1 PH 240A: Chapter 14 Nicholas P. Jewell University of California Berkeley November 15, 2005.

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