Updating the Homeopathic Algorithms: Handling Confirmation Bias.

Homeopathy has always used algorithms, such as giving more weight to peculiar symptoms and repertorisation of symptoms for differential diagnosis of medicines. However, repertory entries are flawed and homeopathic data are liable to heuristic bias. Modernising the homeopathic repertory with statistical tools, such as Bayes' theorem, should be accompanied by handling (confirmation) bias.After systematic collection of 731 'Best Chronic Homeopathic Cases' (BCHC), we analysed patterns in the frequency distribution of likelihood ratios (LRs). We did the same with an existing Bayesian repertory based on historical materia medica data of more uncertain quality. The frequency distributions are assessed with theoretical considerations, mathematical tools such as (exponential) transformations and differentiation, and expert knowledge.The frequency distributions of LRs both showed the same two patterns: the middle part of the frequency distribution showed a loglinear progression, but at both ends there was an increasing slope of the curve. The confirmation bias in the middle part of the LRs can be corrected mathematically with exponentiation (power calculations). Clinical expertise and differentiation of the curve indicate LR = 7 as an eligible maximum for the vast majority of symptoms. There was no clear difference between the BCHC and the historical materia medica data in this respect.It is possible to correct partly for confirmation bias in a repertorisation algorithm by a combination of theoretical consideration, expert knowledge and mathematics. We found a striking similarity between the BCHC and historical data regarding confirmation bias.