Bayes and grade of membership analysis

Sir,

Rutten et al's papers on “Bayesian homeopathy” finally introduce some rational insight in how the homeopathic symptoms question could be analysed.[ ^1,2 ] I believe this approach should be related to another interesting paper by Davidson et al about the existence of the constitutional types and the technique of “grade of membership analysis”.[ ³ ] As Rutten states, “a symptom is an indication for a medicine when it occurs more frequently in the population cured by the medicine than in the rest of the population”.[ ¹ ] The authors propose a clear way to go back from clinical cases to the Materia Medica, with the aim of cleaning and making it more precise so to improve the homeopath's effectivity in daily practice.

It is apparent now that it would be impractical, problematic or impossible to redo the pathogenetic work as many homeopaths claimed during the past decade.[ ⁴ ] In spite of talking about “cured cases” as the “gold standard” of this Bayesian approach, I would personally prefer to speak in terms of “good responders”, “successful homeopathic prescription” or “clearly improved patients”, although I am aware of the difficulties and flaws in defining these concepts and applying them objectively. But on the other hand, homeopathy has been mostly buit on individual clinical cases with outstanding success.

In homeopathic semiology there are two quite different kinds of symptoms and signs: those which are real symptoms and signs, meaning manifestation of abnormality, and those which are not real symptoms but only “patients’ peculiar and individual characteristics” known by different names and schools as “constitutional symptoms” or “sensitive type”. Although there is some overlap between both categories, basically the real symptom can be cured or alleviated while the other ones are usually not modified by treatment and actually not intended to be modified but are only an indication of the reactivity of the patient to certain medicines.

In a “classical” model, which could be termed the “exclusive model”, patients are seen as belonging to one medicine OR to another one (e.g. Sulphur OR Lycopodium). But very soon in practice, the homeopath encounters a Lycopodium-like patient with desire for salty food or a Sulphur-like patient with a dictatorial character. In order to save the exclusive model, two hypotheses arise: (1) Lycopodium patients could also have desire of salt and Sulphur patients could be dictatorial. (2) The Materia Medica is incomplete and there are unknown medicines matching these patients’ pictures. Following the first hypothesis leads to endless adding of medicines to rubrics and to data corruption. The second hypothesis is problematic because if we follow the individuality idea right to the end, there should be a different medicine for each person in the world which seems implausible.

I believe we should definitively switch towards an “inclusive model” where most of the patients are “impure” from the point of view of the Materia Medica and participate with different “grades of membership” to several medicines.[ ³ ] This model explains easily why a patient may obtain relief from more than one medicine and gives a satisfactory explanation to the “dictatorial Sulphurs” and “salt craving Lycopodiums”. Again, I find the “Bayesian method” proposed by Rutten et al the way to a reliably answer to the question whether a “constitutional characteristic” or a symptom should or should be not attributed to a medicine.

In the past few years I have been working with similar ideas to Rutten et al , though in not a fine and complete manner. With the data obtained from a previous work[ ⁵ ] and with the intention to do a pilot proof, I identified 129 “successful homeopathic prescriptions” in 62 bronchial asthma cases, 50 Sulphur and 79 non-Sulphur, and compared the differences between both groups. Because of the small sample and its retrospective character the results don’t have much reliability, but they are in a sense surprising and instructive. With the chi square method, symptoms with a significantly (P<0.05) higher frequency of presentation were detected in each group and sensitivity and specificity were calculated for each one. Cumulative chance of being a Sulphur patient or a non-Sulphur patient was calculated with the Bayes formula.

Results are:

Symptoms significantly in favor of Sulphur patient (sensitivity/specificity):

• Fear of high places (14%/96.2%)

• Head perspiration (16%/94.9%)

• Worse from warm (42%/78.5%)

• Cumulative chance of being a Sulphur patient when these symptoms are present: 70%, 88.1%, 98.6%.

  Symptoms significantly in favor of being a non-Sulphur patient (sensitivity/specificity):

• Sympathetic (36.7%/88%)

• Malicious (15.2%/96%)

• Jealous (16.5%/96%)

• Lack of vital heat (43%/92%)

• Reserved (13.9%/98%)

• Cumulative chance of being a non-Sulphur patient when these symptoms are present: 82.9%, 94.8%, 98.7%, 99.8%, 100%.

  No significantly difference between groups was found for well known Sulphur symptoms such as:

• Uncover feet

• Desire for open air

• Desire for sweets

• Aversion to fish

• Desire of spicy food

• Fear of thieves

• Desire for fat

• References

• 1 Rutten A.L.B., Stolper C.F., Lugten R.F.G., Barthels R.W.J.M. A Bayesian perspective on the reliability of homeopathic repertories. Homeopathy 2006; 95: 88-93.
• 2 Rutten A.L.B. Bayesian homeopathy: talking normal again. Homeopathy 2007; 96: 120-124.
• 3 Davidson J., Fisher P., van Haselen R., Woodbury M., Connor K. Do constitutional types really exist? A further study using grade of membership analysis. Homeopathy 2001; 90: 138-147.
• 4 Dantas F, et al. A systematic review of the quality of the homeopathic pathogenetic trials published from 1945 to 1995. Homeopathy 2007; 96: 4–16.
• 5 Eizayaga F.X., Eizayaga J., Eizayaga F.X. Homoeopathic treatment of bronchial asthma. Br Hom J 1996; 85: 28-33.