Analysis and presentation of quality indicators

1. Analysis and presentation of quality indicators Dr David Harrison Senior Statistician, ICNARC

2. Analysis and presentation of QIs • Principles of statistical process control • Comparison among providers • Continuous monitoring over time

3. Analysis and presentation of QIs • Principles of statistical process control • Common cause variation • Special cause variation • Control limits • Comparison among providers • Continuous monitoring over time

4. Principles of statistical process control • Common cause variation • Variation cannot be eliminated • Some variation is inherent to any process • This is termed “common cause variation” • To reduce common cause variation we need to change the process

5. Five signatures…

6. They are not identical…

7. They are not identical… …but they are all my signature

8. We could rank them… 1. 2. 3. 4. 5. …but this doesn’t make much sense!

9. We could reject some as low quality… …but they are still my signature!

10. This iscommon cause variation

11. Principles of statistical process control • Special cause variation • Some variation is the result of external factors acting on a process • This is termed “special cause variation” • To reduce special cause variation we need to identify the source and eliminate it

12. Now we have a sixth signature…

13. Now we have a sixth signature… …it’s a good try, but I think you can tell which one is the forgery!

14. This isspecial cause variation

15. Control limits • Statistical process control is all about making allowance for common cause variation to detect special cause variation • To do this we place control limits around a process • Control limits represent the acceptable range of common cause variation

16. Control limits • Typically control limits of 2 and 3 SDs represent “alert” and “alarm” • If a system is in control: • 95.4% of values within 2 SDs • 99.7% of values within 3 SDs

17. Analysis and presentation of QIs • Principles of statistical process control • Comparison among providers • League tables • Caterpillar plots • Funnel plots • Over-dispersion • Continuous monitoring over time

18. Comparison among providers • I’ll assume we have a binary event (e.g. death) and an associated risk estimate (e.g. predicted risk of death) • Most common QI is:observed events / expected events • (for mortality this is the standardised mortality ratio) • How should we compare this QI among providers (e.g. critical care units)?

19. League tables • Journalists love them • High impact • Everyone wants to know who is firstand last

20. Seven deadliest hospitals identified in damning Dr Foster reportDaily Telegraph, 29 November 2009 Twelve NHS trusts slammedThe Sun, 29 November 2009 Patient safety at ScarboroughHospital ‘second worst in country’Scarborough Evening News, 29 November 2009

21. League tables • Journalists love them • High impact • Everyone wants to know who is firstand last • Statisticians hate them • Overemphasise unimportant differences • Even if there is no true difference, someone will be first and someone last • No account of role of chance (common cause variation)

22. Marshall & Spiegelhalter, BMJ 1998 • League table of 52 IVF clinics ranked on live birth rate • Monte Carlo simulation to put 95% CI on ranks

23. Marshall & Spiegelhalter, BMJ 1998

24. Marshall & Spiegelhalter, BMJ 1998 • King’s College Hospital – sixth from bottom – is the only one that can reliably be placed in the bottom 25%

25. Marshall & Spiegelhalter, BMJ 1998 • BMI Chiltern Hospital – seventh from bottom – may not even be in the bottom 50%

26. Marshall & Spiegelhalter, BMJ 1998 * * * * * • Five clinics can confidently be placed in the top quarter

27. Marshall & Spiegelhalter, BMJ 1998 • Southmead General – ranked sixth from top – may not be in the top 50%

28. Caterpillar plots (or forest plots) • Plot of QIs with CIs in rank order • Still a league table really • But at least acknowledges variation by including CIs

29. Caterpillar plot – IV clinics

30. Caterpillar plot – ANZICS • SMRs by APACHE III-J for 106 adult ICUs in Australia and New Zealand, 2004(Cook et al. Crit Care Resusc 2008)

31. Funnel plots • Larger sample = greater precision • If you plot QI against sample size, you expect to see a funnel shape • We can plot funnel shaped control limits

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33. Funnel plot – ANZICS • SMRs by APACHE III-J for 106 adult ICUs in Australia and New Zealand, 2004(Cook et al. Crit Care Resusc 2008)

34. Funnel plot – ANZICS • Note: use of normal distribution can result in negative confidence intervals – better methods exist

35. Funnel plot – ANZICS • Note: as SMR is a ratio measure, we would advocate plotting on a log scale (i.e. SMR=2 and SMR=0.5 are equidistant from SMR=1)

36. Funnel plot – SICSAG • SMRs by APACHE II for 25 adult ICUs in Scotland, 2009(SICSAG Audit of critical care in Scotland 2010)

37. Funnel plot – SICSAG • Note: as the model is poorly calibrated, most units are “better than average” – the funnel has been centred on the average SMR not 1

38. Over-dispersion • Variability more than expected by chance • Suggests important factors that vary among providers are not being taken into account • Too many providers classified as “abnormal” (i.e. outside the funnel)

39. Over-dispersion – hospital readmissions (Spiegelhalter. Qual Saf Health Care 2005)

40. Over-dispersion – what to do…? • Don’t use the indicator? • Improve risk adjustment • Adjust for it • Estimate “over-dispersion factor” by “Winsorisation” • Use random effects models • Assumes each provider has their own true rate from a distribution

41. Example – over-dispersion factor • SMRs by ICNARC model for 171 adult ICUs in England, Wales & N Ireland, 2009

42. Example – over-dispersion factors • Over-dispersion factor estimated at 1.4 • Funnel widened

43. Analysis and presentation of QIs • Principles of statistical process control • Comparison among providers • Continuous monitoring over time • RAP chart • EWMA • VLAD • R-SPRT • CUSUM

44. Continuous monitoring over time • Various approaches • In general, they consist of… • an indicator that is updated for each consecutive patient • control limits

45. Example for continuous monitoring • Queen Kate Hospital • Fictitious critical care unit • Random sample of 2000 records from the Case Mix Programme Database • After 1000 records, outcomes changed so that an extra 6% of patients (selected at random) die • Risk adjustment by the ICNARC (2009) model

46. Queen Kate Hospital – SMRs

47. RAP chart • Risk-adjusted p chart • Cohort divided into discrete blocks (e.g. 100 patients) • Indicator is observed mortality • Control limits are predicted mortality +/- 2 or 3 SDs • Pro • Displays observed and expected mortality • Con • Still in blocks, not sensitive

48. Queen Kate Hospital – RAP chart

49. EWMA • Exponentially weighted moving average • Similar to RAP but uses all data up to the current timepoint • Data weighted by a smoothing factor so that most recent data are given most weight

50. EWMA • Pro • Displays observed and expected mortality • Estimates updated continuously not in arbitrary blocks • Con • Choice of smoothing factor is important – too little smoothing and plot is unreadable, too much and plot is insensitive to changes