The data is from the Los Angeles Endometrial Cancer Study (Breslow and Day, vol I), a matched case-contol study of the effect of exogenous estrogens on the risk of endometrial cancer among women in a retirement community. The example makes use of 63 case-control pairs consisting of the case and first control from each matched set in the data set.
Goal of this analysis:
To reproduce some of the analyses described in Section 7.3 of Breslow
and Day (1980). The data is in free format in the file leimod.dat
It contains the following variables: setno-set number; cases
-case\control indicator; gall - gall bladder disease; est
- estrogen; cdose - dose of estrogen; dur - duration in months.
PECAN Version 2.0 July 1996
NAMES setno cases gall hyp ob est dose dur non
dura age cdose @
INPUT leimod.dat @
Input frex\leimod.dat
315 records read 315 records used
0 records rejected
Workspace for 300 variables. 14 are currently
defined.
Up to 286 new variables can be created
63 useable case/control sets with 315 records
The missing command recodes missing vales for dose, ob, and dura to
the EPICURE missing value code. Cases and cdose are categorical
variables. A new 3 level categorical variable is created.
MISS ob 9; cdose 9 @
LEVELS cases cdose @
TRAN ageg = (age >= 65) + (age
>= 75) @
LEVELS ageg @
CASES has 2 levels from 0 to 1
CDOSE has 4 levels from 0 to 3
AGEG has 3 levels from 0 to 2
Compute summary statistics.
MEAN est ; by cases @
MEAN dur; by ageg@
FREQ cases cdose@
Summary for EST
CASES Mean Count Std.
Dev.
0 0.503968 252 0.50098
1 0.888889 63 0.31679
Summary for DUR
AGEG Mean Count Std.
Dev.
0 2.16667 60 2.7257
1 1.68208 173 2.1987
2 1.13415 82 1.9923
TABULATE FREQUENCY:
Entries: count
% of total
% of row
% of col
CDOSE
CASES | 0 1 2 3 | Total
--------+--------------------------------+--------
0 | 143 44 42 19
| 248
| 46.58 14.33 13.68 6.19 | 80.78
| 57.66 17.74 16.94 7.66 |
| 92.26 73.33 73.68 54.29 |
1 | 12 16 15 16
| 59
| 3.91 5.21 4.89 5.21 | 19.22
| 20.34 27.12 25.42 27.12 |
| 7.74 26.67 26.32 45.71 |
--------+--------------------------------+--------
Total |
155 60 57 35
| 307
| 50.49 19.54 18.57 11.40 |
Fit a conditional logistic regression model for the odds ratio. Begin
with a model with no covariates. Define this as the initial null model:
FIT @
NULL @
Conditional-logistic
regression (1:M matching)
Product additive excess
model {T0*(1 + T1 + T2 + ...)}
CASES is used for cases
SETNO is used to define
sets
Deviance = 202.789 Free
parameters = 0
Number of risk sets
= 63
NULL @
Fit a multiplicative model with estrogen exposure status and gall bladder
disease effects. The odds ratio model can be written as:
FIT gall est @
FIT est gall @ LRT
Iter Step Deviance
0 0 202.7892
1 0 160.0688
2 0 157.7848
3 0 157.7426
4 0 157.7426
Conditional-logistic regression (1:M matching)
Product additive excess model {T0*(1 + T1
+ T2 + ...)}
CASES is used for cases
SETNO is used to define sets
Parameter Summary Table
# Name Estimate Std.Err. Test Stat. P value
-- ----------------------- ------------ ----------
----------- -------
Log-linear term 0
1 GALL .................... 1.275
0.4109 3.102
0.002
2 EST ..................... 2.115
0.4398 4.809 <
0.001
Records used = 315
Deviance = 157.743 Free parameters = 2
Number of risk sets = 63
Non-informative risk sets = 4
LR statistic = 45.05 df = 2
P = 0.0000
Compute the Wald and Likelihood based confidence bounds:
CI@
BOUND 1 @
BOUND 2 @
95% Confidence Bounds
# Name
Estimate Std. Error Lower
Upper
-- ------------------------- -----------
----------- ----------- ---------
Log-linear term 0
1 GALL ....................
1.275 0.4109
0.4694 2.080
EXP(estimate)
3.577 1.508
1.599 8.004
2 EST .....................
2.115 0.4398
1.253 2.977
EXP(estimate)
8.288 1.552
3.500 19.62
BOUND 1 @
Likelihood bound for parameter 1 GALL
MLE 1.275 exp(MLE) 3.577
97.50% lower bound 0.47599
exp(bound) 1.6096
97.50% upper bound 2.1027
exp(bound) 8.1886
BOUND 2 @
Likelihood bound for parameter 2 EST
MLE 2.115 exp(MLE) 8.288
97.50% lower bound 1.3158
exp(bound) 3.7279
97.50% upper bound 3.0617
exp(bound) 21.365
Define the last model fit as the null model. Add a gallbladder disease
history by estrogen usage interaction. Fit this model and compute the likelihood
ratio test for the interaction term.
NULL
FIT + gall*est @ LRT
NULL @
FIT + gall*est @ LRT
Iter Step Deviance
0 0
157.7426
1 0
153.7168
2 0
153.4613
3 0
153.4612
Conditional-logistic regression (1:M matching)
Product additive excess model {T0*(1 + T1
+ T2 + ...)}
CASES is used for cases
SETNO is used to define sets
Parameter Summary Table
# Name
Estimate Std.Err. Test Stat. P value
-- ----------------------- ------------ ----------
----------- -------
Log-linear term 0
1 GALL ....................
2.894 0.8831
3.278 0.001
2 EST .....................
2.700 0.6118
4.414 < 0.001
3 GALL * EST ..............
-2.053 0.9950 -2.063
0.039
Records used = 315
Deviance = 153.461 Free parameters = 3
Number of risk sets = 63
Non-informative risk sets = 4
LR statistic = 4.281 df = 1
P = 0.0385
Clear the current model and then specify an alternative form for the
odds ratio. The new model is
NOMODEL @
LINE 1 est gall @
FIT @
Model has been reset
LINE 1 est gall @
FIT @
Iter Step Deviance
0 0
202.7892
1 0
170.3245
2 0
158.3328
3 0
154.4549
4 0
153.5711
5 0
153.4809
6 0
153.4792
7 0
153.4792
Conditional-logistic regression (1:M matching)
Product additive excess model {T0*(1 + T1
+ T2 + ...)}
CASES is used for cases
SETNO is used to define sets
Parameter Summary Table
# Name
Estimate Std.Err. Test Stat. P value
-- ----------------------- ------------ ----------
----------- -------
Linear term 1
1 EST .....................
13.95 9.139
1.526 0.127
2 GALL ....................
18.23 14.43
1.263 0.207
Records used = 315
Deviance = 153.479 Free parameters = 2
Number of risk sets = 63
Non-informative risk sets = 4
Again consider a model with gall bladder disease by estrogen usage status
interaction. Compute the likelihood ratio statsitistic for this model relative
to the last model fit. Also include a hypertension effect with its parameter
fixed at 0. This leads to a single degress of freedom score test for this
effect. The statistic, given in the score column, is the signed square
root of the usual chi-square statistic and can be interpreted as a normal
deviate.
NULL
LINE 1 + gall*est hyp=0 @
FIT @ LRT
Iter Step Deviance
0 0
153.4792
1 0
153.4612
2 0
153.4612
Conditional-logistic regression (1:M matching)
Product additive excess model {T0*(1 + T1
+ T2 + ...)}
CASES is used for cases
SETNO is used to define sets
Parameter Summary Table
# Name
Estimate Std.Err. Test Stat. P value
-- ----------------------- ------------ ----------
----------- -------
Linear term 1
1 EST ..................... 13.88
9.104 1.525
0.127
2 GALL .................... 17.07
15.96 1.070
0.285
3 GALL * EST .............. 2.573
19.17 0.1342
> 0.5
4 HYP ..................... 0
Fixed 0.6390
> 0.5
Records used = 315
Deviance = 153.461 Free parameters = 3
Number of risk sets = 63
LR statistic = 0.1810E-01 df = 1
P = 0.8930
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