Hospitals monitoring is becoming more complex and is increasing both because staff want their data analysed and because of increasing mandated surveillance. This book provides a suite of functions in R, enabling scientists and data analysts working in infection management and quality improvement departments in hospitals, to analyse their often non-independent data which is frequently in the form of trended, over-dispersed and sometimes auto-correlated time series; this is often difficult to analyse using standard office software.

This book provides much-needed guidance on data analysis using R for the growing number of scientists in hospital departments who are responsible for producing reports, and who may have limited statistical expertise.

This book explores data analysis using R and is aimed at scientists in hospital departments who are responsible for producing reports, and who are involved in improving safety. Professionals working in the healthcare quality and safety community will also find this book of interest

Statistical Methods for Hospital Monitoring with R:

• Provides functions to perform quality improvement and infection management data analysis.
• Explores the characteristics of complex systems, such as self-organisation and emergent behaviour, along with their implications for such activities as root-cause analysis and the Pareto principle that seek few key causes of adverse events.
• Provides a summary of key non-statistical aspects of hospital safety and easy to use functions.
• Provides R scripts in an accompanying web site enabling analyses to be performed by the reader http://www.wiley.com/go/hospital_monitoring
• Covers issues that will be of increasing importance in the future, such as, generalised additive models, and complex systems, networks and power laws.

Anthony Morton and Geoffrey Playford, Princess Alexandra Hospital, Brisbane, Australia

Kerrie Mengersen, Science and Engineering Faculty, Queensland University of Technology, Australia

Michael Whitby, Greenslopes Specialist Centre, Queensland, Australia

R Libraries x

R Functions xi

Preface xvi

Introduction 1

0.1 Overview and rationale for this book 1

0.1.1 Motivation for the book 1

0.1.2 Why R? 2

0.1.3 Other reading for R 2

0.2 What methods are covered in the book? 3

0.3 Structure of the book 4

0.4 Using R 5

0.4.1 Entering data 6

0.4.2 Dates 8

0.4.3 Exporting data 10

0.5 Further notes 11

0.6 A brief introduction to rprogs charts and figures 11

0.6.1 What if there is no date column? 18

0.7 Appendix menus 20

0.7.1 IMenu() 20

0.7.2 CCMenu() 21

1 Introduction to analysis of binary and proportion data 24

1.1 Single proportion, samples and population 24

1.1.1 Calculating the confidence interval 26

1.1.2 Comparison with an expected rate 27

1.2 Likelihood ratio (Bayes factor) & supported range 29

1.3 Confidence intervals for a series of proportions 30

1.4 Difference between two proportions 33

1.4.1 Confidence intervals 33

1.4.2 Hypothesis test 35

1.4.3 The twoproportions function 37

1.5 Introducing a Bayesian approach 39

1.6 When the data are not just one or two independent samples 39

1.6.1 More than two independent proportions 40

1.6.2 Example 1, yearly data 40

1.6.3 Example 2, hospital data 43

1.6.4 Prop test and small samples 47

1.7 Summarising stratified proportion data 48

1.8 Stratified proportion data, differences between rates 50

1.8.1 Yearly data 52

1.8.2 Hospital data 54

1.9 Mantel-Haenszel, homogeneity and trend tests 54

1.9.1 Yearly data 56

1.9.2 Data stratified by hospital 59

1.10 Stratified rates and overdispersion 63

2 The analysis of aggregated binary data 67

2.1 Risk-adjustment 68

2.1.1 Using stratification 68

2.1.2 Using logistic regression 70

2.2 Discrimination and calibration 71

2.3 Using 200506 data 76

2.3.1 Displaying and analysing data from multiple institutions 77

2.3.2 Tabulations 78

2.3.3 Funnel plot and plot of multiple confidence intervals 83

2.4 When the Es are not fixed 99

2.5 Complex Surgical Site Infections 102

2.5.1 Funnel plot analysis 102

2.5.2 Shrinkage analysis 104

2.6 Complex SSI risk-adjustment discrimination 106

2.7 Appendix 1 Further tabulation methods 106

2.8 Appendix 2 SMR CIs and tests, further scripts. Hospital expected values from other hospitals in group 109

3 Sequential binary data 116

3.1 CUSUM and related charts for binary data 117

3.2 Cumulative Observed-Expected (O-E) chart and combined CUSUM and O-E chart 120

3.3 Cumulative funnel plot and combined CUSUM and funnel plot 120

3.4 Example 121

3.5 Including risk adjustment 124

3.6 CUSUM chart 125

3.7 Cumulative observed minus expected (O-E) chart 125

3.8 Funnel plot 127

3.9 Discrimination and calibration of risk adjustment 128

3.10 Shewhart P chart and EWMA chart 132

3.11 Note on the Run-sum chart 135

3.12 The EWMA chart 135

3.13 Plotting the expected values 138

3.14 Using a spline or generalised additive model (GAM) chart 139

3.15 When there are few time periods 141

3.16 Charts for quarterly data and data without a first date column 143

3.17 Charts for composite measures 146

3.18 Additional tabulations 146

3.19 The issue of under-reporting 151

3.20 New CUSUM and EWMA charts, low-rate data 151

3.20.1 The risk-adjusted Bernoulli CUSUM 153

3.20.2 The EWMA 156

3.20.3 Quarterly rates 157

3.21 Intervals between uncommon binary adverse events 159

3.22 Appendix, proposed EWMA for low rate data 1...