www.icnarc.o rg Analysis and presentation of quality indicators Dr David Harrison Senior Statistician, ICNARC
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Analysis and presentation of quality indicators
Dr David HarrisonSenior Statistician, ICNARC
Analysis and presentation of quality indicators | Dr David Harrison
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Analysis and presentation of QIs• Principles of statistical process
control• Comparison among providers• Continuous monitoring over time
Analysis and presentation of quality indicators | Dr David Harrison
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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
Analysis and presentation of quality indicators | Dr David Harrison
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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
Analysis and presentation of quality indicators | Dr David Harrison
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Five signatures…
Analysis and presentation of quality indicators | Dr David Harrison
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They are not identical…
Analysis and presentation of quality indicators | Dr David Harrison
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They are not identical…
…but they are all my signature
Analysis and presentation of quality indicators | Dr David Harrison
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We could rank them…
…but this doesn’t make much sense!
1.
2.
3.
4.
5.
Analysis and presentation of quality indicators | Dr David Harrison
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quality…
…but they are still my signature!
Analysis and presentation of quality indicators | Dr David Harrison
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This is common cause variation
Analysis and presentation of quality indicators | Dr David Harrison
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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
Analysis and presentation of quality indicators | Dr David Harrison
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Now we have a sixth signature…
Analysis and presentation of quality indicators | Dr David Harrison
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Now we have a sixth signature…
…it’s a good try, but I think you can tell which one is the forgery!
Analysis and presentation of quality indicators | Dr David Harrison
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This is special cause variation
Analysis and presentation of quality indicators | Dr David Harrison
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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
Analysis and presentation of quality indicators | Dr David Harrison
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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
Analysis and presentation of quality indicators | Dr David Harrison
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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
Analysis and presentation of quality indicators | Dr David Harrison
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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)?
Analysis and presentation of quality indicators | Dr David Harrison
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League tables• Journalists love them
– High impact– Everyone wants to know who is first
and last
Analysis and presentation of quality indicators | Dr David Harrison
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Seven deadliest hospitals identified
in damning Dr Foster reportDaily Telegraph, 29 November 2009
Twelve NHS trusts slammedThe Sun, 29 November 2009
Patient safety at Scarborough
Hospital ‘second worst in country’
Scarborough Evening News, 29 November 2009
Analysis and presentation of quality indicators | Dr David Harrison
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League tables• Journalists love them
– High impact– Everyone wants to know who is first
and 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)
Analysis and presentation of quality indicators | Dr David Harrison
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Marshall & Spiegelhalter, BMJ 1998• League table of 52 IVF clinics
ranked on live birth rate• Monte Carlo simulation to put 95%
CI on ranks
Analysis and presentation of quality indicators | Dr David Harrison
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Marshall & Spiegelhalter, BMJ 1998
Analysis and presentation of quality indicators | Dr David Harrison
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Marshall & Spiegelhalter, BMJ 1998
• King’s College Hospital – sixth from bottom – is the only one that can reliably be placed in the bottom 25%
Analysis and presentation of quality indicators | Dr David Harrison
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Marshall & Spiegelhalter, BMJ 1998
• BMI Chiltern Hospital – seventh from bottom – may not even be in the bottom 50%
Analysis and presentation of quality indicators | Dr David Harrison
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Marshall & Spiegelhalter, BMJ 1998
• Five clinics can confidently be placed in the top quarter
*
****
Analysis and presentation of quality indicators | Dr David Harrison
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Marshall & Spiegelhalter, BMJ 1998
• Southmead General – ranked sixth from top – may not be in the top 50%
Analysis and presentation of quality indicators | Dr David Harrison
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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
Analysis and presentation of quality indicators | Dr David Harrison
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Caterpillar plot – IV clinics
Analysis and presentation of quality indicators | Dr David Harrison
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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)
Analysis and presentation of quality indicators | Dr David Harrison
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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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Analysis and presentation of quality indicators | Dr David Harrison
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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)
Analysis and presentation of quality indicators | Dr David Harrison
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Funnel plot – ANZICS
• Note: use of normal distribution can result in negative confidence intervals – better methods exist
Analysis and presentation of quality indicators | Dr David Harrison
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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)
Analysis and presentation of quality indicators | Dr David Harrison
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Funnel plot – SICSAG
• SMRs by APACHE II for 25 adult ICUs in Scotland, 2009(SICSAG Audit of critical care in Scotland 2010)
Analysis and presentation of quality indicators | Dr David Harrison
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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
Analysis and presentation of quality indicators | Dr David Harrison
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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)
Analysis and presentation of quality indicators | Dr David Harrison
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readmissions
(Spiegelhalter. Qual Saf Health Care 2005)
Analysis and presentation of quality indicators | Dr David Harrison
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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
Analysis and presentation of quality indicators | Dr David Harrison
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Example – over-dispersion factor
0.25
0.50
1.00
2.00
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ICN
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200
9) m
odel
0 500 1000 1500Number of admissions
• SMRs by ICNARC model for 171 adult ICUs in England, Wales & N Ireland, 2009
Analysis and presentation of quality indicators | Dr David Harrison
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Example – over-dispersion factors
0.25
0.50
1.00
2.00
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0 500 1000 1500Number of admissions
Note: Overdispersion factor 1.4 based on 10% Winsorised
• Over-dispersion factor estimated at 1.4• Funnel widened
Analysis and presentation of quality indicators | Dr David Harrison
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Analysis and presentation of QIs• Principles of statistical process
control• Comparison among providers• Continuous monitoring over time
– RAP chart– EWMA– VLAD– R-SPRT– CUSUM
Analysis and presentation of quality indicators | Dr David Harrison
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Continuous monitoring over time• Various approaches• In general, they consist of…
– an indicator that is updated for each consecutive patient
– control limits
Analysis and presentation of quality indicators | Dr David Harrison
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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
Analysis and presentation of quality indicators | Dr David Harrison
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Queen Kate Hospital – SMRs
0.7
0.9
0.8
1.0
1.2
1.4
1.6
Mor
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95%
CI)
Consecutive blocks of 250 patients
Analysis and presentation of quality indicators | Dr David Harrison
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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
Analysis and presentation of quality indicators | Dr David Harrison
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Queen Kate Hospital – RAP chart
10%
20%
30%
40%
Mor
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Observed Predicted 2 SDs 3 SDs
Analysis and presentation of quality indicators | Dr David Harrison
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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
Analysis and presentation of quality indicators | Dr David Harrison
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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
Analysis and presentation of quality indicators | Dr David Harrison
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Queen Kate Hospital – EWMA
20%
25%
30%
35%
40%
Mor
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Observed Predicted +/- 2 SD 3 SD
Analysis and presentation of quality indicators | Dr David Harrison
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VLAD• Variable life adjusted display• Cumulative observed minus
expected deaths• Pro
– Nice easy interpretation
• Con– Control limits are complex to
calculate curved functions
Analysis and presentation of quality indicators | Dr David Harrison
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Queen Kate Hospital – VLAD
-20
0
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Cum
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deat
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0 500 1000 1500 2000Number of admissions
Analysis and presentation of quality indicators | Dr David Harrison
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R-SPRT• Resetting sequential probability
ratio test• Tests evidence for/against a
specific hypothesis (e.g. odds of death are double that predicted by the model)
• Plot of log likelihood ratio• If bottom line is reached (strong
evidence against hypothesis) then line resets to zero
Analysis and presentation of quality indicators | Dr David Harrison
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R-SPRT• Pro
– Nice statistical properties– Control limits are horizontal lines
• Con– Choice of hypothesis to test is
arbitrary – should we test for an OR of 2, 1.5,…?
Analysis and presentation of quality indicators | Dr David Harrison
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Queen Kate Hospital – R-SPRT
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PR
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0.01 0.001 0.0001alpha = beta =
Analysis and presentation of quality indicators | Dr David Harrison
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CUSUM• “Cumulative sum”• Log likelihood ratio – same as R-
SPRT• “Absorbing barrier” at zero (i.e.
never goes below zero)
Analysis and presentation of quality indicators | Dr David Harrison
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CUSUM• Pros/Cons as for the R-SPRT plus…• Pro
– Does not allow credit to build up (as in R-SPRT) so alerts earlier
– Negative CUSUM (e.g. OR=0.5) can be plotted on the same axes
• Con– Cannot detect evidence against
hypothesis
Analysis and presentation of quality indicators | Dr David Harrison
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Queen Kate Hospital – CUSUM
0
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Log
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R=
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0.01 0.001 0.0001alpha = beta =
Analysis and presentation of quality indicators | Dr David Harrison
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Which method(s) to use…?• Comparison among providers
– Funnel plot
• Continuous monitoring over time– EWMA– or R-SPRT– or CUSUM– (VLAD can be used as a display in
conjunction with, e.g., CUSUM for monitoring)
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