[R] Firth logistic regression and odds ratio

[Qinghua He]

Dear all,
I have the following table for a breast cancer study and I was trying to calculate the odds ratio of different subtypes based on AR (AR+ as the base case).
                  AR-    AR+Luminal A    1     19Luminal B    1     15Her2            0     4Basal-like    20    1Normal Like  2     2
I did Firth logistic regression using the model: 
fit <- logistf(AR ~ Age+LumA+LumB+HER2+Basal+Normal-1,data=df).summary(fit)exp(coef(fit))exp(confint(fit))
              coef   se(coef)  lower 0.95  upper 0.95     Chisq          pAge     0.02675758 0.03138425 -0.03462915  0.09404934 0.7210455 0.39580118LumA   -4.04312870 2.08208148 -8.91195072 -0.32580912 4.6216454 0.03157094LumB   -3.74769116 1.96613514 -8.19454796 -0.16290619 4.2262682 0.03980286HER2   -3.71796180 2.45080140 -9.50654675  0.54467296 2.8798910 0.08969209Basal   1.12126338 1.83884710 -2.45335167  5.00553060 0.3763601 0.53955773Normal -1.51899257 2.05597939 -5.97976670  2.40100862 0.5806537 0.44605621
My question is: how come the p-value of Basal is so large? I was expecting a smaller p-value than LumA or LumB.
Some extra information:
> exp(coef(fit))       Age       LumA       LumB       HER2      Basal     Normal 1.02711878 0.01754250 0.02357211 0.02428341 3.06872873 0.21893233 
> exp(confint(fit))          Lower 95%   Upper 95%Age    9.659636e-01   1.0986139LumA   1.347687e-04   0.7219430LumB   2.761551e-04   0.8496709HER2   7.436339e-05   1.7240445Basal  8.600484e-02 149.2362476Normal 2.529416e-03  11.0343002
If I calculate odds ratio using an online calculator based on:            AR-    AR+Basal       20    1Non-basal   4     40
I got:
OR:200 95% CI: 20.9510 to 1909.2138 p < 0.0001
Can someone please help me explain?
Thank you very much!
Peter

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