A question about randomization with unexpected bias I need your advice in the following dilemma: a physician wishes to conduct a double blind randomized prospective study.  The patients are randomly separated in two groups. Each group will be submitted to a particular medical procedure that need additional experts to be completed. However, during the process of randomization of the patients, occasionally, from time to time, a technical failure may occur (or, the expert who is responsible for that procedure is missing). In that case, such an unfortunate event will force the patient to take one path, that is, to be included in a  certain group where an expert is available at that time. Hence, in this case, the randomization process suffers from a bias.
My question is as follows: may we still call this study a "randomized study"  ? or, partially randomized ? the physician does not wish to exclude these patients from the study.
 A: If you consider this as an adaptive randomization and consider these patients to be randomized to their specific intervention in a 1:0 ratio, then an analysis that truly reflects the randomization scheme will assign such patients zero weight in the analysis.
If this sort of thing happend extremely rarely and you only realize the problem after the patient is randomized, another strategy would be to analyze patients according to the treatment they are assigned to at randomization, even if they receive something else. However, it would not be very clever to deliberately create that situation, when you already know you will not be able to provide both treatments.
You may of course take the view that this issue happens completely at random and that it is more or less a coin flip, which intervention will be available. In that case it would more or less like a randomization mechanism in its own right. However, I would be very suspicious of this, because there are presumably some systematic factors in play. These might be certain doctors/specialists being more likely to be available at certain times of the day (or certain days of the weeks) and the patients that arrive at certain times (or that are so severe that the intervention cannot be postponed until the relevant people are available) differing systematically from other patients. Thus, there's a distinct possibility that biases might arise and it may be extremely difficult to quantify these. There may of course be ways of trying to reflect this in the analysis, but that would certainly be techniques for observational studies (e.g. stratifying the analysis for such patients by the propensity scores for being assigned one or the other intervention [for any of the truly randomized patients it's the randomization ratio] taking into account day of the week/time of the day of becoming eligible, severity of state of the patient and any other factors that may explain the intervention chosen etc.).
I would agree that strictly speaking this would no longer be a randomized trial and that from a purist perspective you would have one randomize trial plus an observational cohort (and one can consider combining them somehow). You know more about your specific case and will be able to judge what is the most appropriate.
