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EPI235: Epi Methods in HSR
April 12, 2007 L4
Evaluating Health Services using administrative data 3: Advanced Topics on Risk Adjustment and Sensitivity Analysis (Dr. Schneeweiss)
Risk adjustment in studies using administrative databases is limited to observed confounders. Dr. Schneeweiss will illustrate theory and practice of assessing the sensitivity of epidemiologic risk estimates towards unobserved confounding. An interactive Excel program will be used for illustration.
Background reading: •Walker AM: Observation and inference, Chapter 9. Epidemiology Resources, Newton Lower Falls, 1991.•Schneeweiss S, Glynn RJ, Tsai EH, Avorn J, Solomon DH. Adjusting for unmeasured confounders in pharmacoepidemiologic claims data using external information: The example of COX2 inhibitiors and myocardial infarction. Epidemiology 2005;16:17-24.
2
Unmeasured (residual) Confounding
Confounding factors that are not measured are hard to adjust for in observational analyses
If unadjusted they lead to residual confounding
3
Unmeasured (residual) Confounding:
[smoking,healthy lifestyle, etc.]
Drug exposure
Outcome
RREO
OREC RRCO
CU
CM
4
Unmeasured Confounding in Claims Data
Database studies are criticized for their inability to measure clinical and life-style parameters that are potential confounders in many pharmacoepi studies OTC drug use BMI Clinical parameters: Lab values, blood pressure, X-
ray Physical functioning, ADL (activities of daily living) Cognitive status
5
Strategies to Discuss Residual Confounding
Qualitative discussions of potential biasesSensitivity analysis
SA is often seen as the ‘last line of defense’ A) SA to explore the strength of an association as a
function of the strength of the unmeasured confounder B) Answers the question “How strong must a
confounder be to fully explain the observed association”
Several examples in Occupational Epi but also for claims data
Greenland S et al: Int Arch Occup Env Health 1994
Wang PS et al: J Am Geriatr Soc 2001
6
Foot-in-Mouth Award (Economist ‘04): “… there are known knowns; there are things we know we know. We also know that there are known unknowns; that is to say we know that there are some things we do not know. But there are also unknown unknowns – the ones we don’t know we don’t know. …, it is the latter category that tend to be the difficult ones.”
(Wisely unknowing) Donald Rumsfeld
7
Notation
RR Fully adjusted (“true”) exposure relative
risk
ARR Apparent exposure relative risk
RRCD Association between confounder and
disease outcome
PC Prevalence of confounder
PC1 Prevalence of confounder in the
exposed
PC0 Prevalence of confounder in the
unexposed
PE Prevalence of drug exposure
OREC Association between drug use category
and confounder
8
A simple sensitivity analysis
The apparent RR is a function of the adjusted RR times ‘the imbalance of the unobserved confounder’
After solving for RR we can plug in values ofr the prevalence and strength of the confounder:
1)1(
1)1(
0
1
CDC
CDC
RRP
RRPRRARR
1)1(
1)1(
0
1
CDC
CDC
RRP
RRP
ARRRR
9
A made-up example
Association between TNF-a blocking agents and NH lymphoma in RA patients Let’s assume and observed RR of 2.0 Let’s assume 50% of RA patients have a more
progressive immunologic disease … and that more progressive disease is more likely
to lead to NH lymphoma Let’s now vary the imbalance of the hypothetical
unobserved confounder
10
Bias by residual confounding
4.5
2.5
0.8
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
RRadjusted
RRCD
PC1
Fixed:ARR = 2.0
PC0 = 0.5
11
2. Array approach
fix X Y fix Z2 Z1
ARR RRCD PC1 PC0 RRadjusted % Bias % Bias = [(ARR-RRadj.)/(RRadj.-1)]*100
2.0 4.5 0.0 0.5 5.5 -77.782.0 4.0 0.0 0.5 5.0 -75.002.0 3.5 0.0 0.5 4.5 -71.432.0 3.0 0.0 0.5 4.0 -66.672.0 2.5 0.0 0.5 3.5 -60.002.0 2.0 0.0 0.5 3.0 -50.002.0 1.5 0.0 0.5 2.5 -33.332.0 1.0 0.0 0.5 2.0 0.002.0 0.8 0.0 0.5 1.8 33.332.0 0.5 0.0 0.5 1.5 100.002.0 4.5 0.1 0.5 4.1 -67.472.0 4.0 0.1 0.5 3.8 -64.862.0 3.5 0.1 0.5 3.6 -61.542.0 3.0 0.1 0.5 3.3 -57.142.0 2.5 0.1 0.5 3.0 -51.062.0 2.0 0.1 0.5 2.7 -42.112.0 1.5 0.1 0.5 2.4 -27.592.0 1.0 0.1 0.5 2.0 0.002.0 0.8 0.1 0.5 1.8 25.812.0 0.5 0.1 0.5 1.6 72.732.0 4.5 0.2 0.5 3.2 -55.262.0 4.0 0.2 0.5 3.1 -52.942.0 3.5 0.2 0.5 3.0 -50.002.0 3.0 0.2 0.5 2.9 -46.152.0 2.5 0.2 0.5 2.7 -40.912.0 2.0 0.2 0.5 2.5 -33.332.0 1.5 0.2 0.5 2.3 -21.432.0 1.0 0.2 0.5 2.0 0.002.0 0.8 0.2 0.5 1.8 18.752.0 0.5 0.2 0.5 1.7 50.002.0 4.5 0.3 0.5 2.7 -40.582.0 4.0 0.3 0.5 2.6 -38.712.0 3.5 0.3 0.5 2.6 -36.362.0 3.0 0.3 0.5 2.5 -33.332.0 2.5 0.3 0.5 2.4 -29.272.0 2.0 0.3 0.5 2.3 -23.532.0 1.5 0.3 0.5 2.2 -14.812.0 1.0 0.3 0.5 2.0 0.002.0 0.8 0.3 0.5 1.9 12.122.0 0.5 0.3 0.5 1.8 30.772.0 4.5 0.4 0.5 2.3 -22.582.0 4.0 0.4 0.5 2.3 -21.432.0 3.5 0.4 0.5 2.3 -20.002.0 3.0 0.4 0.5 2.2 -18.182.0 2.5 0.4 0.5 2.2 -15.792.0 2.0 0.4 0.5 2.1 -12.502.0 1.5 0.4 0.5 2.1 -7.692.0 1.0 0.4 0.5 2.0 0.002.0 0.8 0.4 0.5 1.9 5.882.0 0.5 0.4 0.5 1.9 14.292.0 4.5 0.5 0.5 2.0 0.002.0 4.0 0.5 0.5 2.0 0.002.0 3.5 0.5 0.5 2.0 0.002.0 3.0 0.5 0.5 2.0 0.00
4.5
3.5
2.5
1.5
0.8
0.0 0.
2 0.4 0.
6 0.8 1.
0-100
-50
0
50
100
150
200
250
300
350
% Bias
RRCD
PC1
Fixed:ARR = 2.0
PC0 = 0.5
4.5
2.5
0.8
0.0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
RRadjusted
RRCD
PC1
Fixed:ARR = 2.0
PC0 = 0.5
1)1(
1)1(
0
1
.
CDC
CDC
adj
RRP
RRP
ARRRR
12
Pros and cons of “Array approach”
Very easy to perform using ExcelVery informative to explore confounding with
little prior knowledge Problems: It usually does not really provide an answer
to a specific research question4 parameters can vary -> in a 3-D plot 2
parameter have to be kept constantThe optical impression can be manipulated
by choosing different ranges for the axes
13
Same example, different parameter ranges
3.0
1.7
0.8
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6
0.6
0.7
0.7
0.0
0.5
1.0
1.5
2.0
2.5
3.0
RRadjusted
RRCD
PC1
Fixed:ARR = 2.0
PC0 = 0.5
14
Conclusion of “Array Approach”
Great tool but you need to be honest to yourself
For all but one tool that I present today: Assuming conditional independence of CU and CM
given the exposure status If violated than residual bias may be overestimated
Drug exposure
Outcome
RREO
OREC RRCO
CU
CM
Hernan, Robins: Biometrics 1999
?
15
More advanced techniques
Wouldn’t it be more interesting to know How strong and imbalanced does a confounder
have to be in order to fully explain the observed findings?
RRCO OREC
16
Example:
Wang et al: JAGS 2001;49:1685
Zolpidem use and hip fractures in older people.
The issue:
Are there any unmeasured factors that may lead to a preferred prescribing of zolpidem to people at higher risk for falling and fracturing?
> Frailty is a hard to measure concept in claims data
RRCO
OREC
ARR
PC
17
How do we do that?
We want to express as a function of , ARR, PC, PE
OREC
RRCO
Walker AM: Observation and Inference. Epidemiology Resources Inc., Newton, 1991
18
A s s u m i n g a 2 - b y - 2 t a b l e o f a d i c h o t o m o u s e x p o s u r e a n d a d i c h o t o m o u s
c o n f o u n d e r , l e t e b e t h e p r e v a l e n c e o f t h e c o n f o u n d e r a m o n g e x p o s e d ( P C 1 | E 1 ) . T h e
a s s o c i a t i o n b e t w e e n t h e c o n f o u n d e r a n d e x p o s u r e c a n t h e n b e m e a s u r e d b y t h e
c o n f o u n d e r - e x p o s u r e o d d s r a t i o o r O R C E , w h i c h i s a f u n c t i o n o f e a n d t h e m a r g i n a l
p r o b a b i l i t i e s o f e x p o s u r e P r ( E ) a n d c o n f o u n d e r P r ( C ) :
])][Pr()[Pr(
])Pr()Pr(1[
eEeC
eECeOR CE
( 1 )
A s s u m i n g n o u n d e r l y i n g t r u e e x p o s u r e - d i s e a s e a s s o c i a t i o n o r R R E D = 1 ,
W a l k e r s h o w e d t h a t t h e a p p a r e n t R R E D ( A R R E D ) i s a f u n c t i o n o f e , t h e m a r g i n a l
p r o b a b i l i t i e s P r ( E ) a n d P r ( C ) , a n d t h e c o n f o u n d e r - d i s e a s e a s s o c i a t i o n R R C D :
)Pr(
)Pr(1
1)Pr(]1][)[Pr(
)Pr(]1[
E
E
ERReC
ERReARR
CD
CDED
( 2 )
19
])][Pr()[Pr(
])Pr()Pr(1[
eEeC
eECeOR CE
( 1 )
)Pr(
)Pr(1
1)Pr(]1][)[Pr(
)Pr(]1[
E
E
ERReC
ERReARR
CD
CDED
( 2 )
I f t h e p r i m a r y i n t e r e s t i s t o e x p l o r e t h e r e l a t i o n s h i p b e t w e e n O R C E a n d R R C D f o r a g i v e n A R R E D , R R C D ,
P r ( C ) , a n d P r ( E ) t h e n w e n e e d t o s o l v e e q u a t i o n ( 2 ) f o r e ,
)Pr())(Pr(1))Pr())(Pr(
))(Pr())(Pr())Pr()(Pr())Pr()(Pr()()Pr( 22
ERRERRARRRREARRE
ARREARREARRCEARRRRCEEPREe
CDCDEDCDED
EDEDEDEDCD
a n d s u b s t i t u t e t h e d e r i v e d t e r m f o r e i n e q u a t i o n 1 .
20
3. Rule Out Residual ConfoundingHow strong does an unmeasured confounder have to be to fully explain the observed findings?
The relationship between OREC and RRCD for a given ARR, RRC, PC, PE.
Data from Wang et al.: Zolpidem use and hip fractures in older people. J Am Geriatri Soc 2001;49:1685-90.a(prim)
RRCD PC PE ARR=1.95 OREC ARR=1.09 OREC
1.2 0.2 0.01 1.95 1.09 8.09 0.0438671.5 0.2 0.01 1.95 1.09 2.65 0.019562 0.2 0.01 1.95 1.09 1.78 0.011458
2.5 0.2 0.01 1.95 1.09 1.54 0.0087573 0.2 0.01 1.95 24.23 1.09 1.43 0.007406
3.5 0.2 0.01 1.95 13.10 1.09 1.36 0.0065964 0.2 0.01 1.95 9.51 1.09 1.32 0.006056
4.5 0.2 0.01 1.95 7.74 1.09 1.29 0.005675 0.2 0.01 1.95 6.69 1.09 1.27 0.005381
5.5 0.2 0.01 1.95 5.99 1.09 1.25 0.0051566 0.2 0.01 1.95 5.49 1.09 1.24 0.004976
6.5 0.2 0.01 1.95 5.12 1.09 1.22 0.0048287 0.2 0.01 1.95 4.83 1.09 1.22 0.004706
7.5 0.2 0.01 1.95 4.60 1.09 1.21 0.0046028 0.2 0.01 1.95 4.41 1.09 1.20 0.004513
8.5 0.2 0.01 1.95 4.26 1.09 1.19 0.0044369 0.2 0.01 1.95 4.13 1.09 1.19 0.004368
9.5 0.2 0.01 1.95 4.01 1.09 1.19 0.00430910 0.2 0.01 1.95 3.91 1.09 1.18 0.004256
0.00
2.00
4.00
6.00
8.00
10.00
0 2 4 6 8 10
RRCDO
RE
C
ARR=1.95
ARR=1.09
21
Example:
Psaty et al: JAGS 1999;47:749
CCB use and acute MI.
The issue:
Are there any unmeasured factors that may lead to a preferred prescribing of CCB to people at higher risk for AMI?
OREC
RRCO
ARR = 1.57
ARR = 1.30
22
3. Rule Out Residual ConfoundingHow strong does an unmeasured confounder have to be to fully explain the observed findings?
The relationship between OREC and RRCD for a given ARR, RRC, PC, PE.
Data from Psaty et al.: Assessment and control for confounding by indication in observational studies. J Am Geriatri Soc 1999;47:749-54.a(prim)
RRCD PC PE ARR=1.57 OREC ARR=1.3 OREC
1.2 0.2 0.01 1.57 1.3 0.0311771.5 0.2 0.01 1.57 1.3 23.90 0.0143442 0.2 0.01 1.57 28.79 1.3 5.11 0.008733
2.5 0.2 0.01 1.57 9.03 1.3 3.42 0.0068633 0.2 0.01 1.57 5.97 1.3 2.78 0.005928
3.5 0.2 0.01 1.57 4.73 1.3 2.45 0.0053674 0.2 0.01 1.57 4.06 1.3 2.25 0.004993
4.5 0.2 0.01 1.57 3.65 1.3 2.12 0.0047255 0.2 0.01 1.57 3.36 1.3 2.02 0.004525
5.5 0.2 0.01 1.57 3.15 1.3 1.94 0.0043696 0.2 0.01 1.57 2.99 1.3 1.88 0.004244
6.5 0.2 0.01 1.57 2.87 1.3 1.84 0.0041427 0.2 0.01 1.57 2.77 1.3 1.80 0.004057
7.5 0.2 0.01 1.57 2.68 1.3 1.77 0.0039858 0.2 0.01 1.57 2.61 1.3 1.74 0.003924
8.5 0.2 0.01 1.57 2.56 1.3 1.71 0.003879 0.2 0.01 1.57 2.51 1.3 1.69 0.003824
9.5 0.2 0.01 1.57 2.46 1.3 1.68 0.00378210 0.2 0.01 1.57 2.42 1.3 1.66 0.003746
0.00
2.00
4.00
6.00
8.00
10.00
0 2 4 6 8 10
RRCD
OR
EC
ARR=1.57
ARR=1.3
23
Caution!
Psaty et al. concluded that it is unlikely that an unmeasured confounder of that magnitude exists
However, the randomized trial ALLHAT showed no association between CCB use and AMI
Alternative explanations: Joint residual confounding may be larger than
anticipated from individual unmeasured confounders Not an issue of residual confounding but other biases,
e.g. control selection?
24
Pros and cons of “Rule Out Approach”
Very easy to perform using Excel Meaningful and easy to communicate
interpretationStudy-specific interpretationProblems:Still assuming conditional independence of CU
and CM “Rule Out” lacks any quantitative assessment
of potential confounders that are unmeasured
25
External Adjustment
One step beyond sensitivity analysesUsing additional information not available in
the main studyOften survey information
26
Strategies to Adjust residual con-founding using external information
Survey information in a representative sample can be used to quantify the imbalance of risk factors that are not measured in claims among exposure groups
The association of such risk factors with the outcome can be assess from the medical literature (RCTs, observational studies)
Velentgas et al: PDS, under review
Schneeweiss et al: Epidemiology, in press 2004
27
How do we do that?
We want to express ARR as a function of , , ARR, PC, PE
ORECRRCO
Walker AM: Observation an Inference. Epidemiology Resources Inc., Newton, 1991
28
])][Pr()[Pr(
])Pr()Pr(1[
eEeC
eECeOR CE
( 1 )
)Pr(
)Pr(1
1)Pr(]1][)[Pr(
)Pr(]1[
E
E
ERReC
ERReARR
CD
CDED
( 2 )
I f t h e p r i m a r y i n t e r e s t i s t o e s t i m a t e A R R E D a s a f u n c t i o n o f O R C E , R R C D , a n d t h e m a r g i n a l p r o b a b i l i t i e s
P r ( E ) a n d P r ( C ) t h e n w e n e e d t o s o l v e e q u a t i o n ( 1 ) f o r e ,
0)Pr()Pr(]1)Pr()Pr()Pr()Pr([)1(2 EORCCEOREORCeORe CECECECE
a b c
a n d e c a n b e f o u n d a s t h e s o l u t i o n o f a q u a d r a t i c e q u a t i o n o f t h e f o r m
a
acbbe
2
42
w h i c h w i l l t h e n b e s u b s t i t u t e d f o r e i n e q u a t i o n 2 .
29
Example: COX-2 inhibitors use and MI
Ray et al., Lancet 2002: >25mg roficoxib vs. non NSAID users, RR=1.9 (1.1-
3.4) Medicaid patients, new users
Solomon et al., Circulation in press: >25mg roficoxib vs. non NSAID users, RR=1.6 (1.04-
2.4) Medicare patients with drug coverage through PACE
Can these associations be due to confounding by factors not measured in claims data? e.g. BMI, OTC aspirin use, smoking, education etc.
30
In our example:
Rofecoxib Acute MI
RREO
From Survey data in a
subsampleFrom medical
literature
OREC RRCO
[smoking,aspirin, BMI, etc.]
CU
CM
31
Where can we get detailed information on unmeasured confounders?
MCBS: Medicare Current Beneficiary Survey Representative Sample 12,000 Medicare beneficiaries each year (majority
> 65y) Face-to-face interview in beneficiary’s home ‘Cost and Use’ file include drug utilization 98% response rate >95% data completeness Low cost ($900 / year) Readily available, but 2-year lag time)
32
Unobserved confounders in our example
Independent predictors of MI: Aspirin use Smoking BMI Educational attainment Income status
Expl. 2: Independent predictors of hip fracturs: Cognitive impairment Physical impairment Restrictions in ADL (Rubinstein L)
33
Our survey population
1999 MCBSRestricted to >64 yearsRestricted to community sample (no proxi
interviews)N = 8,785
34
Distribution of unmeasured confounders among drug users
Any COX-2 Inhibitors Any non-selective NSAIDs Non-users
(N=872) (N=1,302) (N=6,611) N % N % N %
Gender Female 607 69.6 777 59.7 3746 56.7 Male 265 30.4 525 40.3 2865 43.3 Age 65 to 74 436 50.0 731 56.1 3335 50.5 75 and older 436 50.0 571 43.9 3276 49.6 BMI Not Obese (BMI<30) 662 75.9 982 75.4 6484 83.0 Obese (BMI30) 206 23.6 315 24.2 1096 16.6 Aspirin Aspirin Use 80 9.2 133 10.2 614 9.3 No Aspirin Use 792 90.8 1169 89.8 5997 90.7 Smoking status Current 71 8.1 127 9.8 669 10.1 Former 396 45.4 661 50.8 3278 49.6 Never 405 46.4 514 39.5 2663 40.3 Education High school or less 603 69.2 937 72.0 4566 69.1 College or more 266 30.5 357 27.4 1976 29.9 Income $20,000 415 47.6 730 56.1 3507 53.1 > $20,000 457 52.4 572 43.9 3104 47.0
35
Celecoxib vs. Rofecoxib users … Celecoxib only Rofecoxib only (N=562) (N=244) N % N %
Gender Female 381 67.8 175 71.7 Male 181 32.2 69 28.3 Age 65 to 74 289 51.4 119 48.8 75 and older 273 48.6 125 51.2 BMI Not obese (BMI<30) 423 75.3 197 80.7 Obese (BMI30) 136 24.2 47 19.3 Aspirin Aspirin Use 46 8.2 28 11.5 No Aspirin Use 516 91.8 216 88.5 Smoking status Current 49 8.7 17 7.0 Former 254 45.2 120 49.2 Never 259 46.1 107 43.9 Education High school or less 388 69.0 161 66.0 College or more 174 31.0 80 32.8 Income $20,000 260 46.3 116 47.5 > $20,000 302 53.7 128 52.5
36
Literature estimates of RRCO
Adjustment of primary
estimate Potential confounder Relative
risk Age-sex adjusted
Multivariate adjusted
Obesity (BMI30) 1.7 a) yes
Aspirin use (non-use vs. use) 0.7 b) yes
Smoking (current vs. never) 3.1 c) yes
Educational attainment ( high school vs. >high school)
2.1 d) yes
Income ($20,000 vs. >$20,000) 2.1 e) yes
* In case of conflicting literature estimates the more extreme estimate was used. This will potentially lead to an overestimation of the magnitude of bias.
37
Calculating bias
Cox-2 inhibitor use vs. non-selective NSAID use and myocardial infarction.
RRCD p(C)
Adjusted OREC**
True RRED p(E)
Apparent RRED
† % Bias†† Data source: Literature MCBS MCBS assumed MCBS
Potential confounder:*
Obesity (BMI30 vs. BMI<30)
1.7 0.24 0.99 1.00 0.40 0.99 -0.11
Aspirin use (use vs. non-use)
0.7 0.10 0.90 1.00 0.40 1.00 0.29
Smoking (current vs. never)
3.1 0.09 0.87 1.00 0.40 0.98 -1.97
Educational Attainment ( high school vs. >high school)
2.1 0.71 0.83 1.00 0.40 0.98 -2.36
Income status ($20,000 vs. >$20,000)
2.1 0.53 0.92 1.00 0.40 0.99 -1.44
38
More contrasts
% Bias††
COX-2 (872) vs.
non-selective NSAIDs (1,302)
COX-2 (872) vs.
non-users (6,611)
COX-2 (872) vs.
naproxen (238)
Rofecoxib (244) vs.
naproxen (238) Potential confounder:*
Obesity (BMI30 vs. BMI<30)
-0.11 4.31 2.42 0.01
Aspirin use (use vs. non-use)
0.29 -0.08 -0.34 -1.28
Smoking (current vs. never)
-1.97 -2.41 -2.36 -0.61
Educational Attainment ( high school vs. >high school)
-2.36 -1.13 -3.67 -5.61
Income status ($20,000 vs. >$20,000)
-1.44 -1.08 -1.47 -1.65
Net confounding:
Sum of all negative biases: -5.88 -4.69 -5.08 -9.15
Weighted average: -1.56 -0.54 -1.86 -3.15
Sum of all positive biases: 0.29 4.31 -0.34 0.01
39
What does it mean?
Ray et al.: RR of 1.9 is an underestimation of the unconfounded RR by 5% (max) So the effect estimate corrected for 5 unobserved
confounders would be about 2.0
Solomon et al.: RR of 1.6 would move to 1.7
40
Sensitivity of Bias as a Function of a Misspecified RRCD :
-20
-15
-10
-5
0
5
10
15
20
1 1.5 2 2.5 3 3.5 4 4.5RRCD
Bia
s o
f R
RE
D i
n %
COX-2 vs. non-selective NSAIDsCOX-2 vs. non-usersCOX-2 vs. naproxenRofecoxib vs. naproxen
Literature estimate
RRCD = 1.7
Obesity (BMI >=30 vs. BMI<30)
41
Sensitivity towards a misspecified RRCO from the literature:OTC aspirin use (y/n)
-20
-15
-10
-5
0
5
10
15
20
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
RRCD
Bia
s o
f R
RE
D i
n %
COX-2 vs. non-selective NSAIDsCOX-2 vs. non-usersCOX-2 vs. naproxenRofecoxib vs. naproxen
Literature estimate
RRCD = 0.7
42
4. External AdjustmentGiven external information for selected factors on OREC from survey data and RRCD from the literature,
how much confounding is caused by not controling for these factors?
Data from Schneeweiss et al.: Assessment of bias by unmeasured confoundersin pharmacoepidemiologic claims data studies using external information. Epidemiology 2004, in press.
Unmeasured covariate: Aspirin (use vs. non-use) Bias as a function of misspecification of the RRCD from the literature:Data source: Lit MCBS MCBS assumed MCBSParameter: RRCD p(C) OREC true RRED p(E) app RRED CRR % biasSensitivity: varry const const const const calc calc
COX vs. 0.1 0.1 0.9 1 0.4 1.0093282 1.009 0.933
NSAID 0.2 0.1 0.9 1 0.4 1.0081979 1.008 0.820
0.3 0.1 0.9 1 0.4 1.0070929 1.007 0.709
0.4 0.1 0.9 1 0.4 1.0060124 1.006 0.601
0.5 0.1 0.9 1 0.4 1.0049555 1.005 0.496
0.6 0.1 0.9 1 0.4 1.0039215 1.004 0.392
0.7 0.1 0.9 1 0.4 1.0029096 1.003 0.291
0.8 0.1 0.9 1 0.4 1.0019192 1.002 0.192
0.9 0.1 0.9 1 0.4 1.0009495 1.001 0.095
1 0.1 0.9 1 0.4 1 1.000 0.000COX vs. 0.1 0.09 1.03 1 0.12 0.997608 0.998 -0.239
non-user 0.2 0.09 1.03 1 0.12 0.9978943 0.998 -0.211
0.3 0.09 1.03 1 0.12 0.9981752 0.998 -0.182
0.4 0.09 1.03 1 0.12 0.9984507 0.998 -0.155
0.5 0.09 1.03 1 0.12 0.998721 0.999 -0.128
0.6 0.09 1.03 1 0.12 0.9989863 0.999 -0.101
0.7 0.09 1.03 1 0.12 0.9992468 0.999 -0.075
0.8 0.09 1.03 1 0.12 0.9995024 1.000 -0.050
0.9 0.09 1.03 1 0.12 0.9997535 1.000 -0.025
1 0.09 1.03 1 0.12 1 1.000 0.000COX vs. 0.1 0.09 1.15 1 0.79 0.9892571 0.989 -1.074
naproxen 0.2 0.09 1.15 1 0.79 0.9905337 0.991 -0.947
0.3 0.09 1.15 1 0.79 0.9917884 0.992 -0.821
0.4 0.09 1.15 1 0.79 0.9930216 0.993 -0.698
0.5 0.09 1.15 1 0.79 0.9942339 0.994 -0.577
0.6 0.09 1.15 1 0.79 0.9954259 0.995 -0.457
0.7 0.09 1.15 1 0.79 0.996598 0.997 -0.340
0.8 0.09 1.15 1 0.79 0.9977507 0.998 -0.225
0.9 0.09 1.15 1 0.79 0.9988846 0.999 -0.112
1 0.09 1.15 1 0.79 1 1.000 0.000Rofecox vs. 0.1 0.1 1.6 1 0.51 0.9597175 0.960 -4.028
naproxen 0.2 0.1 1.6 1 0.51 0.9644945 0.964 -3.551
0.3 0.1 1.6 1 0.51 0.9691917 0.969 -3.081
0.4 0.1 1.6 1 0.51 0.9738113 0.974 -2.619
0.5 0.1 1.6 1 0.51 0.9783551 0.978 -2.164
0.6 0.1 1.6 1 0.51 0.9828249 0.983 -1.718
0.7 0.1 1.6 1 0.51 0.9872227 0.987 -1.278
0.8 0.1 1.6 1 0.51 0.99155 0.992 -0.845
0.9 0.1 1.6 1 0.51 0.9958085 0.996 -0.419
1 0.1 1.6 1 0.51 1 1.000 0.000
Unmeasured covariate: BMI (obese vs. non-obese)Data source: Lit MCBS MCBS assumed MCBSParameter: RRCD p(C) OREC true RRED p(E) app RRED CRR % bias
-20
-10
0
10
20
1 2 3 4 5 6 7 8
R RCD
-20-15-10-505101520
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
R RCD
-20
-10
0
10
20
1 1.5 2 2.5 3 3.5 4 4.5
R RCD
-20
-10
0
10
20
1 1.5 2 2.5 3 3.5 4 4.5
R RCD
-20
-10
0
10
20
1 1.5 2 2.5 3 3.5 4 4.5
R RCD
-20
-10
0
10
20
0 1 2 3 4 5 6 7 8
R RCD
COX-2 vs. non-selective NSAIDs
COX-2 vs. non-users
COX-2 vs. naproxen
Rofecoxib vs. naproxen
-20
-15
-10
-5
0
5
10
15
20
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
RRCD
Bia
s o
f R
R ED i
n %
COX-2 vs. non-selective NSAIDsCOX-2 vs. non-users
COX-2 vs. naproxenRofecoxib vs. naproxen Literature estimate
RRCD = 0.7
43
Variance estimate of externally adjusted parameters
RR = ARR * F
Var (ARR) from main study
Var (F) from survey study and medical literature
Var (RR) = Var (ARR * F)
= ARR2 Var(F) + F2 Var(ARR)
44
Summary External Adjustment
This method provides a quantitative assessment of the effect of selected unobserved confounders
Easy to use (Excel program available from author)
MCBS is available from CMS for $900 per annual survey
Should be more frequently used in Pharmacoepi studies using claims data
45
Limitations (1)
Example is limited to 5 potential confounders No lab values, physical activity, blood pressure etc. What about the ‘unknow unknowns’?
We currently explore NHANES ’99/’00 Lab values, dietary suppl. (Ca2+), Drug data quality?
To assess the bias we assume an exposure–disease association of 1 (null hypothesis) The more the truth is away from the null the more bias in
our bias estimate However the less relevant unmeasured confounders
become
46
Limitations (2)
Validity depends on representativenes of sampling with regard to the unmeasured confounders
We could not consider the joint distribution of confounders
Limited to a binary world
47
Solving the Main Limitations
Need a method That addresses the joint distribution of several
unmeasured confounders That can handle binary, ordinal or normally distributed
unmeasured confounders Lin et al. (Biometrics 1998):
Can handle a single unmeasured covariate of any distribution
But can handle only 1 covariate Sturmer, Schneeweiss et al. (AJE 2005 in press):
Propensity Score Calibration can handle multiple unmeasured covariates of any distribution
Recommended