# [R] bootcov or robcov for odds ratio?

khosoda at med.kobe-u.ac.jp khosoda at med.kobe-u.ac.jp
Sat Apr 30 16:47:40 CEST 2011

```Dear list,

I made a logistic regression model (MyModel) using lrm and penalization
by pentrace for data of 104 patients, which consists of 5 explanatory
variables and one binary outcome (poor/good). Then, I found bootcov and
robcov function in rms package for calculation of confidence range of
coefficients and odds ratio by bootstrap covariance matrix and
Huber-White sandwich method, respectively.

> MyModel.boot <- bootcov(MyModel, B=1000, coef.reps=T)
> MyModel.robcov <- robcov(MyModel)

> anova(MyModel)
Wald Statistics          Response: outcome

Factor        Chi-Square d.f. P
stenosis       0.20      1    0.6547
x1            10.69      1    0.0011
x2             2.33      1    0.1270
procedure      3.27      1    0.0708
ClinicalScore  2.55      1    0.1102
TOTAL         18.71      5    0.0022

> anova(MyModel.boot)
Wald Statistics          Response: outcome

Factor        Chi-Square d.f. P
stenosis       0.16      1    0.6921
x1            17.90      1    <.0001
x2             3.36      1    0.0669
procedure      4.62      1    0.0316
ClinicalScore  1.82      1    0.1774
TOTAL         31.82      5    <.0001

> anova(MyModel.robcov)
Wald Statistics          Response: outcome

Factor        Chi-Square d.f. P
stenosis       0.17      1    0.6758
x1            20.52      1    <.0001
x2             3.83      1    0.0505
procedure      5.09      1    0.0241
ClinicalScore  1.84      1    0.1744
TOTAL         34.80      5    <.0001

The confidence intervals are narrower in bootcov model, and further
narrower in robcov model than in original model, as demonstrated in the
followings.

I am wondering which confidence interval should be used.
I would appreciate anybody's help in advance.
--
KH

> summary(MyModel, stenosis=c(70, 80), x1=c(1.5, 2.0), x2=c(1.5, 2.0))
Effects              Response : outcome

Factor              Low  High Diff. Effect S.E. Lower 0.95 Upper 0.95
stenosis            70.0 80   10.0  -0.11  0.24 -0.59      0.37
Odds Ratio         70.0 80   10.0   0.90    NA  0.56      1.45
x1                   1.5  2    0.5   1.21  0.37  0.49      1.94
Odds Ratio          1.5  2    0.5   3.36    NA  1.63      6.95
x2                   1.5  2    0.5  -0.29  0.19 -0.65      0.08
Odds Ratio          1.5  2    0.5   0.75    NA  0.52      1.08
ClinicalScore        3.0  5    2.0   0.61  0.38 -0.14      1.36
Odds Ratio          3.0  5    2.0   1.84    NA  0.87      3.89
procedure - CA:CE    2.0  1     NA   0.83  0.46 -0.07      1.72
Odds Ratio          2.0  1     NA   2.28    NA  0.93      5.59

> summary(MyModel.boot, stenosis=c(70, 80), x1=c(1.5, 2.0), x2=c(1.5, 2.0))
Effects              Response : outcome

Factor              Low  High Diff. Effect S.E. Lower 0.95 Upper 0.95
stenosis            70.0 80   10.0  -0.11  0.28 -0.65      0.43
Odds Ratio         70.0 80   10.0   0.90    NA  0.52      1.54
x1                   1.5  2    0.5   1.21  0.29  0.65      1.77
Odds Ratio          1.5  2    0.5   3.36    NA  1.92      5.89
x2                   1.5  2    0.5  -0.29  0.16 -0.59      0.02
Odds Ratio          1.5  2    0.5   0.75    NA  0.55      1.02
ClinicalScore        3.0  5    2.0   0.61  0.45 -0.28      1.50
Odds Ratio          3.0  5    2.0   1.84    NA  0.76      4.47
procedure - CAS:CEA  2.0  1     NA   0.83  0.38  0.07      1.58
Odds Ratio          2.0  1     NA   2.28    NA  1.08      4.85

> summary(MyModel.robcov, stenosis=c(70, 80), T1=c(1.5, 2.0), T2=c(1.5,
2.0))
Effects              Response : outcome

Factor              Low  High Diff. Effect S.E. Lower 0.95 Upper 0.95
stenosis            70.0 80   10.0  -0.11  0.26 -0.62      0.40
Odds Ratio         70.0 80   10.0   0.90    NA  0.54      1.50
x1                   1.5  2    0.5   1.21  0.27  0.69      1.74
Odds Ratio          1.5  2    0.5   3.36    NA  1.99      5.68
x2                   1.5  2    0.5  -0.29  0.15 -0.57      0.00
Odds Ratio          1.5  2    0.5   0.75    NA  0.56      1.00
ClinicalScore        3.0  5    2.0   0.61  0.45 -0.27      1.49
Odds Ratio          3.0  5    2.0   1.84    NA  0.76      4.44
procedure - CAS:CEA  2.0  1     NA   0.83  0.37  0.11      1.54
Odds Ratio          2.0  1     NA   2.28    NA  1.11      4.68

```