Transcript Multilevel_Modeling_..

Multilevel Modeling in Cardiac
Drug Utilization Research
Outline


PROC GLIMMIX introduction
Cardiac drug utilization research
using multilevel models.
Multilevel data
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Multilevel data are common in
observational study in social science,
health care field.
Clinical trials carried out in serveral
random selected center or groups of
subjects create data hierarchies
The Research Question
Investigate clinical and non-clinical factors
associated with prescription of cardiac drugs for
patients discharged after catheterization.
Heart Catheterization
Inclusion/Exclusion
Criteria
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Include All patients underwent the
1st CATH from 1999/07 to 2002/10
Exclude patients with age<20, nonBC patients, prior CABG or PCI, in
hospital death, discharged to
extended care
Exclude patients with normal
angiogram
Drugs of interests
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ACE Inhibitor
Beta Blocker
Statin
Optimum drug
Factor of Interest
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Patient level:
sex, age, extent of disease (blockage), prior drug,
ejection fraction, prior MI, DM, renal, HPD, HTN,
PVD, CVA, CHF, COPD, liver disease, urgency,
indication, cardiac re-hospitalization, transfer
history, length of hospital stay, revascularization,
Hospital level: teaching hospital
Physician level: year of service, volume of service
Neighbourhood level:
Median family income, univeristy education rate,
immigration rate
Assumption
1st Catheterization
Admission
Discharge
120 days
Data Structure
The data set consists 22847 patients
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Hospital level: Patients discharged from 67 BC hospitals
with hospital cluster size from 1 to 4403 patients; 97%
patients discharged from hospital with cluster size>100.
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Physician level: Patients discharged by 1059 physicians
(with anywhere between 1 to 785); 72% patients
discharged by physician with cluster size >100).
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Census tract level: Patients came from 695 census tract
with census tract cluster size from 1 to 342, 73% patients
came from census tract with cluster size>30.
Data Structure
Hospital
Physician
Neighbourhoods
Patient
Cross random intercept
model
yi ~ Bernouilli ( πi )
Logit(πi) = β0i + β1 x1i
β0i = β0 + δhosp(i)(2) + δdoc(i)(3) + δtract(i)(4)
Where i indexes the patient i, and hosp(i),
doc(i), and tract(i) are functions that
return the unit number of the hospital,
doctor, and census tract, respectively,
that patient i belong to.
Cross random intercept
model
yi ~ Bernouilli ( πi )
Logit(πi) =β0 + β1 x1i + δhosp(i)(2) + δdoc(i)(3) + δtract(i)(4)
δhosp(i)(2) ~ N (0, σδ(2)2 )
δdoc(i)(3) ~ N (0, σδ(3)2 )
δtract(i)(4) ~ N (0, σδ(4)2 )
Allow coefficient to vary
across the classification
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Suppose β1i represent heart failure, we
want to know whether the impact of
heart failure vary across the hospital
classification, we would use cross
random coefficient model to investigate
that.
Cross random coefficient
model
yi ~ Bernouilli ( πi )
Logit(πi) = β0i + β1i x1i
β0i = β0 + δhosp(i),0(2) + δdoc(i)(3) + δtract(i)(4)
β1i = β1 + δhosp(i),1(2)
Where δhosp(i),0(2) and δhosp(i),1(2) representing
the hospital random intercept effects
and random slope effects, respectively.
Which procedure to use?
Model
Response type
Random effects
LOGISTIC Binary
NO
GLM
NO
Interval
GENMOD Categorical, Interval NO
MIXED
Interval
Yes
NLMIXED Categorical, Interval Yes, but not suitable for
complex random effects
GLIMMIX Categorical, Interval Yes, suitable for complex
random effects
Where to get proc glimmix
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The glimmix procedure is a new
procedure in SAS/STAT software. It
is an add-on for the SAS/STAT
product in SAS 9.1 on either the
Windows or Linux platform. It is
currently downloadable for the SAS
9.1 release from software
downloads at support.sas.com.
Two level glimmix
proc glimmix data=glim_dataF IC=Q;
class sex ageGP65 dis_hosp ;
model drug(event='YES')=sex
ageGP65/solution dist=binary
link=logit ddfm=bw oddsratio;
random int / subject=dis_hosp;
run;
Three level glimmix
proc glimmix data=glim_dataF IC=Q;
class sex ageGP65 dis_hosp dis_phy;
model drug(event='YES')=sex ageGP65/solution
dist=binary link=logit ddfm=bw
oddsratio;
random int / subject=dis_phy(dis_hosp);
run;
Order in the class
statement
Value of ORDER=
DATA
Levels Sorted By
order of appearance in the input data set
FORMATTED
external formatted value, except for
numeric variables with no explicit format, which are
sorted by their unformatted (internal) value
FREQ descending frequency count; levels with the
most observations come first in the order
INTERNAL
unformatted value
Proc glimmix
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Advantage
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Allows multiple random effects, nested and
crossed random effects
Allows subject-specific and populationaveraged inference
Allows nonnormal distribution of response
Disadvantage
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The absence of a true log likelihood
The computation of cross effects model is
time consuming
Upcoming features in proc
glimmix in SAS 9.2
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The COVTEST statement for
likelihood-based testing and
confidence intervals for covariance
parameters.
Better output format?
Effects of ignoring Nested
Structure
Covariance Estimates
ACE Inhibitor Hospital
Physician
Physician(Hospital)
Physician(Hospital)
*census tract
Beta Blocker Hospital
Physician
Physician(Hospital)
Physician(Hospital)
*census tract
Statin
Hospital
Physician
Physician(Hospital)
Physician(Hospital)
*census tract
Optimum Rx Hospital
Physician
Physician(Hospital)
Physician(Hospital)
*census tract
Hospital(SE) Physician(SE) Census Tract(SE)
0.17(0.07)
0.32(0.06)
0.14(0.06)
0.22(0.04)
0.14(0.06)
0.18(0.07)
0.19(0.07)
0.19(0.07)
0.19(0.07)
0.20(0.08)
0.19(0.07)
0.20(0.07)
0.22(0.04)
0.02(0.01)
0.26(0.04)
0.10(0.02)
0.10(0.02)
0
0.39(0.06)
0.21(0.04)
0.20(0.04)
0.20(0.07)
0.24(0.04)
0.09(0.02)
0.19(0.07)
0.10(0.02)
0.02(0.01)
0.02(0.01)
Effects of ignoring Nested
Structure
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Ignoring the hospital hierarchy
leads to inflation of physician
variance estimates drasticly
Adding the cross effect of census
tract on hospital-physician nested
hierarchy doesn’t change the
hospital and physician variance.
Does Teaching hospital help to
explain the variation at hospital level?
Covariance Estimates
ACE Ihibitor intercept model
patient level variable model
Patient level variable +
high level variable model
Beta Blocker intercept model
patient level variable model
Patient level variable +
high level variable model
Statin
intercept model
patient level variable model
Patient level variable +
high level variable model
Optimum Rx intercept model
patient level model
Patient level variable +
high level variable model
Hospital(SE) Phyician(SE) census Tract(SE)
0.11(0.04)
0.25(0.04)
0.03(0.01)
0.14(0.06)
0.26(0.05)
0.02(0.01)
0.14(0.06)
0.14(0.05)
0.17(0.07)
0.22(0.04)
0.11(0.02)
0.11(0.03)
0.02 (0.01)
0.004(0.006)
0
0.19(0.07)
0.14(0.05)
0.19(0.07)
0.10(0.02)
0.21(0.04)
0.20(0.04)
0
0.04(0.01)
0.03(0.01)
0.19(0.07)
0.16(0.05)
0.18(0.06)
0.20(0.04)
0.14(0.02)
0.10(0.02)
0.02(0.01)
0.03(0.01)
0.02(0.01)
0.19(0.07)
0.10(0.02)
0.02(0.01)
Cross
effects
model
Does Teaching hospital help to
explain the variation at hospital level?
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Teaching hospital effect does not
explain the variation at hospital
level
Service years of physician and
physician service volume only
explain very little of the variation at
physician level
ACE Inhibitor
single level LR vs. multilevel LR
Years of service
Q1 vs Q4
Q2 vs Q4
Q3 vs Q4
Volume of service Q1 vs Q4
Q2 vs Q4
Q3 vs Q4
Teaching Hospital
Immigration Rate
Q5 vs Q1
Q4 vs Q1
Q3 vs Q1
Q2 vs Q1
OR
LowerCL UpperCL
1.34
1.22
1.48
1.24
1.05
1.47
0.91
0.83
1.01
0.87
0.74
1.03
0.99
0.90
1.10
1.01
0.86
1.17
0.68
0.72
0.91
0.87
0.83
0.92
1.39
1.20
0.61
0.60
0.83
0.74
0.75
0.79
1.28
0.68
0.77
0.86
1.01
1.03
0.91
1.06
1.51
2.13
0.90
0.93
1.00
1.04
0.90
0.97
0.94
0.97
0.81
0.81
0.90
0.92
0.81
0.86
0.84
0.86
1.01
1.06
1.12
1.19
1.01
1.09
1.04
1.09
1st row:: Single
level LR results
2nd row: multilevel
LR results
Beta Blocker
single level LR vs. multilevel LR
Years of service
Q1 vs Q4
Q2 vs Q4
Q3 vs Q4
Volume of service Q1 vs Q4
Q2 vs Q4
Q3 vs Q4
Teaching Hospital
Immigration Rate
Q5 vs Q1
Q4 vs Q1
Q3 vs Q1
Q2 vs Q1
OR
LowerCL UpperCL
1.19
1.08
1.30
1.16
1.01
1.35
1.07
0.97
1.18
1.10
0.94
1.28
0.97
0.88
1.07
1.08
0.94
1.24
0.86
0.76
0.82
0.78
0.94
0.93
1.70
1.36
0.77
0.65
0.74
0.68
0.86
0.81
1.57
0.71
0.96
0.89
0.90
0.91
1.04
1.06
1.84
2.58
0.91
0.93
0.77
0.88
0.86
0.97
0.92
0.97
0.81
0.82
0.69
0.78
0.78
0.87
0.83
0.87
1.02
1.06
0.86
0.99
0.96
1.08
1.02
1.08
1st row:: Single
level LR results
2nd row: multilevel
LR results
Statin
single level LR vs. multilevel LR
OR
Years of service
Q1 vs Q4
Q2 vs Q4
Q3 vs Q4
Volume of service Q1 vs Q4
Q2 vs Q4
Q3 vs Q4
Teaching Hospital
Immigration Rate
Q5 vs Q1
Q4 vs Q1
Q3 vs Q1
Q2 vs Q1
LowerCL UpperCL
1.31
1.18
1.45
1.16
0.98
1.38
1.18
1.06
1.32
1.17
0.98
1.39
1.20
1.08
1.33
1.14
0.97
1.33
0.99
0.88
1.12
1.00
0.83
1.20
1.13
1.02
1.26
1.04
0.88
1.23
0.95
0.86
1.06
0.95
0.82
1.11
0.97
0.89
1.06
1.03
0.53
1.98
0.68
0.61
0.77
0.75
0.65
0.86
0.87
0.77
0.98
0.94
0.81
1.08
0.93
0.82
1.04
0.91
0.80
1.04
1.09
0.96
1.22
1st row:: Single
level LR results
2nd row: multilevel
LR results
Optimum Rx
single level LR vs. multilevel LR
Years of service
Q1 vs Q4
Q2 vs Q4
Q3 vs Q4
Volume of service Q1 vs Q4
Q2 vs Q4
Q3 vs Q4
Teaching Hospital
Immigration Rate
Q5 vs Q1
Q4 vs Q1
Q3 vs Q1
Q2 vs Q1
OR
LowerCL UpperCL
1.33
1.22
1.44
1.22
1.07
1.38
1.13
1.04
1.23
1.11
0.97
1.27
0.99
0.91
1.07
1.08
0.95
1.22
0.86
0.83
1.00
0.93
0.90
0.92
1.42
1.28
0.77
0.84
0.86
0.98
0.86
0.95
0.93
0.97
0.78
0.72
0.91
0.82
0.83
0.82
1.32
0.68
0.70
0.75
0.78
0.88
0.78
0.85
0.85
0.88
0.95
0.96
1.09
1.06
0.98
1.04
1.52
2.42
0.84
0.94
0.94
1.10
0.94
1.06
1.02
1.08
1st row:: Single
level LR results
2nd row: multilevel
LR results
Implication of the results
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Compared to the cross effects models,
the standard errors of teaching hospital
effect from the single-level logistic
regression are much smaller and lead to
an invalid finding of significant teaching
hospital effect.
Between census tract variance is fairly
small. We keep the census tract random
effects in the model as we want to
examine the influence of immigration
rate on drug utilization.
Reference

Judith D.Singer. Using SAS PROC MIXED to fit multilevel
models, Hierarchical models, and individual growth
models. Journal of Educational and Behavioral Statistics
1998; 24, 323-355

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Jone Rasbash , William Brown. Non-hierarchical multilevel
models.
Tony Blakely, S V Subramanian. Multilevel Studies. In
Oakes M, Kaufman J, eds, Methods for social
epidemiology, Jossey Bass: San Francisco. 2005: in press.