Contents

Cover

Series

Title Page

Copyright

R Libraries

R Functions

Epigraph

Preface

Introduction

0.1 Overview and rationale for this book

0.2 What methods are covered in the book?

0.3 Structure of the book

0.4 Using R

0.5 Further notes

0.6 A brief introduction to rprogs charts and figures

0.7 Appendix menus

1 Introduction to analysis of binary and proportion data

1.1 Single proportion, samples and population

1.2 Likelihood ratio (Bayes factor) & supported range

1.3 Confidence intervals for a series of proportions

1.4 Difference between two proportions

1.5 Introducing a Bayesian approach

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

1.7 Summarising stratified proportion data

1.8 Stratified proportion data, differences between rates

1.9 Mantel-Haenszel, homogeneity and trend tests

1.10 Stratified rates and overdispersion

2 The analysis of aggregated binary data

2.1 Risk-adjustment

2.2 Discrimination and calibration

2.3 Using 2005–06 data

2.4 When the Es are not fixed

2.5 Complex Surgical Site Infections

2.6 Complex SSI risk-adjustment discrimination

2.7 Appendix 1 – Further tabulation methods

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

3 Sequential binary data

3.1 CUSUM and related charts for binary data

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

3.3 Cumulative funnel plot and combined CUSUM and funnel plot

3.4 Example

3.5 Including risk adjustment

3.6 CUSUM chart

3.7 Cumulative observed minus expected (O-E) chart

3.8 Funnel plot

3.9 Discrimination and calibration of risk adjustment

3.10 Shewhart P chart and EWMA chart

3.11 Note on the Run-sum chart

3.12 The EWMA chart

3.13 Plotting the expected values

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

3.15 When there are few time periods

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

3.17 Charts for composite measures

3.18 Additional tabulations

3.19 The issue of under-reporting

3.20 New CUSUM and EWMA charts, low-rate data

3.21 Intervals between uncommon binary adverse events

3.22 Appendix, proposed EWMA for low rate data

4 Introduction to analysis of count and rate data

4.1 Introduction

4.2 Rate and count data

4.3 Single count or rate

4.4 Confidence limits for columns of counts and rates

4.5 Two independent rates

4.6 Chi-squared and trend tests for count and rate data

4.7 Stratified count and rate data

4.8 Mantel-Haenszel, homogeneity and trend tests

4.9 Illustration of dealing with overdispersed rates

4.10 The importance of count data variation

4.11 Complex systems, networks and variation

5 Tables and charts for aggregated count data

5.1 Introduction, data, limitations of aggregated count data analysis

5.2 Confidence intervals for Staphylococcus aureus bacteraemia SMR data

5.3 Funnel plots for Staphylococcus aureus bacteraemia SMR data

5.4 Tabulations and Z-scores

5.5 More on overdispersion, false discovery, very small expected counts

5.6 Bayesian shrinkage plot

5.7 Performing further tabulations in R

5.8 Adjusting hospital levels for MRSA bacteraemia

5.9 Bacteraemia risk adjustment

6 Sequential count and rate data

6.1 Grouping data

6.2 Means and variances, predictability

6.3 Tabulations

6.4 Denominators

6.5 Shewhart, EWMA and GAM control charts without denominators

6.6 Shewhart, EWMA and GAM control charts with denominators

6.7 Charts for quarterly data and data without a first date column

6.8 When there are few time periods

6.9 Cross-tabulation in wide format

6.10 Uncommon count data AEs

6.11 Additional scripts for tabulations and charts

6.12 Intervals between uncommon count data events

6.13 Note on calculation of negative binomial parameters for control charts when denominators vary

7 Miscellaneous AEs

7.1 MRO prevalence

7.2 Antibiotic usage

7.3 Spurious proportions, some blood culture data

7.4 RIDIT charts, ECG data

7.5 Numerical data – theatre utilisation

7.6 Length of stay (LOS) data

7.7 Changepoint

7.8 Assessing agreement

7.9 Making decisions (decision analysis)

7.10 Investigating outbreaks, further analysis of stratified data

8 Hospital safety and adverse event prevention

8.1 Introduction

8.2 An overview of hospital quality improvement, five pillars

8.3 Medical error

8.4 Improving the system

8.5 Error-proofing systems

8.6 Discipline and accountability

8.7 Limitations of imposing quality

8.8 Performance and predictable variation

8.9The keys to a good system

8.10 Analysing and implementing evidence-based systems

8.11 The role of patient-care staff

8.12 The role of central authority

8.13 Change management, the fourth pillar

8.14 Feedback loops, the fifth pillar

8.15 Implementation of the Quality Improvement Process

8.16 The hospital as a network

References

Index

Statistics in Practice

STATISTICS IN PRACTICE

Series Advisors

Human and Biological Sciences

Stephen Senn
CRP-Santé, Luxembourg

Earth and Environmental Sciences

Marian Scott
University of Glasgow, UK

Industry, Commerce and Finance

Wolfgang Jank
University of Maryland, USA

Founding Editor

Vic Barnett

Nottingham Trent University, UK

Statistics in Practice is an important international series of texts which provide detailed coverage of statistical concepts, methods and worked case studies in specific fields of investigation and study.

   With sound motivation and many worked practical examples, the books show in down-to-earth terms how to select and use an appropriate range of statistical techniques in a particular practical field within each title's special topic area.

   The books provide statistical support for professionals and research workers across a range of employment fields and research environments. Subject areas covered include medicine and pharmaceutics; industry, finance and commerce; public services; the earth and environmental sciences, and so on.

   The books also provide support to students studying statistical courses applied to the above areas. The demand for graduates to be equipped for the work environment has led to such courses becoming increasingly prevalent at universities and colleges.

   It is our aim to present judiciously chosen and well-written workbooks to meet everyday practical needs. Feedback of views from readers will be most valuable to monitor the success of this aim.

A complete list of titles in this series appears at the end of the volume.

This edition first published 2013
© 2013 John Wiley & Sons, Ltd

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For details of our global editorial offices, for customer services and for information about how to apply for
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Library of Congress Cataloging-in-Publication Data

Morton, Anthony Park, 1933– author.
 Statistical methods for hospital monitoring with R / Anthony Morton, Kerrie Mengersen, Geoffrey Playford,
Michael Whitby.
  p. ; cm.
 Includes bibliographical references and index.
 ISBN 978-1-118-59630-2 (cloth)
 I. Mengersen, Kerrie L., author. II. Playford, Geoffrey, author. III. Whitby, Michael, 1950– author. IV. Title.
 [DNLM: 1. Hospital Administration. 2. Statistics as Topic. WX 150.1]
 RA971
 362.11068–dc23

2013008301

A catalogue record for this book is available from the British Library.

ISBN: 978-1-118-59630-2

R Libraries

arm | gee | PropCIs
bmem | geepack | psy
chron | hglm | qAnalyst
Epi | Kendall | qcc
epibasix | lme4 | rmeta
epicalc | MASS | spc
epiR | meta | splines
epitools | mgcv | surveillance
exactci | MKmisc | tseries

R Functions

1. bardenom() – rate data bar chart.

2. barnodenom() – count data bar chart.

3. bbar() – binomial data bar chart.

4. bbaradj() – risk-adjusted binary data bar chart.

5. bewma() – binomial data Shewhart/EWMA chart.

6. bewmacusum() – binary data EWMA/CUSUM chart.

7. bewmaqtr() – binomial data Shewhart/EWMA chart, quarterly data or data with no date column (requires first column e.g. 1:20).

8. bfunnelcusum() – cumulative funnel plot with CUSUM for binary data.

9. bgam() – binomial data generalized additive model (GAM) spline chart.

10. bgamqtr() – binomial data generalized additive model (GAM) spline chart, quarterly data, data with no date column (requires first column e.g. 1:20).

11. bgroupfunnelinstitution() – aggregated binary data funnel plot with institutions on horizontal axis.

12. bgroupfunnelprocedure()– aggregated binary data funnel plot with numbers of procedures on horizontal axis.

13. binarl() – average run length for binomial data.

14. binarladj() – average run length for risk-adjusted binary data.

15. binmonths() – arrange daily binary data by months.

16. binmonthsra() – arrange daily risk-adjusted binary data by months.

17. binqtrs() – arrange daily binary data by quarters.

18. binqtrsra() – arrange daily risk-adjusted binary data by quarters.

19. boecusum() – binary data Cumulative Observed – Expected (O-E) with CUSUM for binary data.

20. boecusumqtr()– binary data Cumulative Observed – Expected (O-E) with CUSUM for binary data (requires first column e.g. 1:100).

21. bshew() – binomial data Shewhart chart.

22. bshewqtr() – binomial data Shewhart chart, quarterly data, data with no date column (requires first column e.g. 1:20).

23. CCMenu() – control chart menu.

24. countewma() – count data Shewhart/EWMA chart.

25. countewmacusum – count data EWMA/CUSUM for uncommon AEs.

26. countewmao() – count data Shewhart/EWMA chart with overdispersion correction.

27. countewmaqtr() – count data Shewhart/EWMA chart, quarterly data, data with no date column (requires first column e.g. 1:20).

28. countewmaqtro() – count data Shewhart/EWMA chart, quarterly data, data with no date column (requires first column e.g. 1:20), with overdispersion correction.

29. countgam() – count data GAM chart.

30. countgamauto() – count data GAM chart with autocorrelation.

31. countgamautoqtr() – count data GAM chart with autocorrelation, quarterly data, data with no date column (requires first column e.g. 1:20).

32. countgamqtr() – count data GAM chart, quarterly data, data with no date column (requires first column e.g. 1:20).

33. countoecusum() – cumulative observed minus expected chart with CUSUM for uncommon count data AEs.

34. countquarters() – arranging count data by quarters.

35. countshew() – count data Shewhart chart.

36. countshewo() – count data Shewhart chart, with overdispersion correction.

37. countshewqtr() – count data Shewhart chart, quarterly data, data with no date column (requires first column e.g. 1:20).

38. countshewqtro() – count data Shewhart chart, quarterly data, data with no date column (requires first column e.g. 1:20), with overdispersion correction.

39. do.acf() – plot of ACF & PACF.

40. ebshrinkageb() – binary data empirical Bayes shrinkage analysis.

41. ewmacountdenom() – count data Shewhart/EWMA chart with separate denominators.

42. ewmacountdenomo() – count data Shewhart/EWMA chart with separate denominators, with overdispersion correction.

43. ewmacountdenomqtr() – count data Shewhart/EWMA chart with separate denominators, quarterly data, data with no date column (requires first column e.g. 1:20).

44. ewmacountdenomqtro() – count data Shewhart/EWMA chart with separate denominators, quarterly data, data with no date column (requires first column e.g. 1:20), with overdispersion correction.

45. g.d() – generic function for importing data into R.

46. getc4() – calculates the Shewhart chart constant c.

47. gammapoisson.odc/count.odc – OpenBUGS script for shrinkage analysis.

48. getnegbinparams() – negative binomial parameters with differing sized denominators (Bissell).

49. iewmachart() – Shewhart/EWMA i chart.

50. iewmachartqtr() – Shewhart/EWMA i chart, quarterly data, data with no date column (requires first column e.g. 1:20).

51. IMenu() – menu for Chapters 1 and 4.

52. ishewchart() – Shewhart i chart.

53. ishewchartqtr() – Shewhart i chart, quarterly data, data with no date column (requires first column e.g. 1:20).

54. manyproportions() – more than two independent proportions.

55. manyrates() – more than two independent rates.

56. mg.d(), ms.d() – generic functions for importing data into R and exporting from R (MAC).

57. monthlyaverage() – monthly averages of daily data.

58. monthlycounts() – arranges count data by months.

59. monthlynumbers() – arranges numerical data by months (aggregates).

60. multiplecounts() – confidence intervals for a series of counts.

61. multipleproportions() – confidence intervals for a series of proportions.

62. numgam() – GAM chart for numerical data without autocorrelation.

63. numgamauto() – GAM chart for numerical data with autocorrelation.

64. numgamautoqtr() – GAM chart for numerical data with autocorrelation, quarterly data, data with no date column (requires first column e.g. 1:20).

65. numgamqtr() – GAM chart for numerical data without autocorrelation, quarterly data, data with no date column (requires first column e.g. 1:20).

66. overdispersed() – to calculate Laney's correction for overdispersion in count and rate control charts.

67. pgroupfunnelinstitution() – funnel plot for aggregated rates sorted by institution.

68. pgroupfunnelprocedure() – funnel plot for aggregated rates sorted by number of procedures.

69. poiarl() – count data ARL.

70. proportion() – analysis involving a single proportion.

71. rate() – single count or rate.

72. rateewma() – rate data Shewhart/EWMA chart.

73. rateewmao() – rate data Shewhart/EWMA chart with overdispersion correction.

74. rateewmaqtr() – rate data Shewhart/EWMA chart, quarterly data, data with no date column (requires first column e.g. 1:20).

75. rateewmaqtro() – rate data Shewhart/EWMA chart, quarterly data, data with no date column (requires first column e.g. 1:20), with overdispersion correction.

76. rategam() – rate data GAM chart.

77. rategamauto() – rate data GAM chart with autocorrelation.

78. rategamautoqtr() – rate data GAM chart with autocorrelation, quarterly data, data with no date column (requires first column e.g. 1:20).

79. rategamqtr() – rate data GAM chart without autocorrelation, quarterly data, data with no date column (requires first column e.g. 1:20).

80. ratenegbin() – negative binomial Shewhart with differing sized denominators (Bissell).

81. ratequarters() – arranges rate data by quarters.

82. rateshew() – rate data Shewhart chart.

83. rateshewo() – rate data Shewhart chart, with overdispersion correction.

84. rateshewqtr() – rate data Shewhart chart, quarterly data, data with no date column (requires first column e.g. 1:20).

85. rateshewqtro() – rate data Shewhart chart, quarterly data, data with no date column (requires first column e.g. 1:20), with overdispersion correction.

86. riditewma() – Shewhart/EWMA RIDIT i chart.

87. riditewmaqtr() – Shewhart/EWMA RIDIT i chart, quarterly data, data with no date column (requires first column e.g. 1:20).

88. riditshew() – Shewhart RIDIT i chart.

89. riditshewqtr() – Shewhart RIDIT i chart, quarterly data, data with no date column (requires first column e.g. 1:20).

90. rocchart() – area under receiver operating characteristic (ROC) chart.

91. runchart() – count data run chart.

92. runchartdenom() – count data run chart with denominators.

93. s.d() – generic function for exporting data from R.

94. schart() – Shewhart Sbar chart.

95. schartqtr() – Shewhart Sbar chart, quarterly data, data with no date column (requires first column e.g. 1:20).

96. shewcountdenom() – count data Shewhart chart with separate denominators.

97. shewcountdenomo() – count data Shewhart chart with separate denominators, with correction for overdispersion.

98. shewcountdenomqtr() – count data Shewhart chart with separate denominators, data with no date column (requires first column e.g. 1:20).

99. shewcountdenomqtro() – count data Shewhart chart with separate denominators, data with no date column (requires first column e.g. 1:20), with correction for overdispersion.

100. shrink() – analysis of shrinkage data in R from OpenBUGS.

101. stratified2proportionsn() – weighted average of differences between two series of proportions using the method of Newcombe.

102. stratified2ratesn() – weighted average of differences between two series of rates using the method of Newcombe.

103. stratifiedproportionsn() – weighted average of a series of proportions using the method of Newcombe.

104. stratifiedratesn() – weighted average of a series of rates using the method of Newcombe.

105. twoproportions() – two independent proportions.

106. tworates() – two independent rates or counts.

107. wtdvar() – weighted variance of counts with denominators.

108. xbarewma() – Shewhart/EWMA XBAR chart.

109. xbarewmaqtr() – Shewhart/EWMA XBAR chart, quarterly data, data with no date column (requires first column e.g. 1:20).

110. xbarshew() – Shewhart XBAR chart.

111. xbarshewqtr() – Shewhart XBAR chart, quarterly data, data with no date column (requires first column e.g. 1:20).

For those who seek to understand the complex dynamic systems that are at the heart of hospital safety. We hope our book will provide them with encouragement.

Counting hospital adverse events is obviously important. However, it is more important to realise that the counted adverse events are not the ones that we have been able to prevent.

Any royalties from this book are to go to a fund to aid students from developing countries in their studies of hospital safety at our universities and hospitals.

Preface

This book had its beginnings when, as director of an intensive care unit, I became interested in analysing acute care hospital outcome data and in trying to understand how such monitoring could prevent care from becoming unsafe. Attempts at data analysis were initially made using a spreadsheet. I retired from clinical practice in 1989 and for several years I worked part-time as a research associate at the then Australian Centre in Strategic Management. In 1994 Professor Michael Whitby invited me to work with him in his department, Infection Management Services at the Princess Alexandra Hospital. I then became acutely aware of the challenges presented by the clustering, high variability and sometimes autocorrelation among adverse event data, particularly but not only that which is due to hospital-acquired infection and colonisation.

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