Journal of Probability and Statistics / 2012 / Article / Tab 1 / Research Article
Secondary Analysis under Cohort Sampling Designs Using Conditional Likelihood Table 1 Maximum likelihood estimates of the parameters
š¼
of the all-cause mortality model
š
š
(
š”
)
=
(
š¼
4
/
š¼
0
)
(
š”
/
š¼
0
)
š¼
4
ā
1
e
x
p
{
š¼
1
š
š
+
š¼
2
š
š
+
š¼
3
š
š
}
,
š½
of the BMI model
š
š
ā£
š
š
,
š
š
,
š½
ā¼
š
(
š½
0
+
š½
1
š
š
+
š½
2
š
š
,
š½
2
3
)
, and
š¾
, the population frequency of the simulated covariate (true value 0.25). Parameters of main interest are
š¼
2
and
š½
2
, which characterize the association between the simulated covariate and primary (all-cause mortality) and secondary (BMI) outcomes, respectively. The values are means and standard deviations over 1000 replications. SE stands for the standard errors of the maximum likelihood estimates.
š¼
3
š½
2
Lik.
ī
š¼
0
ī
š¼
1
ī
š¼
2
ī
š¼
3
S
D
(
ī
š¼
3
)
S
E
(
ī
š¼
3
)
ī
š¼
4
Ģ
š½
0
Ģ
š½
1
Ģ
š½
2
Ģ
š½
S
D
(
2
)
Ģ
š½
S
E
(
2
)
Ģ
š½
3
Ģ
š¾
0.0 0.0 Full 23.72 0.09
ā
0
.
0
1
ā
0
.
0
1
0.10 0.10 1.33 0.00
ā
0
.
0
8
0.01 0.22 0.22 4.10 0.25 Cond. 23.74 0.09
ā
0
.
0
1
0.00 0.10 0.10 1.33 0.00
ā
0
.
0
8
0.00 0.23 0.23 4.17 ā Weighted ā ā ā ā ā ā ā
ā
0
.
0
1
ā
0
.
0
8
0.03 0.30 0.30 4.10 ā 0.5 0.0 Full 26.30 0.09
ā
0
.
0
1
0.49 0.09 0.09 1.33 0.00
ā
0
.
0
8
0.01 0.22 0.21 4.10 0.25 Cond. 26.33 0.09
ā
0
.
0
1
0.50 0.09 0.09 1.33 0.00
ā
0
.
0
8
0.00 0.22 0.22 4.17 ā Weighted ā ā ā ā ā ā ā
ā
0
.
0
1
ā
0
.
0
8
0.03 0.30 0.30 4.10 ā 0.0 0.5 Full 23.73 0.09
ā
0
.
0
1
ā
0
.
0
1
0.10 0.10 1.33
ā
0
.
1
3
ā
0
.
0
8
0.53 0.25 0.23 4.09 0.25 Cond. 23.75 0.09
ā
0
.
0
1
0.00 0.10 0.10 1.33
ā
0
.
1
3
ā
0
.
0
8
0.52 0.24 0.23 4.17 ā Weighted ā ā ā ā ā ā ā
ā
0
.
1
3
ā
0
.
0
8
0.53 0.31 0.31 4.09 ā 0.5 0.5 Full 26.32 0.09
ā
0
.
0
2
0.49 0.09 0.09 1.33
ā
0
.
1
4
ā
0
.
0
8
0.55 0.23 0.22 4.09 0.25 Cond. 26.34 0.09
ā
0
.
0
1
0.50 0.09 0.09 1.33
ā
0
.
1
4
ā
0
.
0
8
0.54 0.22 0.22 4.17 ā Weighted ā ā ā ā ā ā ā
ā
0
.
1
4
ā
0
.
0
8
0.54 0.31 0.31 4.09 ā 1.0 0.0 Full 29.62 0.09
ā
0
.
0
1
0.99 0.09 0.09 1.35 0.00
ā
0
.
0
8
0.02 0.21 0.21 4.10 0.25 Cond. 29.64 0.09
ā
0
.
0
1
1.00 0.09 0.09 1.35 0.00
ā
0
.
0
8
0.01 0.22 0.21 4.17 ā Weighted ā ā ā ā ā ā ā
ā
0
.
0
1
ā
0
.
0
8
0.03 0.29 0.29 4.10 ā 0.0 1.0 Full 23.77 0.09
ā
0
.
0
1
0.00 0.10 0.10 1.33
ā
0
.
2
8
ā
0
.
0
8
1.11 0.26 0.23 4.07 0.25 Cond. 23.77 0.09
ā
0
.
0
1
0.00 0.10 0.10 1.33
ā
0
.
2
7
ā
0
.
0
8
1.06 0.24 0.23 4.15 ā Weighted ā ā ā ā ā ā ā
ā
0
.
2
6
ā
0
.
0
8
1.05 0.32 0.32 4.07 ā 1.0 1.0 Full 29.67 0.09
ā
0
.
0
3
1.00 0.09 0.09 1.35
ā
0
.
2
9
ā
0
.
0
8
1.14 0.24 0.22 4.07 0.25 Cond. 29.65 0.09
ā
0
.
0
2
1.00 0.09 0.09 1.35
ā
0
.
2
8
ā
0
.
0
8
1.08 0.22 0.21 4.14 ā Weighted ā ā ā ā ā ā ā
ā
0
.
2
7
ā
0
.
0
8
1.07 0.31 0.31 4.07 ā
