Relation of pooled logistic regression to time dependent Cox regression analysis

Question

I found on this paper (D'Agostino, et al. 1990) that pooled logistic regression is close to the time dependent covariate Cox regression analysis.

I would like to be able to reproduce estimates obtained from a pooled logistic model with those from a time dependent Cox regression analysis.

My data looks like this :

A

id age female time0 time1 death

1 1 20 0 0 1 1

2 2 21 1 0 1 0

3 2 21 1 1 2 0

4 3 19 0 0 1 0

5 3 19 0 1 2 1

6 4 22 1 0 1 0

7 4 22 1 1 2 0

8 4 22 1 2 3 1

9 5 20 0 0 1 0

10 5 20 0 1 2 0

11 5 20 0 2 3 0

12 5 20 0 3 4 0

13 6 24 1 0 1 0

14 6 24 1 1 2 0

15 6 24 1 2 3 0

16 6 24 1 3 4 1

I tried to fit these 2 models :

glm(death~ age + female, data= A, family=binomial)
coxph(Surv(time0,time1, death) ~ age + female, A)

Estimates of the 1st model are :

Estimate Std. Error z value Pr(>|z|)

(Intercept) -2.65425 12.06138 -0.220 0.826

age 0.08814 0.61009 0.144 0.885

female -0.59971 2.17734 -0.275 0.783

Estimates of the 2nd model are :

    coef exp(coef) se(coef)     z    p

age -0.140 0.869 0.622 -0.23 0.82

female 0.156 1.168 2.121 0.07 0.94

I dont understand why I get very different estimates with the 2 models (I also had the same problem with different datasets). Do you have any idea ?