# Expected distribution of population with missing data, based on smaller sample with known distributions

#### maurih00

##### New Member
Hello!

I am trying to wrap my head around a quality assurance project at my academic health center. Due to COVID-19 lockdowns, the hospital I work for ran short of contrast agent for CT scans for a couple of months, so several patients had to be scanned without it for complaints (trauma, abdominal pain, etc.) that would have normally called for contrast-enhanced scans. I collected data on the different kinds of complaints (categorical, ordinal) coming into the Emergency Department, whether an acute finding (binary) or an incidental (non-acute) finding (binary) was noted on the initial (non-contrast scan). I also collected whether these patients had follow up imaging (binary), and if so, whether the additional imaging confirmed the original report, lumping acute and incidental findings, or whether the follow up report showed a "miss" (binary).

I was asked for the sensitivity, specificity, PPV and NPV of the sample, which I was able to calculate. However, from the "population" of 426 patients that had the original non-contrast scan (due to the different complaints), only 96 received follow up imaging, of which 93 reports were confirmed and 3 were considered misses. My question is - what should I do with the additional 330 who had initial scans but not follow up scans? I hoped to extrapolate how many would have been called correctly/had missed findings using the same proportion of the sample data, also based on the same distribution of complaints for which the 96 patients originally came in.

Is such extrapolation possible/recommended for missing values (proportion of 330 nonexistent follow up scans) in a population (426), based on the distribution of confirmation/misses (93/3), so that assessing observed/expected statistics is sound? I mean I can do the division and get 319/330, but would analyzing this "created/imagined" data using statistics be bad practice?

Otherwise, I just plan to present descriptives and the sensitivity analyses I calculated.

Thank you in advance,
MH

#### katxt

##### Well-Known Member
In my view, if the distribution of complaints is the same for both groups and there is no special reason why some were not followed up, then I don't see why you can't do the extrapolation you suggest. A large portion of industrial quality assurance is based on taking a sample proportion for a shipment of some product and using that proportion on the whole batch.
Depending on who the report is for, it may be a good idea to explain what you did, pointing out possible fishhooks. For a more formal answer, you could establish that the distribution of complaints is the same for both groups, and work out a confidence interval for the final answer.

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#### maurih00

##### New Member
In my view, if the distribution of complaints is the same for both groups and there is no special reason why some were not followed up, then I don't see why you can't do the extrapolation you suggest. A large portion of industrial quality assurance is based on taking a sample proportion for a shipment of some product and using that proportion on the whole batch.
Depending on who the report is for, it may be a good idea to explain what you did, pointing out possible fishhooks. For a more formal answer, you could establish that the distribution of complaints is the same for both groups, and work out a confidence interval for the final answer.
Thank you for confirming my assumptions! All I need to do is then compare distributions of initial complaints (categorical, ordinal) between the group that had follow up imaging (n=96) and the group that did not (n=330) (categorical, binary) using Fisher's exact test (some initial complaints had small n's) and see if the p>0.05. This would essentially verify my assumption that extrapolating proportions of confirmed findings vs. missed findings for the 330 patients that did not get follow up imaging is warranted. Like a non-parametric Levene's?

#### katxt

##### Well-Known Member
Yes, unless there was reason to think that there was some clinical reason that some were retested and some not and that would make a difference.