1 ph 240a: chapter 14 nicholas p. jewell university of california berkeley november 15, 2005
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1
PH 240A: Chapter 14
Nicholas P. JewellUniversity of California Berkeley
November 15, 2005
2
Logistic Regression: Assessment of Confounding
21**
,
,
1
121
21
1
1
1log
1log
cxxbap
p
bxap
p
xxx
xx
x
x
3
Logistic Regression: Assessment of Confounding
Consider two risk factors for CHD incidence (eg. serum cholesterol, X1, and body weight, X2)
Two models:
21**
,
,
1
121
21
1
1
1log
1log
cxxbap
p
bxap
p
xxx
xx
x
x
*ˆ and ˆ Compare bb
4
Coding for WCGS Variables
behavior B Type 0
behaviorA Type 1X
lbs 180 wt4
lbs180wt1703
lbs170wt1602
lbs160wt1501
lbs150wt0
Z
otherwise0
lbs180wt1
otherwise0
lbs180wt1701
otherwise0
lbs170wt1601
otherwise0
lbs160wt1501
43
21
ZZ
ZZ
(lbs)t Body weighWt
20
150)-(WtNwt
20
170)-(WtMwt
5
WCGS: Fitted Logistic Regression Models
(#) Model Param.
Estimate
SD OR p-value Max. log lik.
(1) a -2.422 0.065
<0.001 -890.6
(2) ab
-2.9340.864
0.115
0.140
2.373<0.001<0.001 -870.2
(3) ab1
b2
b3
b4
-2.8590.0680.3840.8320.610
0.182
0.259
0.234
0.224
0.217
1.0701.4682.2971.840
<0.0010.7930.101
<0.0010.005 -879.9
(4) ab
-2.8390.180
0.132
0.046
1.198 <0.001<0.001 -882.8
(5) ab
-4.2150.010
0.512
0.003
1.010 <0.001<0.001 -884.5
(6) ab
-2.6510.208
0.096
0.058
1.232 <0.001<0.001 -884.5
app )1/log(
bxapp )1/log(
bzapp )1/log(
)()1/log( wtbapp
)()1/log( nwtbapp
44
11
)1/log(
zb
zbapp
6
WCGS: Fitted Logistic Regression Models
(#) Model Param.
Estimate
SD OR p-value Max. log lik.
(7) abc1
c2
c3
c4
-3.3300.8430.0590.3550.7980.561
0.204
0.141
0.261
0.235
0.225
0.218
2.3241.0611.4262.2201.752
<0.001<0.0010.8200.131
<0.0010.010 -860.6
(8) abc
-3.3110.8430.168
0.161
0.141
0.047
2.3231.183
<0.001<0.001<0.001 -863.5
(9) abc
-4.6070.8490.010
0.524
0.140
0.003
2.3371.010
<0.001<0.0010.001 -864.8
(10) abc
-3.1400.8490.196
0.134
0.140
0.059
2.3371.216
<0.001<0.0010.001 -864.8
czbxa
pp
)1/log(
)(
)1/log(
wtcbxa
pp
)(
)1/log(
nwtcbxa
pp
4411
)1/log(
zczcbxa
pp
7
Logistic Regression: Introducing Interaction
8
Coding for Pancreatic Cancer Example
cups/day) 0(abstainer Coffee 0
cups/day) 1(drinker Coffee 1X
cups/day 53
cups/day 432
cups/day 211
cups/day 00
Z
otherwise0
cups/day 51
otherwise0
cups/day 431
otherwise0
cups/day 211
3
21
Z
ZZ
Male 0
Female 1Y
9
Pancreatic Cancer: Fitted Logistic Regression Models
(#) Model Param.
Estimate
SD OR p-value Max. log lik.
(1) a -661.9
(2) ab 1.012 0.25
72.751 <0.001 -652.8
(3) ab1
b2
b3
0.9101.1081.091
0.268
0.278
0.284
2.4843.0292.978
0.001<0.001<0.001 -651.8
(4) ab 0.234 0.07
01.263 0.001 -656.3
app )1/log(
bxapp )1/log(
bzapp )1/log(
33
11
)1/log(
zb
zbapp
10
Pancreatic Cancer: Fitted Logistic Regression Models
(#) Model Param.
Estimate
SD OR p-value Max. log lik.
(5) abc
0.957-0.406
0.258
0.133
2.6030.667
<0.0010.002 -648.1
(6) abcd
0.984-0.359-0.050
0.388
0.501
0.520
2.6760.6980.951
0.0110.4740.923 -648.1
cybxa
pp
)1/log(
)(
)1/log(
yxdcybxa
pp
11
Pancreatic Cancer: Fitted Logistic Regression Models
(#) Model Param.
Estimate
SD OR p-value Max. log lik.
(7) ab1
b2
b3
c
0.8671.0730.990-0.404
0.269
0.279
0.286
0.135
2.3792.9232.6910.668
0.001<0.0010.0010.003 -647.3
(8) ab1
b2
b3
cd1
d2
d3
1.0330.9350.956-0.359-0.3520.2810.132
0.402
0.418
0.414
0.501
0.542
0.561
0.589
2.8092.5472.6020.6980.7041.3241.141
0.0100.0250.0210.4740.5170.6170.620
-645.1
)(
)(
)1/log(
33
11
332211
yzd
yzd
cyzbzbzba
pp
cyzbzbzba
pp
332211
)1/log(
12
Pancreatic Cancer: Fitted Logistic Regression Models
(#) Model Param.
Estimate
SD OR p-value Max. log lik.
(9) abc
0.206-0.398
0.071
0.133
1.2290.672
0.0040.003 -651.8
(10) abcd
0.097-0.8090.254
0.093
0.269
0.143
1.1020.4451.289
0.2970.0030.076 -650.2
cybza
pp
)1/log(
)(
)1/log(
yzdcybza
pp
13
Pancreatic Cancer: Fitted Logistic Regression Models
14
Coding for WCGS Variables
behavior B Type 0
behaviorA Type 1X
lbs 180 wt4
lbs180wt1703
lbs170wt1602
lbs160wt1501
lbs150wt0
Z
otherwise0
lbs180wt1
otherwise0
lbs180wt1701
otherwise0
lbs170wt1601
otherwise0
lbs160wt1501
43
21
ZZ
ZZ
(lbs)t Body weighWt
20
150)-(WtNwt
20
170)-(WtMwt
15
WCGS: Fitted Logistic Regression Models
(#) Model Param.
Estimate
SD OR p-value Max. log lik.
(7) abc1
c2
c3
c4
-3.3300.8430.0590.3550.7980.561
0.204
0.141
0.261
0.235
0.225
0.218
2.3241.0611.4262.2201.752
<0.001<0.0010.8200.131
<0.0010.010 -860.6
(8) abc
-3.3110.8430.168
0.161
0.141
0.047
2.3231.183
<0.001<0.001<0.001 -863.5
(9) abc
-4.6070.8490.010
0.524
0.140
0.003
2.3371.010
<0.001<0.0010.001 -864.8
(10) abc
-3.1400.8490.196
0.134
0.140
0.059
2.3371.216
<0.001<0.0010.001 -864.8
czbxa
pp
)1/log(
)(
)1/log(
wtcbxa
pp
)(
)1/log(
nwtcbxa
pp
4411
)1/log(
zczcbxa
pp
16
WCGS: Fitted Logistic Regression Models
(#) Model Param.
Estimate
SD OR p-value Max. log lik.
(11) abc1
c2
c3
c4
d1
d2
d3
d4
-3.4180.9750.1220.7690.8290.473-0.095-0.653-0.0500.112
0.321
0.391
0.455
0.393
0.400
0.398
0.555
0.491
0.484
0.477
2.6521.1302.1572.2911.6050.9100.5210.9521.118
<0.0010.0130.7890.0500.0380.2350.8650.1840.9280.815 -858.6
)()(
)1/log(
4411
4411
xzdxzd
zczcbxa
pp
17
WCGS: Fitted Logistic Regression Models
(#) Model Param.
Estimate
SD OR p-value Max. log lik.
(12) abc1
c2
c3
c4
d
-3.2370.6970.0220.2790.6800.3990.061
0.252
0.282
0.267
0.266
0.297
0.346
0.102
2.0071.0221.3211.9741.4911.063
<0.0010.0130.9350.2950.0220.2480.550 -860.4
(13) abcd
-3.2260.7140.1330.054
0.220
0.275
0.0810.099
2.0421.1421.055
<0.0010.0100.1000.588 -863.4
)(
)1/log(
xzdczbxa
pp
)(
)1/log(
4411
xzd
zczcbxa
pp
18
WCGS: Fitted Logistic Regression Models
(#) Model Param.
Estimate
SD OR p-value Max. log lik.
(14) abcd
-4.9991.4400.012-0.003
0.884
1.088
0.005
0.006
4.2201.0120.997
<0.0010.1860.0170.583 -864.7
(15) abcd
-3.1930.9300.241-0.068
0.168
0.205
0.1010.124
2.5341.2720.934
<0.001<0.0010.0170.583 -864.7
)()(
)1/log(
wtxdwtcbxa
pp
)()(
)1/log(
nwtxdnwtcbxa
pp
collinearity
19
CHD Incidence Versus Body Weight
20
WCGS: Fitted Logistic Regression Models
(#) Model Param.
Estimate
SD OR p-value Max. log lik.
(5) ab
-4.2150.010
0.512
0.003
1.010 <0.001<0.001 -884.5
(6) ab
-2.6510.208
0.096
0.058
1.232 <0.001<0.001 -884.5
)()1/log( wtbapp
)()1/log( nwtbapp
Background: quadratic models & collinearity
21
WCGS: Fitted Logistic Regression Models
(#) Model Param.
Estimate SD OR p-value
Max. log lik.
(16) abc
-6.3020.034
-0.00006
2.5070.028
0.00008
1.0341.000
0.0120.2220.398
-884.1
(17) abc
-2.6830.291-0.025
0.1050.1130.030
1.3380.975
<0.001
0.0100.398
-884.1
(18) ab
-2.4420.208
0.0660.058 1.232
<0.001
<0.001
-884.5
(19) abc
-2.4170.240-0.025
0.0720.0700.030
1.2720.975
<0.001
0.0010.398
-884.1
)(
)1/log(
mwtba
pp
2)()(
)1/log(
wtcwtba
pp
2)()(
)1/log(
nwtcnwtba
pp
quadratic models & collinearity
2)()(
)1/log(
mwtcmwtba
pp