Classifications of Logically Coherent Concurrent Diagnoses According to ICHD3: A Pilot Application of Automated Diagnosis Through Prime Representation

Abstract

Introduction: In clinical practice, headache presentations may fit more than one ICHD3 diagnoses. This project seeks to exhaustively list all logically consistent "codiagnoses" according to ICHD3 criteria. We limit our project to cases where only two diagnoses are involved. Methods: We included the ICHD3 criterias 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), as well as all "Other primary headache disorders". We excluded "Complications of migraine"(1.5) and "Episodic syndrome that may be associated with migraine" (1.6) since these diagnoses require codiagnoses of migraine as first assumption. We also excluded "probable" diagnosis criteria. Each phenotype in the above criteria is assigned an unique prime number. We then encoded each ICHD3 criteria into integers, call "criteria representations", through multiplication in a list format. "Codiagnoses representations" are generated by multiplying all possible pairings of criteria representations. To eliminate logical inconsistent codiagnses, we manually encode a list of logically inconsistent phenotypes through multiplication: For example, headache lasting "seconds" would be logically inconsistent with "headache lasting hours"; the prime representation for both are multiplied together. We called this list the "inconsistency representations". All codiagnoses representation divisible by any inconsistency representations are filtered out, generating a list of codiagnoses represenation that are logically consistent. This list is then translated back into ICHD3 diagnoses. Results: A total of 103 prime numbers were used to encode phenotypes from the included ICHD3 criteria diagnosis with 434 encodings generated. We generated 99 pairs of illogical phenotypes. Once illogical phenotypes were excluded, a total of 133,106 composite numbers representing unique dual-diagnosis clinical profiles were obtained. The number of profiles, although unique, yields duplicate dual diagnoses; once these duplicates are removed, we obtained 138 possible logical dual diagnoses. Of the dual diagnoses, 2 contains with intersecting phenotypes due to subset relationships, 15 dual diagnoses with intersecting phenotype without subset relationships, 101 contains dual diagnoses as a result of non-intersecting phenotypes. There are 20 co-diagnoses containing three disorders, all of them are super-sets of some dual diagnoses and contain chronic migraine as one of the diagnoses. Conclusion: Prime number representations of primary headache disorders not only offer clinicians with an automated way of diagnosing headaches but also provides a powerful method of investigating concurrent diagnosis in headache classifications. Applications of this method to the investigations of dual diagnosis and headaches may offer insight into "loopholes" in the ICHD3 as well as potential explanation for sources of a number of controversies in headache disorders. Futures applications of the method includes extending the methodology to all of ICHD3.