How many imputations?

14.12 Multivariate multiple imputation

14.12.1 Monotone imputation

14.12.2 Data augmentation

14.12.3 Categorical variables

14.12.4 What to do when DA fails

14.12.5 Chained equations

14.12.6 Longitudinal data

14.13 When is it worth imputing?

Exercises

Appendix A Materials available on the website for this book

Appendix B Statistical tables

Appendix C Additional datasets for exercises

References

Index