Which headache disorders can be diagnosed concurrently? An analysis of ICHD3 criteria using prime encoding system.

Introduction: Real-life headache presentations may fit more than one ICHD3 diagnosis. This project seeks to exhaustively list all logically consistent "co-diagnoses" according to the ICHD3 criteria. We limited our project to cases of two concurrent diagnoses. Methods: We included the criteria for "Migraine" (1.1, 1.2, 1.3), "Tension-type headache" (2.1, 2.2, 2.3, 2.4), "Trigeminal autonomic cephalalgias" (3.1, 3.2, 3.3, 3.4, 3.5), and "Other primary headache disorders." We also excluded "probable" diagnosis criteria. Each characteristic in the above criteria is assigned a unique prime number. We then encoded each ICHD3 criteria into integers through multiplication in a list format; we called these criteria representations. "Codiagnoses representations" were generated by multiplying all possible pairings of criteria representations. We then manually encoded a list of logically inconsistent characteristics through multiplication. All co-diagnoses representations divisible by any inconsistency representations were filtered out, generating a list of co-diagnoses representations that were logically consistent. This list was then translated back into ICHD3 diagnoses. Results: We used a total of 103 prime numbers to encode 578 ICHD3 criteria. Once illogical characteristics were excluded, we obtained 145 dual diagnoses. Of the dual diagnoses, two contained intersecting characteristics due to subset relationships, 14 contained intersecting characteristics without subset relationships, and 129 contained dual diagnoses as a result of non-intersecting characteristics. Conclusion: Analysis of dual diagnosis in headaches offers insight into "loopholes" in the ICHD3 as well as a potential explanation for the source of a number of controversies regarding headache disorders. The existence of dual diagnoses and their identification may carry implications for future developments and testing of machine-learning diagnostic algorithms for headaches.