The health screening for immigration to the US includes a mandatory chest x-ray screening for all adults, with the aim of detecting signs of tuberculosis. If the x-ray indicates the possibility of TB, the applicant then submits sputum samples for culturing. That's a lot of x-rays - and many of them don't result in positive cultures, especially among older applicants (whose lungs can be funky for many reasons).
In a study, 1,500 applicants (out of 24,000 during the study period) were given a new TB diagnostic in addition to the standard screening process.* People with chest x-rays indicative of TB were oversampled to ensure a fair number of applicants with culture-positive sputa. Now, the researchers would like to know (for example): if we had performed this additional diagnostic on all applicants, how many people would have tested positive? Of those, how many would have had a TB-indicative x-ray? Of those, how many would have had positive cultures? Demographic, x-ray, and culture results are known for all applicants; new-diagnostic result is only known for study participants.
Two approaches for this study have been proposed.
- Build a logistic regression on the sample and use to predict for all applicants. There are concerns that the standard errors will be too small, as age, x-ray result, and culture result are quite correlated.
- Pseudo-bootstrap. Sample 24,000 results from the participants' results (with replacement), assigning a sampling probability to each participant based on the number of all applicants with matching characteristics (demographics, x-ray result, culture result). From the resample, calculate desired quantities. Repeat, calculate confidence intervals for the estimates.
Which of these two would you use, if either? Why?
I'm happy to clarify any questions. Thanks for your help!
*Some study details changed to protect the word count.