Thanks in advance for any help you can offer. I'm a PhD student and have just finished recruiting for an observational clinical study.

Basically, we have recruited 100 patients and performed imaging of their coronary arteries. The measurements of the coronary arteries (e.g. diameter of vessel, whether a rupture was present or not) are the dependent variables that I am interested in. However, not every patient could have imaging of all 4 coronary arteries (LMS, LAD, Cx, RCA) due to technical difficulties with the technology.

This has led to a mismatch in my data. Each patient has a different number of variables depending on how many arteries were imaged. However, their baseline demographics (age, sex etc) and follow up data (whether they died or not etc) is all measured at a patient-level i.e. they have one dependent variable per patient.

Is there a way of accounting for these differences in measurements statistically? I'm using SPSS. I've shared an example of my data below:



  • $\begingroup$ Could you please say more about the hypotheses you wish to test with these data? And how sure are you that "technical difficulties" unrelated to vessel status are responsible for the missing data? For example, is it possible that a highly occluded vessel would not provide useful data, so that missingness might be related to what you are trying to measure? $\endgroup$ – EdM Jun 27 '16 at 11:50
  • $\begingroup$ Hi Ed, thanks for your reply. I would like to present my results in several ways e.g. is age associated with plaque measurements?, is gender associated with plaque measurements?, do plaque measurements predict adverse outcomes at 1 year? I have tried adding all the continuous plaque measurements together for each patient and just analysing the average, but this seems to lose the fidelity of the data. In addition, I can't do the same for the categorical measurements. $\endgroup$ – Hannah Jun 27 '16 at 12:03
  • $\begingroup$ In addition, you're right about the missing data. It is highly likely that it is related to factors that we are trying to measure (eg occluded vessel couldn't accommodate the imaging catheter) $\endgroup$ – Hannah Jun 27 '16 at 12:05

Data for which missing values are related to what you are trying to measure pose a difficult problem, which requires some careful thought about what you are trying to accomplish with your study. If data are "missing at random" (in a particular technical sense) then multiple imputation can provide a solution, but that's not appropriate in your case where a missing value might simply represent a very narrow vessel diameter. Your non-missing plaque measurements thus represent a biased sample of values, making it difficult to evaluate relations of age or gender to those values or the relation of plaque measurements to later outcomes.

One way to proceed would be to go back to the clinical records and determine the reason for the missingness in as many cases as possible. For each of the 4 arteries, include an additional predictor variable that is something like "too narrow to perform measurement." That predictor by itself, or combined with values that could be obtained, could be very useful.

If you could identify the cases for which narrowness per se was preventing the measurement, then imputation of the other cases (true technical failures unrelated to measurement values) could be considered. You also have to consider subject-matter knowledge, for example, how highly correlated you expect measurements on the 4 vessels to be within an individual, and prior related work on these matters. Consultation with a local statistician would be wise.

  • $\begingroup$ Hi Ed. That's very helpful, thanks. It's certainly quite easy to go back and retrospectively find out which arteries have missing measurements due to the artery being too narrow or calcified etc. Other reasons for missing data include things like not having enough time to image an artery (which wouldn't impact on the variables I am measuring). If I therefore have data on all 4 vessels for each patient, would I be able to analyse my data in the normal way (using simple statistical tests such as ANOVA, Kruskal-Wallis etc)? $\endgroup$ – Hannah Jun 27 '16 at 14:59
  • $\begingroup$ This is the paper I'm trying to emulate: drive.google.com/file/d/0B2X_Qpu07mtUck9IOXJpazNUeTg/… $\endgroup$ – Hannah Jun 27 '16 at 14:59
  • $\begingroup$ You would have to find some useful way to combine your "too narrow" cases with the measured cases, but usual types of analyses should then be OK. If you perform multiple imputation of the data truly missing at random, you should follow the strategy of performing your analyses separately on each of your imputed data sets and then combining the results, as described in the page that I linked and in other references on imputation. You could ask the authors of the paper you're trying to emulate about how they handled missing data; didn't see much on that in a brief reading of it. $\endgroup$ – EdM Jun 27 '16 at 15:11

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