Partial Identification arising from Nondifferential Exposure Misclassification: How Informative are Data on the Unlikely, Maybe, and Likely Exposed?

There is quite an extensive literature on the deleterious impact of exposure misclassification when inferring exposure-disease associations, and on statistical methods to mitigate this impact. Virtually all of this work, however, presumes a common number of states for the true exposure status and the classified exposure status. In the simplest situation, for instance, both the true status and the classified status are binary. The present work diverges from the norm, in considering classification into three states when the actual exposure status is simply binary. Intuitively, the classification states might be labeled as `unlikely exposed,' `maybe exposed,' and `likely exposed.' While this situation has been discussed informally in the epidemiological literature, we provide some theory concerning what can be learned about the exposure-disease relationship, under various assumptions about the classification scheme. We focus on the challenging situation whereby no validation data is available from which to infer classification probabilities, but some prior assertions about these probabilities might be justified.