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Transcript of Term 4, 2006BIO656--Multilevel Models 1 Midterm Open “book” and notes; closed mouth 20-25...
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BIO656--Multilevel Models 1Term 4, 2006
MidtermMidterm
• Open “book” and notes; closed mouth• 20-25 minutes to read carefully and answer
completely 60 minutes to think• 4 problems, with possible topics:
– Some debriefing on the role of MLMs– Something on linear MLMs variances, etc.– MLMs and shrinkage– Some basic computations and interpretations of
logit-linear models
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BIO656--Multilevel Models 2Term 4, 2006
PART 6PART 6
PROFILING, RANKING“League Tables”
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BIO656--Multilevel Models 3Term 4, 2006
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BIO656--Multilevel Models 4Term 4, 2006
RANKING IN THE NEWSRANKING IN THE NEWS
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BIO656--Multilevel Models 5Term 4, 2006
LETTERMAN’S LETTERMAN’S TOP 10 LISTTOP 10 LIST
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BIO656--Multilevel Models 6Term 4, 2006
NEW YORK’S MOST DEADLY NEW YORK’S MOST DEADLY CARDIAC SURGEONS!!!!CARDIAC SURGEONS!!!!
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BIO656--Multilevel Models 7Term 4, 2006
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BIO656--Multilevel Models 8Term 4, 2006
THE LEADING SPH IS THE LEADING SPH IS HARVARDHARVARD
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BIO656--Multilevel Models 9Term 4, 2006
HOPKINSHOPKINS IS THE IS THELEADING SPH!!!LEADING SPH!!!
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BIO656--Multilevel Models 10Term 4, 2006
PROFILINGPROFILING(League Tables)(League Tables)
• The process of comparing “units” on an outcome measure with relative or normative standards– Quality of care, use of services, cost– Educational quality– Disease rates in small areas– Gene expression
• Developing and implementing performance indices to compare physicians, hospitals, schools, teachers, genes, ........
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BIO656--Multilevel Models 11Term 4, 2006
PROFILING OBJECTIVESPROFILING OBJECTIVES(in health services)
• Estimate and compare provider-specific performance measures:– Utilization/cost– Process measures– Clinical outcomes– Patient satisfaction/QoL
• Compare using a normative (external) or a relative (internal) standard
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BIO656--Multilevel Models 12Term 4, 2006
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BIO656--Multilevel Models 13Term 4, 2006
RANKING IS EASYRANKING IS EASY
Just compute estimates & order themJust compute estimates & order them
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BIO656--Multilevel Models 14Term 4, 2006
MLE ESTIMATED SMRsMLE ESTIMATED SMRs
Provider
ML
E S
MR
0 20 40 60 80 100 120
02
46
81
0
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BIO656--Multilevel Models 15Term 4, 2006
RANKING IS DIFFICULTRANKING IS DIFFICULT
Need to trade-off the estimates and uncertainties
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BIO656--Multilevel Models 16Term 4, 2006
MLE ESTIMATED SMRs & 95% CIsMLE ESTIMATED SMRs & 95% CIs
Provider
ML
E S
MR
0 20 40 60 80 100 120
02
46
81
0
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BIO656--Multilevel Models 17Term 4, 2006
Sampling variability &Sampling variability &Systematic variabilitySystematic variability
Systematic variability• Variability among physicians/hospitals that might be
explained by hospital-specific characteristics
Sampling variability• Statistical uncertainty of physician/hospital-specific
performance measures
Use MLMs that• Incorporate patient, physician and hospital-level
characteristics• Capture all important uncertainties• Produce appropriate statistical summaries
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BIO656--Multilevel Models 18Term 4, 2006
Statistical ChallengesStatistical Challenges
Need a valid method of adjusting for case mix and other features• Patient, physician and hospital characteristics
– But, beware of over adjustment
Need a valid model for stochastic properties• Account for variation at all levels• Account for within-hospital, within-patient correlations
Need to • Adjust for systematic variation• Estimate and account for statistical variation
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BIO656--Multilevel Models 19Term 4, 2006
PROPER USE OF PROPER USE OF STATISTICAL SUMMARIESSTATISTICAL SUMMARIES
The challenge• Differences in standard errors of hospital-specific
estimates invalidate direct comparisons• In any case, large SEs make comparisons imprecise
Consequence • Even after valid case mix adjustment, differences in
directly estimated performance are due, in part, to sampling variability
(Partial) Solution, use:• Shrinkage estimates to balance and reduce variability• Goal-specific estimates to hit the right target
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BIO656--Multilevel Models 20Term 4, 2006
Comparing performance measuresComparing performance measures
Ranks/percentiles, of:• Direct estimates (MLEs)• Shrunken estimates (BLUPs, Posterior Means)• Z-scores testing H0 that a unit is just like others• Optimal (best) ranks or percentiles
Other measures• Probability of a large difference between unit-specific
“true” and H0-generated event rates• Probability of “excess mortality”
– For the “typical patient, on average or for a specific patient type
• Z-score/P-value declarations• ....
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BIO656--Multilevel Models 21Term 4, 2006
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BIO656--Multilevel Models 22Term 4, 2006
USRDSUSRDS
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BIO656--Multilevel Models 23Term 4, 2006
USRDSUSRDS
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BIO656--Multilevel Models 24Term 4, 2006
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BIO656--Multilevel Models 25Term 4, 2006
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BIO656--Multilevel Models 26Term 4, 2006
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BIO656--Multilevel Models 27Term 4, 2006
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BIO656--Multilevel Models 28Term 4, 2006
MLE ESTIMATED SMRs & CIs
Provider
ML
E S
MR
0 20 40 60 80 100 120
02
46
81
0
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BIO656--Multilevel Models 29Term 4, 2006
Poisson-Normal ModelPoisson-Normal Model(N, Y[k] , emort[k]) are inputs
model{{prec~dgamma(0.00001,0.00001)for (k in 1:N) {logsmr[k]~dnorm(00,prec)smr[k]<-exp(logsmr[k])rate[k]<-emort[k]*smr[k]Y[k] ~ dpois(rate[k])}} Monitor the SMR[k]
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BIO656--Multilevel Models 30Term 4, 2006
0.0 0.5 1.0 1.5 2.0 2.5
SE
MLE
PM
MLE, SE & POSTERIOR MEAN SMRsMLE, SE & POSTERIOR MEAN SMRs(using a log-normal/Poisson model)
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BIO656--Multilevel Models 31Term 4, 2006
Posterior Mean: estimated SMRs & CIsPosterior Mean: estimated SMRs & CIsusing a log-normal/Poisson model
(original scale)
Provider
PM
SM
R
0 20 40 60 80 100 120
02
46
81
0
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BIO656--Multilevel Models 32Term 4, 2006
Posterior Mean: estimated SMRs & CIsPosterior Mean: estimated SMRs & CIsusing a Gamma/Poisson model
(expanded scale)
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BIO656--Multilevel Models 33Term 4, 2006
• Estimated relative, physician-specific visit rate and 95% CI• Adjusted for patient demographic and case-mix (1.0 is the “typical” rate)
Caterpillar PlotCaterpillar Plot(Hofer et al. JAMA 1999)(Hofer et al. JAMA 1999)
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BIO656--Multilevel Models 34Term 4, 2006
• Amount that physician-specific, laboratory costs for diabetic patients deviates from the mean for all physicians [$/(pt. yr.)]• Lines show the path from the direct estimate (the MLE) to the shrunken estimate (Hofer et al JAMA 1999)
DIRECTDIRECT ADJUSTEDADJUSTED
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BIO656--Multilevel Models 35Term 4, 2006
Example using BUGS forExample using BUGS forhospital performance rankinghospital performance ranking
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BIO656--Multilevel Models 36Term 4, 2006
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BIO656--Multilevel Models 37Term 4, 2006
BUGS Model specificationBUGS Model specificationmodel{for k in 1:K {b[k]~dnorm(0, prec)r[k]~dbin(p[k], n[k])logit(p[k]) <- mu + b[k]}pop.mean<-exp(mu + bb)/(1+exp(mu + bb))mu~dnorm(0, 1E-6)prec~dgamma(.0001,.0001)tausq<-1/precadd~dnorm(0, prec)bb<- mu + add}
Monitor the p[k] and ask for ranks
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BIO656--Multilevel Models 38Term 4, 2006
Summary StatisticsSummary Statistics
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BIO656--Multilevel Models 39Term 4, 2006
Posterior distributions of the ranksPosterior distributions of the ranks
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BIO656--Multilevel Models 40Term 4, 2006
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BIO656--Multilevel Models 41Term 4, 2006
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BIO656--Multilevel Models 42Term 4, 2006
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BIO656--Multilevel Models 43Term 4, 2006
X = (Posterior Mean-Based Ranks) – (Optimal Ranks)
LOSLOS
==
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BIO656--Multilevel Models 44Term 4, 2006
LOSLOS
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BIO656--Multilevel Models 45Term 4, 2006
Relations among percentiling methodsRelations among percentiling methods1998 USRDS Percentiles
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BIO656--Multilevel Models 46Term 4, 2006
BACK TO THE USRDS, SMR EXAMPLEBACK TO THE USRDS, SMR EXAMPLE
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BIO656--Multilevel Models 47Term 4, 2006
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BIO656--Multilevel Models 48Term 4, 2006
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BIO656--Multilevel Models 49Term 4, 2006
False detection and non-detectionFalse detection and non-detection
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BIO656--Multilevel Models 50Term 4, 2006
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BIO656--Multilevel Models 51Term 4, 2006
K is large and we can use K is large and we can use a completely non-parametric priora completely non-parametric prior
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BIO656--Multilevel Models 52Term 4, 2006
= (1-B) = = (1-B) = 22/(/(22 + + 22) = ICC) = ICC
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BIO656--Multilevel Models 53Term 4, 2006
Probability of being in the upper 10%Probability of being in the upper 10%as a function of true percentileas a function of true percentile
= intra-class correlation
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BIO656--Multilevel Models 54Term 4, 2006