Modeling Multiple Source Risk
Factor Data and Health
Outcomes in Twins
Andy Bogart, MS
Jack Goldberg, PhD
Multiple Informant Data
Military Service in
Vietnam
id
pairid
PTSD
self report
military rec.
1
2
3
4
1
1
2
2
45
17
66
58
yes
yes
no
yes
no
yes
yes
yes
Vietnam service by self report and military record
Self Report
Yes
No
Yes
6,322
450
6,772
No
221
3,706
3,927
6,543
4,156
10,699
Military
Record
Kappa=0.87
Table 1: Participant Characteristics
Characteristic
Age in 2007, mean (sd)
All Veterans
Veterans
serving in
Vietnam
n=10,809
n=4,377
58 (3.1)
59 (2.5)
Zygosity, %
monozygotic
dizygotic
indeterminate
52
45
2
51
47
2
Military branch, %
Army
Navy
Air Force
Marines
Coast Guard
51
23
18
7
0.5
49
27
15
9
0.1
Table 1: Participant Characteristics
Characteristic
All Veterans
Veterans
serving in
Vietnam
n=10,809
n=4,377
Post traumatic stress
disorder score, %
15 - 17
18 - 23
24 - 31
32 - 75
22
27
26
25
16
23
25
36
Vietnam Service, %
self report
military record
39
37
95
90
Command
regress ptsd sr, robust
Self Report
sr | .1793066
Linear regression
.0070909
Number of obs =
10796
F( 1, 10794) = 639.43
Prob > F
= 0.0000
R-squared
= 0.0599
Root MSE
= .34613
-----------------------------------------------------------------------------|
Robust
ptsd |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------sr |
.1793066
.0070909
25.29
0.000
.1654071
.193206
_cons |
3.130085
.0039722
788.00
0.000
3.122299
3.137871
------------------------------------------------------------------------------
Command
regress ptsd mr, robust
Self Report
sr | .1793066
Linear regression
.0070909
Military Record
mr |
.152672
.0072727
Number of obs =
10712
F( 1, 10710) = 440.68
Prob > F
= 0.0000
R-squared
= 0.0423
Root MSE
= .34992
-----------------------------------------------------------------------------|
Robust
ptsd |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------mr |
.152672
.0072727
20.99
0.000
.138416
.1669279
_cons |
3.144166
.0040245
781.26
0.000
3.136277
3.152054
------------------------------------------------------------------------------
Model 1: The General Multiple Source Model
expected
Generates same estimates as the k marginal source-specific models
outcome
       
k 1
*
ij
gE Y
0
m1
intercept
m1
m ij
source
indicators
Allows testing for a difference in sources
H 0 :  1   2  ...   k
s
k
  z
m1
m
m ij
source by
exposure
interaction
terms
Multiple Informant Data
id
pairid
PTSD
self report
military rec.
1
2
3
4
1
1
2
2
45
17
66
58
yes
yes
no
yes
no
yes
yes
yes
Command
expand 2
id
pairid
PTSD
sr
mr
1
1
2
2
3
2
4
1
1
1
2
1
2
45
45
17
17
66
17
58
1
1
1
0
1
0
0
1
1
1
3
2
66
0
1
3
2
66
0
1
4
4
2
2
58
58
1
1
1
1
Command
expand 2
id
pairid
PTSD
sr
mr
1
1
2
2
1
1
1
1
45
45
17
17
1
1
1
1
0
0
1
1
3
2
66
0
1
3
2
66
0
1
4
4
2
2
58
58
1
1
1
1
Command
generate service=0
id
pairid
PTSD
sr
mr
service
1
1
2
2
1
1
1
1
45
45
17
17
1
1
1
1
0
0
1
1
0
0
0
0
3
2
66
0
1
0
3
2
66
0
1
4
4
2
2
58
58
1
1
1
1
0
0
0
Command
by id: replace service = sr if _n==1
id
pairid
PTSD
sr
mr
service
1
1
2
2
1
1
1
1
45
45
17
17
1
1
1
1
0
0
1
1
1
0
1
0
3
2
66
0
1
0
3
2
66
0
1
4
4
2
2
58
58
1
1
1
1
0
1
0
Command
by id: replace service = mr if _n==2
id
pairid
PTSD
sr
mr
service
1
1
2
2
1
1
1
1
45
45
17
17
1
1
1
1
0
0
1
1
1
0
1
1
0
3
2
66
0
1
0
3
2
66
0
1
4
4
2
2
58
58
1
1
1
1
1
0
1
1
0
Command
id
pairid
PTSD
service
1
1
2
2
1
1
1
1
45
45
17
17
1
0
1
1
3
2
66
0
3
2
66
4
4
2
2
58
58
1
1
1
Command
generate s1 = 0
generate s2 = 0
id
pairid
PTSD
service
s1
s2
1
1
2
1
1
1
45
45
17
1
0
1
0
0
0
0
0
0
2
1
17
1
0
0
3
2
66
0
0
0
3
2
66
1
0
0
4
4
2
2
58
58
1
1
0
0
0
0
Command
by id: replace s1 = 1 if _n==1
by id: replace s2 = 1 if _n==2
id
pairid
PTSD
service
s1
s2
1
1
2
1
1
1
45
45
17
1
0
1
1
0
1
0
1
0
2
1
17
1
0
1
3
2
66
0
1
0
3
2
66
1
0
1
4
4
2
2
58
58
1
1
1
0
0
1
Command
generate z1 = service * s1
generate z2 = service * s2
id
pairid
PTSD
service
s1
s2
z1
z2
1
1
2
1
1
1
45
45
17
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
2
1
17
1
0
1
0
1
3
2
66
0
1
0
0
0
3
2
66
1
0
1
0
1
4
4
2
2
58
58
1
1
1
0
0
1
1
0
0
1
Command
xtgee ptsd s1 z1 z2, i(pin) corr(ind) family(gau) robust
Self Report
sr | .1793066
.0070909
Iteration 1: tolerance = 7.894e-14
GEE population-averaged model
Group variable:
pin
Link:
identity
Family:
Gaussian
Correlation:
independent
Military Record
mr |
.152672
.0072727
Number of obs
=
21508
Number of groups
=
10809
Obs per group: min =
1
avg =
2.0
max =
2
Wald chi2(3)
=
640.25
Scale parameter:
.1210952
Prob > chi2
=
0.0000
Pearson chi2(21508):
2604.52
Deviance
=
2604.52
Dispersion (Pearson):
.1210952
Dispersion
= .1210952
(Std. Err. adjusted for clustering on pin)
-----------------------------------------------------------------------------|
Semi-robust
ptsd |
Coef.
Std. Err.
z
P>|z|
[95% Conf. Interval]
-------------+---------------------------------------------------------------s1 | -.0140807
.0016444
-8.56
0.000
-.0173037
-.0108576
z1 |
.1793066
.0070906
25.29
0.000
.1654093
.1932038
z2 |
.152672
.0072724
20.99
0.000
.1384183
.1669256
_cons |
3.144166
.0040243
781.30
0.000
3.136278
3.152053
------------------------------------------------------------------------------
But wait . . . these guys are twins!
Data within twin pairs might be correlated . . .
Summary of pair types for analysis
Vietnam Service
Analysis
Pair Types
Total Pairs = 6207
Contributing pairs
Complete pairs
4567
Half pairs
Two twins present, but only
one eligible
Only one eligible twin present
in data
172
1433
Non-contributing pairs
Neither twin eligible
35
Command
svyset id [pweight = sampweight], strata(pairid)
pweight:
VCE:
Strata 1:
SU 1:
FPC 1:
sampweight
linearized
pairid
id
<zero>
Command
svy: regress ptsd s1 z1 z2
Self Report
sr | .1793066
.0070909
Survey: Linear regression
Number of strata
=
6172
Number of PSUs
=
12344
Military Record
mr |
.152672
.0072727
Number of obs
=
24557
Population size
=
21508
Design df
=
6172
F(
3,
6170)
=
230.51
Prob > F
=
0.0000
R-squared
=
0.0511
-----------------------------------------------------------------------------|
Linearized
logptsd2 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------s1 | -.0140807
.001642
-8.58
0.000
-.0172995
-.0108619
z1 |
.1793066
.006818
26.30
0.000
.1659408
.1926723
z2 |
.152672
.0069024
22.12
0.000
.1391409
.166203
_cons |
3.144166
.0035541
884.66
0.000
3.137198
3.151133
-----------------------------------------------------------------------------Note: 35 strata omitted because they contain no population members
Command
test z1 = z2
Self Report
sr | .1793066
.00618
. test z1 = z2
Military Record
mr |
.152672
.0069024
Moral of the story:
.(test
1) z1 = z2 = 0
Adjusted Wald
chi2(
test1) =
Prob > chi2 =
( 1) z1 - z2 = 0
44.89
0.0000
chi2( 1) =
Prob > chi2 =
45.66
0.0000
The two sources contain
different information.
We should not combine them.
Or, should we??
Model 2: Multiple Source Model of Within- and
Between-pair exposure effects
Same estimates as k separate marginal within & between models
       
k 1
*
ij
gE Y
0
m1
m1
m ij
s

k

k
 
m
m
m



   m zij  zi    m zi
m1
m1
source
source by
source by
intercept
indicators
Allows testing for a difference
in reports ofwithin-pair
within effects & between
between-pair
effects
effect
effect

interaction
H 0  within pair : 1  2  ...  interaction
k
terms
terms



H 0 between pair :  1   2  ...   k
Command
id
pairid
s1
z1
1
1
2
1
1
1
1
0
1
1
0
1
2
1
0
0
Command
bysort pairid: egen z1bar = mean(z1) if s1==1
id
pairid
s1
z1
z1bar
1
1
2
1
1
1
1
0
1
1
0
1
1
.
1
2
1
0
0
.
Command
bysort pairid: egen z1bar = mean(z1) if s1==1
bysort pairid: replace z1bar=0 if s1==0
id
pairid
s1
z1
z1bar
1
1
2
1
1
1
1
0
1
1
0
1
1
0
1
2
1
0
0
0
Command
bysort pairid: egen z1bar = mean(z1) if s1==1
bysort pairid: replace z1bar=0 if s1==0
id
pairid
s1
z1
z1bar
3
2
1
0
0.5
3
2
0
0
0
4
4
2
2
1
0
1
0
0.5
0
Command
bysort pairid: egen z1bar = mean(z1) if s1==1
bysort pairid: replace z1bar=0 if s1==0
id
pairid
s1
z1
z1bar
1
1
2
1
1
1
1
0
1
1
0
1
1
0
1
2
1
0
0
0
3
2
1
0
0.5
3
2
0
0
0
4
4
2
2
1
0
1
0
0.5
0
Command
bysort pairid: egen z1bar = mean(z1) if s1==1
bysort pairid: replace z1bar=0 if s1==0
generate z1diff = z1 – z1bar
id
pairid
s1
z1
z1bar
z1diff
1
1
2
1
1
1
1
0
1
1
0
1
1
0
1
0
0
0
2
1
0
0
0
0
3
2
1
0
0.5
-0.5
3
2
0
0
0
0
4
4
2
2
1
0
1
0
0.5
0
0.5
0
Command
(Repeat that procedure to make z2bar and z2diff)
Command
svy: regress ptsd s1 z1diff z1bar z2diff z2bar
Survey: Linear regression
Number of strata
=
6172
Number of PSUs
=
12344
Number of obs
=
24557
Population size
=
21508
Design df
=
6172
F(
3,
5,
6170)
6168)
=
230.51
154.41
Prob > F
=
0.0000
R-squared
=
0.0511
0.0512
-----------------------------------------------------------------------------|
Linearized
logptsd2
ptsd |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------s1 | -.0182144
-.0140807
.0016726
.001642
-10.89
-8.58
0.000
-.0172995
-.0214933
-.0108619
-.0149355
z1diff
z1 |
.1669005
.1793066
.0134838
.006818
12.38
26.30
0.000
.1404675
.1659408
.1933335
.1926723
z1bar
z2 |
.1857651
.152672
.0074393
.0069024
24.97
22.12
0.000
.1711816
.1391409
.2003487
.166203
z2diff
_cons |
3.144166
.1618065
.0035541
.0138901
884.66
11.65
0.000
3.137198
.134577
3.151133
.189036
-----------------------------------------------------------------------------z2bar |
.1482027
.0074941
19.78
0.000
.1335116
.1628937
Note: 35
_cons
strata
| omitted
3.145802
because
.0037693
they contain
834.58no 0.000
population3.138413
members
3.153191
-----------------------------------------------------------------------------Note: 35 strata omitted because they contain no population members
Command
svy: regress ptsd s1 z1diff z1bar z2diff z2bar
Survey: Linear regression
Number of strata
=
6172
Number of PSUs
=
12344
Number of obs
=
24557
Population size
=
21508
Design df
=
6172
F(
3,
5,
6170)
6168)
=
230.51
154.41
Prob > F
=
0.0000
R-squared
=
0.0511
0.0512
-----------------------------------------------------------------------------|
Linearized
logptsd2
ptsd |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------s1 | -.0182144
-.0140807
.0016726
.001642
-10.89
-8.58
0.000
-.0172995
-.0214933
-.0108619
-.0149355
z1diff
z1 |
.1669005
.1793066
.0134838
.006818
12.38
26.30
0.000
.1404675
.1659408
.1933335
.1926723
z1bar
z2 |
.1857651
.152672
.0074393
.0069024
24.97
22.12
0.000
.1711816
.1391409
.2003487
.166203
z2diff
_cons |
3.144166
.1618065
.0035541
.0138901
884.66
11.65
0.000
3.137198
.134577
3.151133
.189036
-----------------------------------------------------------------------------z2bar |
.1482027
.0074941
19.78
0.000
.1335116
.1628937
Note: 35
_cons
strata
| omitted
3.145802
because
.0037693
they contain
834.58no 0.000
population3.138413
members
3.153191
-----------------------------------------------------------------------------Note: 35 strata omitted because they contain no population members
Command
svy: regress ptsd s1 z1diff z1bar z2diff z2bar
Survey: Linear regression
Number of strata
=
6172
Number of PSUs
=
12344
Number of obs
=
24557
Population size
=
21508
Design df
=
6172
F(
3,
5,
6170)
6168)
=
230.51
154.41
Prob > F
=
0.0000
R-squared
=
0.0511
0.0512
-----------------------------------------------------------------------------|
Linearized
logptsd2
ptsd |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------s1 | -.0182144
-.0140807
.0016726
.001642
-10.89
-8.58
0.000
-.0172995
-.0214933
-.0108619
-.0149355
z1diff
z1 |
.1669005
.1793066
.0134838
.006818
12.38
26.30
0.000
.1404675
.1659408
.1933335
.1926723
z1bar
z2 |
.1857651
.152672
.0074393
.0069024
24.97
22.12
0.000
.1711816
.1391409
.2003487
.166203
z2diff
_cons |
3.144166
.1618065
.0035541
.0138901
884.66
11.65
0.000
3.137198
.134577
3.151133
.189036
-----------------------------------------------------------------------------z2bar |
.1482027
.0074941
19.78
0.000
.1335116
.1628937
Note: 35
_cons
strata
| omitted
3.145802
because
.0037693
they contain
834.58no 0.000
population3.138413
members
3.153191
-----------------------------------------------------------------------------Note: 35 strata omitted because they contain no population members
Command
test z1diff = z2diff
AdjustedLinear
Survey:
Wald test
regression
Number of strata
=
6172
Number
( 1) z1diff
of PSUs- z2diff
=
= 0
12344
Number of obs
=
24557
Population size
=
21508
Design df
=
6172
F( 1, 6172) =
0.36
F(
3,
6170)
=
230.51
Prob > F =
0.5509
Prob > F
=
0.0000
R-squared
=
0.0511
-----------------------------------------------------------------------------|
Linearized
logptsd2 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------s1 | -.0182144
-.0140807
.0016726
.001642
-10.89
-8.58
0.000
-.0172995
-.0214933
-.0108619
-.0149355
z1diff
z1 |
.1669005
.1793066
.0134838
.006818
12.38
26.30
0.000
.1404675
.1659408
.1933335
.1926723
z1bar
z2 |
.1857651
.152672
.0074393
.0069024
24.97
22.12
0.000
.1711816
.1391409
.2003487
.166203
z2diff
_cons |
3.144166
.1618065
.0035541
.0138901
884.66
11.65
0.000
3.137198
.134577
3.151133
.189036
-----------------------------------------------------------------------------z2bar |
.1482027
.0074941
19.78
0.000
.1335116
.1628937
Note: 35
_cons
strata
| omitted
3.145802
because
.0037693
they contain
834.58no 0.000
population3.138413
members
3.153191
-----------------------------------------------------------------------------Note: 35 strata omitted because they contain no population members
Command
test z1diff = z2diff
test z1bar = z2bar
Adjusted Wald test
( 1)
z1diff - z2diff = 0
F(
1, 6172) =
Prob > F =
0.36
0.5509
Within-pair
Moral of theestimates
story:
don’t differ much
1. Combine the within-pair info.
|
Linearized
logptsd2 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------Adjusted
Wald test
s1 | -.0182144
.0016726
-10.89
0.000
-.0214933
-.0149355
( 1) z1diff
z1bar |
- z2bar
.1669005
= 0
.0134838
12.38
0.000
.1404675
.1933335
Between-pair
z1bar |
.1857651
.0074393
24.97
0.000
.1711816
.2003487
estimates
z2diff
F( 1,| 6172)
.1618065
=
83.66
.0138901
11.65
0.000
.134577
.189036
z2barProb
|
.1482027
> F =
0.0000
.0074941
19.78
0.000
.1335116
.1628937
do!!
_cons |
3.145802
.0037693
834.58
0.000
3.138413
3.153191
-----------------------------------------------------------------------------Note: 35 strata omitted because they contain no population members
2. Keep between-pair info. separate
Model 3: Multiple Source Model with a
Combined within-pair effect
Assumes within-pair effect to be common to all k sources
       
k 1
*
ij
gE Y
0
m1
m1
m ij
s

source
indicators
 
m
~



  zij  zi    m zi
combined
source
within-pair
effect
Often yields a more precise estimate
of the within-pair effect
intercept

k
m1
source by
between-pair
effect
interaction
terms
Command
id
pairid
z1diff
z2diff
1
1
2
1
1
1
0
0
0
0
-0.5
0
2
1
0
0.5
3
2
-0.5
0
3
2
0
0
4
4
2
2
0.5
0
0
0
Command
generate wservice = z1diff + z2diff
id
pairid
z1diff
z2diff
wservice
1
1
2
1
1
1
0
0
0
0
-0.5
0
0
-0.5
0
2
1
0
0.5
0.5
3
2
-0.5
0
-0.5
3
2
0
0
0
4
4
2
2
0.5
0
0
0
0.5
0
Command
svy: regress ptsd s1 wservice z1bar z2bar
Survey:
Survey: Linear
Linear regression
regression
Number
of
strata
=
6172
Number of strata
=
6172
Number
of
PSUs
=
12344
Number of PSUs
=
12344
Number
=
24557
Number of
of obs
obs
=
24557
Population
size
=
21508
Population size
=
21508
Design
df
=
6172
Design df
=
6172
F(
4,
6169)
=
192.48
F(
3,
6170)
=
230.51
Prob
>
F
=
0.0000
Prob > F
=
0.0000
R-squared
=
0.0512
R-squared
=
0.0511
----------------------------------------------------------------------------------------------------------------------------------------------------------|
Linearized
|
Linearized
logptsd2
|
Coef.
Std.
t
P>|t|
[95%
logptsd2 |
Coef.
Std. Err.
Err.
t
P>|t|
[95% Conf.
Conf. Interval]
Interval]
-------------+----------------------------------------------------------------------------+---------------------------------------------------------------s1
.0016722
-10.89
0.000
-.0214919
-.0149358
s1 |
| -.0182138
-.0140807
.001642
-8.58
0.000
-.0172995
-.0108619
wservice
|
.1644434
.0129988
12.65
0.000
.1389611
.1899256
z1 |
.1793066
.006818
26.30
0.000
.1659408
.1926723
z1bar
|
.1857654
.0074392
24.97
0.000
.1711819
.2003489
z2 |
.152672
.0069024
22.12
0.000
.1391409
.166203
z2bar
|
.1482022
.0074941
19.78
0.000
.1335111
.1628933
_cons |
3.144166
.0035541
884.66
0.000
3.137198
3.151133
_cons
|
3.145802
.0037693
834.59
0.000
3.138412
3.153191
----------------------------------------------------------------------------------------------------------------------------------------------------------Note: 35 strata omitted because they contain no population members
Note: 35 strata omitted because they contain no population members
Command
svy: regress ptsd s1 wservice z1bar z2bar
Survey:
Survey: Linear
Linear regression
regression
Number
of
strata
=
6172
Number of strata
=
6172
Number
of
PSUs
=
12344
Number of PSUs
=
12344
Number
=
24557
Number of
of obs
obs
=
24557
Population
size
=
21508
Population size
=
21508
Design
df
=
6172
Design df
=
6172
F(
4,
6169)
=
192.48
F(
3,
6170)
=
230.51
Prob
>
F
=
0.0000
Prob > F
=
0.0000
R-squared
=
0.0512
R-squared
=
0.0511
----------------------------------------------------------------------------------------------------------------------------------------------------------|
Linearized
|
Linearized
logptsd2
|
Coef.
Std.
t
P>|t|
[95%
logptsd2 |
Coef.
Std. Err.
Err.
t
P>|t|
[95% Conf.
Conf. Interval]
Interval]
-------------+----------------------------------------------------------------------------+---------------------------------------------------------------s1
.0016722
-10.89
0.000
-.0214919
-.0149358
s1 |
| -.0182138
-.0140807
.001642
-8.58
0.000
-.0172995
-.0108619
wservice
|
.1644434
.0129988
12.65
0.000
.1389611
.1899256
z1 |
.1793066
.006818
26.30
0.000
.1659408
.1926723
z1bar
|
.1857654
.0074392
24.97
0.000
.1711819
.2003489
z2 |
.152672
.0069024
22.12
0.000
.1391409
.166203
z2bar
|
.1482022
.0074941
19.78
0.000
.1335111
.1628933
_cons |
3.144166
.0035541
884.66
0.000
3.137198
3.151133
_cons
|
3.145802
.0037693
834.59
0.000
3.138412
3.153191
----------------------------------------------------------------------------------------------------------------------------------------------------------Note: 35 strata omitted because they contain no population members
Note: 35 strata omitted because they contain no population members
Survey regression results: PTSD regressed on multiple Vietnam
service reports
Model 1
̂
Estimates
Overall effects
Self-report
Military record

se ̂
Model 2
ˆ

se ̂
Model 3
ˆ

se ̂
0.1793 0.0068
0.15672 0.0069
Within-pair effects
Self-report
Military record
Combined report
0.1669 0.0135
0.1618 0.0139
0.1644 0.0130
Between-pair
effects
Self-report
Military record
Hypothesis Tests
H0:
βSR(overall)=βMR(overall)
H0: βSR(within)=βMR(within)
H0: βSR(between)=βMR(between)
0.1858 0.0074
0.1482 0.0075
<0.0001
0.55
<0.0001
0.1858 0.0074
0.1482 0.0075
Survey regression results: PTSD regressed on multiple Vietnam
service reports
Model 1
̂
Estimates
Overall effects
Self-report
Military record

se ̂
Model 2
ˆ

se ̂
Model 3
ˆ

se ̂
0.1793 0.0068
0.15672 0.0069
Within-pair effects
Self-report
Military record
Combined report
0.1669 0.0135
0.1618 0.0139
0.1644 0.0130
Between-pair
effects
Self-report
Military record
Hypothesis Tests
H0:
βSR(overall)=βMR(overall)
H0: βSR(within)=βMR(within)
H0: βSR(between)=βMR(between)
0.1858 0.0074
0.1482 0.0075
<0.0001
0.55
<0.0001
0.1858 0.0074
0.1482 0.0075
Conclusions from VET Registry analysis
Sources differed in Model 1, so we did not combine
them overall
Within-pair estimates in Model 2 did not differ
much by source, so . . . Model 3 combined within-pair
estimates
Within-pair estimate:
Combined Record
0.16 (0.14, 0.19)
7 – 14% gain in
efficiency over
individual sources
Conclusions from VET Registry analysis
Between-pair estimates in Model 2 differed
significantly
Model 3 estimates separate between-pair
effects for each source
Source-specific between-pair estimates:
Self Report
Military Record
0.19 (0.17, 0.20)
0.15 (0.13, 0.16)
Future Directions
Accommodate covariate adjustment
Compare pooled estimators to “AND” and “OR”
type derived exposure variables
Address zygosity within regression models
Acknowledgements & References
Jack Goldberg at UW
Margaret Pepe at UW
1. Pepe MS, Whitaker RC, Seidel K. Estimating and
comparing univariate associations with application
to the prediction of adult obesity. Statistics in
Medicine 1999; 18: 163-173.
Nicholas Horton at Harvard
2. Horton NJ, Fitzmaurice GM. Regression
analysis of multiple source and multiple
informant data from complex survey samples.
Statistics in Medicine 2004; 23:2911-2933.
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