bootstrap for internal validation: how can we get the bootstrap estimated AUC with a multiply imputed data?

[Jing Pan]

Dear Statalist,
I wish to get the apparent AUC of bootstrap internal validation in a multiple imputed sample. Many thanks for this valuable forum, I have learned how to get the coef. of each predictor in the prediction model with helps from https://stats.idre.ucla.edu/stata/faq/how-can-i-perform-bootstrap-estimation-with-multiply-imputed-data/ .

And I found the code for the imputed AUC as follow:

---

cap program drop eroctab
program eroctab, eclass properties(mi)

1. version 15.1
2. args refvar classvar
3. roctab `refvar' `classvar'
4. tempname b V
5. mat `b' = r(area)
6. mat `V' = r(se)^2
7. local N = r(N)
8. mat colnames `b' = AUC
9. mat colnames `V' = AUC
10. mat rownames `V' = AUC
11. ereturn post `b' `V', obs(`N')
12. ereturn local cmd "eroctab"
13. ereturn local title "ROC area"

end

---

But I can not find the correct code for the bootstrap estimated AUC with my multiply imputed data. I tried this code, but failed to get anything.

---

mi set flong
mi register imputed jobm snec bmi mrcyn lungsymp edu3
set seed 20039
mi stset, clear
mi impute chained (regress) bmi (mlogit)jobm (ologit)snec (ologit) edu3 (logit)mrcyn (logit)lungsymp = AO agec sex diaasthma, add(10)
mi describe,detail
mi estimate,saving(preao): logistic AO agec i.sex i.jobm i.snec bmi i.mrcyn i.lungsymp i.diaasthma
mi predict xb_mi using preao
mi passive: generate phat = invlogit(xb_mi)
mi estimate: eroctab AO phat
matrix list e(b_mi)
drop xb_mi phat

cap program drop myboot
program define myboot, rclass
1. mi estimate: eroctab AO phat
2. return scalar b_auc = e(b_mi)
end

. set seed 23543
. bootstrap b_AUC=r(b_auc) , reps(100) : myboot

---

But the response is "1. is not a valid command name
an error occurred when bootstrap executed myboot"

The eroctab command had been defined at the upper code.

I did not know how to get the bootstrap estimated AUC with a multiply imputed data, would anyone help me with this problem?
And I did not know how to draw a calibration plot of internal bootstrap validation in our multiply imputed data.
Any helps would be appreciated.
Jing Pan

[Mike Murphy]

The immediate error is having "1." and "2." in the text of the program definition