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

2. 2 Logistic Regression: Assessment of Confounding

3. 3  Consider two risk factors for CHD incidence (eg. serum cholesterol, X 1, and body weight, X 2 )  Two models: 

4. 4 Coding for WCGS Variables

5. 5 WCGS: Fitted Logistic Regression Models (#) ModelParam.EstimateSDORp-valueMax. log lik. (1)a-2.4220.065<0.001-890.6 (2)abab -2.934 0.864 0.115 0.1402.373 <0.001 -870.2 (3)ab1b2b3b4ab1b2b3b4 -2.859 0.068 0.384 0.832 0.610 0.182 0.259 0.234 0.224 0.217 1.070 1.468 2.297 1.840 <0.001 0.793 0.101 <0.001 0.005 -879.9 (4)abab -2.839 0.180 0.132 0.046 1.198<0.001 -882.8 (5)abab -4.215 0.010 0.512 0.003 1.010<0.001 -884.5 (6)abab -2.651 0.208 0.096 0.058 1.232<0.001 -884.5

6. 6 WCGS: Fitted Logistic Regression Models (#) ModelParam.EstimateSDORp-valueMax. log lik. (7)abc1c2c3c4abc1c2c3c4 -3.330 0.843 0.059 0.355 0.798 0.561 0.204 0.141 0.261 0.235 0.225 0.218 2.324 1.061 1.426 2.220 1.752 <0.001 0.820 0.131 <0.001 0.010 -860.6 (8)abcabc -3.311 0.843 0.168 0.161 0.141 0.047 2.323 1.183 <0.001 -863.5 (9)abcabc -4.607 0.849 0.010 0.524 0.140 0.003 2.337 1.010 <0.001 0.001 -864.8 (10)abcabc -3.140 0.849 0.196 0.134 0.140 0.059 2.337 1.216 <0.001 0.001 -864.8

7. 7 Logistic Regression: Introducing Interaction

8. 8 Coding for Pancreatic Cancer Example

9. 9 Pancreatic Cancer: Fitted Logistic Regression Models (#) ModelParam.EstimateSDORp-valueMax. log lik. (1)a-661.9 (2)abab1.0120.2572.751<0.001 -652.8 (3)ab1b2b3ab1b2b3 0.910 1.108 1.091 0.268 0.278 0.284 2.484 3.029 2.978 0.001 <0.001 -651.8 (4)abab0.2340.0701.2630.001 -656.3

10. 10 Pancreatic Cancer: Fitted Logistic Regression Models (#) ModelParam.EstimateSDORp-valueMax. log lik. (5)abcabc 0.957 -0.406 0.258 0.133 2.603 0.667 <0.001 0.002 -648.1 (6)abcdabcd 0.984 -0.359 -0.050 0.388 0.501 0.520 2.676 0.698 0.951 0.011 0.474 0.923 -648.1

11. 11 Pancreatic Cancer: Fitted Logistic Regression Models (#) ModelParam.EstimateSDORp-valueMax. log lik. (7)ab1b2b3cab1b2b3c 0.867 1.073 0.990 -0.404 0.269 0.279 0.286 0.135 2.379 2.923 2.691 0.668 0.001 <0.001 0.001 0.003 -647.3 (8)ab1b2b3cd1d2d3ab1b2b3cd1d2d3 1.033 0.935 0.956 -0.359 -0.352 0.281 0.132 0.402 0.418 0.414 0.501 0.542 0.561 0.589 2.809 2.547 2.602 0.698 0.704 1.324 1.141 0.010 0.025 0.021 0.474 0.517 0.617 0.620 -645.1

12. 12 Pancreatic Cancer: Fitted Logistic Regression Models (#) ModelParam.EstimateSDORp-valueMax. log lik. (9)abcabc 0.206 -0.398 0.071 0.133 1.229 0.672 0.004 0.003 -651.8 (10)abcdabcd 0.097 -0.809 0.254 0.093 0.269 0.143 1.102 0.445 1.289 0.297 0.003 0.076 -650.2

13. 13 Pancreatic Cancer: Fitted Logistic Regression Models

14. 14 Coding for WCGS Variables

15. 15 WCGS: Fitted Logistic Regression Models (#) ModelParam.EstimateSDORp-valueMax. log lik. (7)abc1c2c3c4abc1c2c3c4 -3.330 0.843 0.059 0.355 0.798 0.561 0.204 0.141 0.261 0.235 0.225 0.218 2.324 1.061 1.426 2.220 1.752 <0.001 0.820 0.131 <0.001 0.010 -860.6 (8)abcabc -3.311 0.843 0.168 0.161 0.141 0.047 2.323 1.183 <0.001 -863.5 (9)abcabc -4.607 0.849 0.010 0.524 0.140 0.003 2.337 1.010 <0.001 0.001 -864.8 (10)abcabc -3.140 0.849 0.196 0.134 0.140 0.059 2.337 1.216 <0.001 0.001 -864.8

16. 16 WCGS: Fitted Logistic Regression Models (#) ModelParam.EstimateSDORp-valueMax. log lik. (11)abc1c2c3c4d1d2d3d4abc1c2c3c4d1d2d3d4 -3.418 0.975 0.122 0.769 0.829 0.473 -0.095 -0.653 -0.050 0.112 0.321 0.391 0.455 0.393 0.400 0.398 0.555 0.491 0.484 0.477 2.652 1.130 2.157 2.291 1.605 0.910 0.521 0.952 1.118 <0.001 0.013 0.789 0.050 0.038 0.235 0.865 0.184 0.928 0.815 -858.6

17. 17 WCGS: Fitted Logistic Regression Models (#) ModelParam.EstimateSDORp-valueMax. log lik. (12)abc1c2c3c4dabc1c2c3c4d -3.237 0.697 0.022 0.279 0.680 0.399 0.061 0.252 0.282 0.267 0.266 0.297 0.346 0.102 2.007 1.022 1.321 1.974 1.491 1.063 <0.001 0.013 0.935 0.295 0.022 0.248 0.550 -860.4 (13)abcdabcd -3.226 0.714 0.133 0.054 0.220 0.275 0.081 0.099 2.042 1.142 1.055 <0.001 0.010 0.100 0.588 -863.4

18. 18 WCGS: Fitted Logistic Regression Models (#) ModelParam.EstimateSDORp-valueMax. log lik. (14)abcdabcd -4.999 1.440 0.012 -0.003 0.884 1.088 0.005 0.006 4.220 1.012 0.997 <0.001 0.186 0.017 0.583 -864.7 (15)abcdabcd -3.193 0.930 0.241 -0.068 0.168 0.205 0.101 0.124 2.534 1.272 0.934 <0.001 0.017 0.583 -864.7 collinearity

19. 19 CHD Incidence Versus Body Weight

20. 20 WCGS: Fitted Logistic Regression Models (#) ModelParam.EstimateSDORp-valueMax. log lik. (5)abab -4.215 0.010 0.512 0.003 1.010<0.001 -884.5 (6)abab -2.651 0.208 0.096 0.058 1.232<0.001 -884.5 Background: quadratic models & collinearity

21. 21 WCGS: Fitted Logistic Regression Models (#) ModelParam.EstimateSDORp-valueMax. log lik. (16)abcabc -6.302 0.034 -0.00006 2.507 0.028 0.00008 1.034 1.000 0.012 0.222 0.398 -884.1 (17)abcabc -2.683 0.291 -0.025 0.105 0.113 0.030 1.338 0.975 <0.001 0.010 0.398 -884.1 (18)abab -2.442 0.208 0.066 0.0581.232 <0.001 -884.5 (19)abcabc -2.417 0.240 -0.025 0.072 0.070 0.030 1.272 0.975 <0.001 0.001 0.398 -884.1 quadratic models & collinearity