Statistical Methods for Hospital Monitoring with R

Anthony Morton and Geoffrey Playford, Princess Alexandra Hospital, Brisbane, AustraliaKerrie Mengersen, Science and Engineering Faculty, Queensland University of Technology, AustraliaMichael Whitby, Greenslopes Specialist Centre, Queensland, Australia

• R Libraries xR Functions xiPreface xviIntroduction 10.1 Overview and rationale for this book 10.1.1 Motivation for the book 10.1.2 Why R? 20.1.3 Other reading for R 20.2 What methods are covered in the book? 30.3 Structure of the book 40.4 Using R 50.4.1 Entering data 60.4.2 Dates 80.4.3 Exporting data 100.5 Further notes 110.6 A brief introduction to rprogs charts and figures 110.6.1 What if there is no date column? 180.7 Appendix menus 200.7.1 IMenu() 200.7.2 CCMenu() 211 Introduction to analysis of binary and proportion data 241.1 Single proportion, samples and population 241.1.1 Calculating the confidence interval 261.1.2 Comparison with an expected rate 271.2 Likelihood ratio (Bayes factor) & supported range 291.3 Confidence intervals for a series of proportions 301.4 Difference between two proportions 331.4.1 Confidence intervals 331.4.2 Hypothesis test 351.4.3 The twoproportions function 371.5 Introducing a Bayesian approach 391.6 When the data are not just one or two independent samples 391.6.1 More than two independent proportions 401.6.2 Example 1, yearly data 401.6.3 Example 2, hospital data 431.6.4 Prop test and small samples 471.7 Summarising stratified proportion data 481.8 Stratified proportion data, differences between rates 501.8.1 Yearly data 521.8.2 Hospital data 541.9 Mantel-Haenszel, homogeneity and trend tests 541.9.1 Yearly data 561.9.2 Data stratified by hospital 591.10 Stratified rates and overdispersion 632 The analysis of aggregated binary data 672.1 Risk-adjustment 682.1.1 Using stratification 682.1.2 Using logistic regression 702.2 Discrimination and calibration 712.3 Using 2005–06 data 762.3.1 Displaying and analysing data from multiple institutions 772.3.2 Tabulations 782.3.3 Funnel plot and plot of multiple confidence intervals 832.4 When the Es are not fixed 992.5 Complex Surgical Site Infections 1022.5.1 Funnel plot analysis 1022.5.2 Shrinkage analysis 1042.6 Complex SSI risk-adjustment discrimination 1062.7 Appendix 1 – Further tabulation methods 1062.8 Appendix 2 – SMR CIs and tests, further scripts. Hospital expected values from other hospitals in group 1093 Sequential binary data 1163.1 CUSUM and related charts for binary data 1173.2 Cumulative Observed-Expected (O-E) chart and combined CUSUM and O-E chart 1203.3 Cumulative funnel plot and combined CUSUM and funnel plot 1203.4 Example 1213.5 Including risk adjustment 1243.6 CUSUM chart 1253.7 Cumulative observed minus expected (O-E) chart 1253.8 Funnel plot 1273.9 Discrimination and calibration of risk adjustment 1283.10 Shewhart P chart and EWMA chart 1323.11 Note on the Run-sum chart 1353.12 The EWMA chart 1353.13 Plotting the expected values 1383.14 Using a spline or generalised additive model (GAM) chart 1393.15 When there are few time periods 1413.16 Charts for quarterly data and data without a first date column 1433.17 Charts for composite measures 1463.18 Additional tabulations 1463.19 The issue of under-reporting 1513.20 New CUSUM and EWMA charts, low-rate data 1513.20.1 The risk-adjusted Bernoulli CUSUM 1533.20.2 The EWMA 1563.20.3 Quarterly rates 1573.21 Intervals between uncommon binary adverse events 1593.22 Appendix, proposed EWMA for low rate data 1644 Introduction to analysis of count and rate data 1684.1 Introduction 1684.2 Rate and count data 1694.3 Single count or rate 1694.3.1 Confidence interval 1704.3.2 Significance test 1714.4 Confidence limits for columns of counts and rates 1734.5 Two independent rates 1754.5.1 Confidence interval 1754.5.2 Hypothesis test 1764.5.3 Bayesian approach 1774.6 Chi-squared and trend tests for count and rate data 1774.7 Stratified count and rate data 1804.7.1 Obtaining a summary rate 1804.7.2 Stratified count and rate data, two sets of rates 1814.7.3 Indirect standardisation 1824.7.4 Direct standardisation 1844.8 Mantel-Haenszel, homogeneity and trend tests 1874.8.1 Fixed effects analysis, stratification by years 1874.8.2 Random effects analysis, stratification by hospitals 1904.9 Illustration of dealing with overdispersed rates 1934.10 The importance of count data variation 1964.11 Complex systems, networks and variation 2015 Tables and charts for aggregated count data 2035.1 Introduction, data, limitations of aggregated count data analysis 2035.2 Confidence intervals for Staphylococcus aureus bacteraemia SMR data 2065.3 Funnel plots for Staphylococcus aureus bacteraemia SMR data 2125.4 Tabulations and Z-scores 2195.5 More on overdispersion, false discovery, very small expected counts 2215.5.1 Proposal for Benjamini-Hochberg modified funnel plot 2235.6 Bayesian shrinkage plot 2275.6.1 Using OpenBUGS 2285.6.2 Using empirical Bayes methods 2295.7 Performing further tabulations in R 2315.8 Adjusting hospital levels for MRSA bacteraemia 2345.9 Bacteraemia risk adjustment 2376 Sequential count and rate data 2426.1 Grouping data 2436.2 Means and variances, predictability 2436.3 Tabulations 2446.4 Denominators 2466.5 Shewhart, EWMA and GAM control charts without denominators 2476.5.1 Shewhart/EWMA charts 2576.6 Shewhart, EWMA and GAM control charts with denominators 2646.6.1 Overdispersed data 2736.7 Charts for quarterly data and data without a first date column 2806.8 When there are few time periods 2826.9 Cross-tabulation in wide format 2866.10 Uncommon count data AEs 2916.11 Additional scripts for tabulations and charts 2976.12 Intervals between uncommon count data events 3006.13 Note on calculation of negative binomial parameters for control charts when denominators vary3036.13.1 Simple weighted variance 3036.13.2 Linear approximation (Bissell) 3036.13.3 Comparison of simple weighted variance and Bissell’s linear approximation 3047 Miscellaneous AEs 3077.1 MRO prevalence 3087.2 Antibiotic usage 3157.3 Spurious proportions, some blood culture data 3167.4 RIDIT charts, ECG data 3217.5 Numerical data – theatre utilisation 3267.6 Length of stay (LOS) data 3297.7 Changepoint 3397.8 Assessing agreement 3467.8.1 Numerical data agreement 3487.9 Making decisions (decision analysis) 3507.10 Investigating outbreaks, further analysis of stratified data 3527.10.1 Reviewing stratified data analysis 3557.10.2 Outbreak investigation example 3618 Hospital safety and adverse event prevention 3748.1 Introduction 3748.2 An overview of hospital quality improvement, five pillars 3758.2.1 The Customer, the first pillar 3758.2.2 The Practitioner, the second pillar 3758.2.3 The System, the third and main pillar 3758.3 Medical error 3768.3.1 Background of medical error (Vincent, Taylor-Adams & Vincent) 3768.4 Improving the system 3778.4.1 Evidence-based systems 3778.4.2 The role of bundles and checklists 3778.5 Error-proofing systems 3798.6 Discipline and accountability 3798.7 Limitations of imposing quality 3808.8 Performance and predictable variation 3808.9 The keys to a good system 3818.10 Analysing and implementing evidence-based systems 3818.11 The role of patient-care staff 3828.12 The role of central authority 3828.13 Change management, the fourth pillar 3838.14 Feedback loops, the fifth pillar 3838.15 Implementation of the Quality Improvement Process 3848.15.1 Implementation 3848.15.2 Obtaining data 3868.15.3 Special issues with QI studies 3868.16 The hospital as a network 389References 391Index 399