Pandolfi M, Homeopathy: Ex nihilo fit nihil, Eur J Intern Med (2010), doi:10.1016/j.ejim.2010.03.003
Homeopathy is an eloquent example of the natural tendency of human beings to delude themselves. It is a cure that does not make sense in the light of science and whose usefulness has not been firmly demonstrated in any disease. At best it probably is a waste of resources. Yet still the popularity of this practice seems to be intact if not on the increase. In Europe, pharmacies continue to sell questionable products like Oscillococcinum alongside “real” medi- cines, many doctors practice homeopathy full or part-time, medical faculties hold courses and confer Master qualifications in homeopa- thy, sympathizers react angrily to any factual criticism. Why?
Saying that homeopathy cannot possibly work because it has no scientifically plausible grounds has proven useless. Strangely enough, a clear-cut argument like the one stating that a molecule cannot have any biological effect after it has been totally removed from a given remedy has failed to dissuade patients and many health operators. Denounciations of the improbable water chemistry of homeopathy, the gratuitousness of the “Law of Infinitesimals” and of the principle of “similia similibus curantur” have proved equally ineffective. And finding faults in homeopathy – as well as in any other alternative medicine – is now seen in a broad sense as unbecoming. As the American mathematician Norman Levitt says, “we have moved from the concept of equality of individuals to equality of ideas and beliefs. Today it is politically incorrect to call something a dumb idea.”
Supporters of homeopathy have answered accusations of ground- lessness with an array of doubtful though ingenious explanations which have apparently been successful. They concede – and how could they do otherwise? – that the scientific foundations of homeopathy are not strictly proven but they maintain that the practice is plausible in the light of modern developments of science like quantum mechanics.
Here are a few aspects of this type of argumentation. According to Richard Feynman nobody understands quantum mechanics. However, quantum mechanics “works”, and according to supporters of homeopathy this shows that ignoring the mechanism of a physical action (such as the supposed transfer of information from the solute to the solvent) is not a sufficient reason to deny its existence. Similarly, Heisenberg's “uncertainty principle” is often quoted as a statement in support of the fact that the world is unpredictable and, therefore, that in nature nothing can be ruled out a priori. Nonintuitive quantistic concepts like “entanglement” and “collapse of the wave function” have been invoked to explain negative results of clinical studies. It is postulated that in homeopathy patient, doctor and remedy are “entangled” in one functional state with reciprocal sharing of information which is comparable to that formed by couples of electrons, photons and other subatomic particles. And as with quantum mechanics, it is argued that trying to pinpoint the characteristics (position, spin etc) of these particles brings about the collapse of their wave function interrupting the flow of information, the procedure used in randomized clinical trials (RCTs) would annul the unit patient–doctor–homeopathic remedy thereby cancelling the curative effect. There is an amusing essay on this theme entitled “Towards a Quantum Mechanical Interpretation of Homeopathy” available on the internet. The article, full of fanciful mathematical formulae and expressions, ends with the recommendation that after having prescribed the cure the homeopath should abstain from any follow-up (best if he or she moves to another town) lest causing the collapse of the patient's wave function and rendering the treatment ineffective!
The value of all these arguments is uncertain since metaphors and analogies in themselves prove nothing. Events like “entanglement” and “collapse of the wave function” concern subatomic entities and cannot be applied to patients which are not exactly quantistic objects. Furthermore quantum mechanics is an extremely successful branch of science substantiated by experiments and countless technological applications while homeopathy has not moved from the state of clinical hypothesis. Therefore no proper parallel can be drawn between them.
Pointing out the unproven clinical usefulness of homeopathy has had no better dissuading effect. One reason for this failure is that the background noise prevailing in the clinical literature enables biased reviewers to justify almost any treatment by cherry picking suitable studies. Thus supporters of homeopathy have, time and again, been able to find favourable publications to neutralize, at least in the eyes of the public, the negative results produced by accurate studies. This tactic, however, is becoming less applicable because of the progress of clinical methodology. Criteria of appraisal like presence of controls, adequate number of subjects, randomization, blinding, low drop out rate etc make now possible to objectively evaluate the quality of a paper. This means that supporters of homeopathy are now less credible when they counter a “certified” high-quality paper giving a negative result with the positive result of an inferior study.
In medical literature, an inverse relationship between quality of clinical trials and the reported efficacy of a treatment is often seen . In other words, well done studies are less likely then inferior ones to produce evidence of genuine efficacy. This tendency becomes an almost constant feature when homeopathy is concerned. The disharmony convincingly disproves the usefulness of this practice because in experimental science when a theory is correct if we continue observations and improve the quality of the observations the effects predicted by that theory manifest themselves more clearly, not less.
This inverse relationship is well illustrated by the following few examples. According to a review of clinical studies by Linde et al  homeopathy has a beneficial action which is not entirely explainable with the placebo effect. However the authors found no convincing evidence that “any single type of homeopathic treatment [was] clearly effective in any one clinical condition.” Which, in a broad sense, is like saying that a medicine is beneficial to everybody except men, women and children. Irrespective of the disclaimer the meta-analysis raised doubts because it included lesser quality studies which might have influenced the overall verdict in favour of homeopaty. Later Linde et al re-analyzed the data  and found that more rigorous studies tended to give smaller effect sizes. Their conclusion was that the previous meta-analysis at least over-estimated the effect of homeopathic treatments. Incidentally, this case illustrates how sensitive the outcome of a meta-analysis is to the varying standards of the studies reviewed.
Perhaps the most convincing evidence of the inverse ratio of quality of study to favourable results is a meta-analysis made by a team of researchers led by the clinical methodologist Matthias Egger . The paper, full of statistical technicalities, does not make for easy reading, and may lend itself to misunderstandings. However, it appears to have all the requisites for scientific credibility and its message is unequivocal: judging only from the restricted number of studies that really count (those conducted on a large clinical material and methodologically faultless) it is legitimate to conclude that the clinical effects of homeopathy are placebo effects. To a similar judgement we are led after perusing any one segment of the immense homeopathic literature available. Just as Linde et al  said, there is no convincing evidence that homeopathy is clearly effective in any one clinical condition.
During the last two decades the inferential statistics commonly used in clinical trials (frequentist statistics) has been questioned. Theoreticians  have pointed out that the P value, a key component of this approach, is an unsatisfactory measure of the evidence provided by the data obtained. One shortcoming of the P value is that it is computed without taking into account the plausibility of the hypothesis tested. This limitation may have no special consequence on RCTs of mainstream medicine, where plausible theories are generally examined. However, it remarkably exaggerates the statis- tical significance of results when the hypothesis under scrutiny is weak — which is the case with most alternative medicine trials. Hence a P value, which would be otherwise regarded as “significant”, may correspond in trials of homeopathy to a sizeable probability that the result has occurred soley by the working of fortune. Using a different measure of evidence (the Bayesian statistics) it can been found that under very general conditions  a P value = 0.01 in a trial where the prior probability of the hypothesis is estimated to be only 10% actually corresponds to a posterior probability that the result is due to chance alone of 0.37. Seen in this light almost all the “significant” results reported by homeopathic RTCs become questionable. Presently a second measure of significance, the confidence intervals (CIs), is often reported together with the P value. CIs are a useful inferential complement because, unlike the P value, they disclose the range of the observed effect size. However also CIs belong to frequentist statistics and they are prone to the errors affecting the P value.
The debate on homeopathy shows no sign of being settled any time soon. This situation persists also because many supporters of homeopathy seem to conceive research as a means to confirm their convictions rather than a way to ascertain the truth. They accept without discussion positive results but affirm that “more research is necessary” every time they are confronted with negative evidence. But the fact that absence of evidence is not evidence of absence does not justify the endless continuation of efforts which cannot be but fruitless. As the Latin poet Lucretius stated, “Ex nihilo fit nihil”.
Arguments advocating for higher standard of science in medicine may not equally impress everyone. However, we can hope that they are taken into consideration by independent bodies and especially by those public administrations and universities which seem to be attracted to homeopathy. Patient satisfaction and absence of side- effects alone are not sufficient grounds for making a cure available on the national or regional health service. And medical faculties should realize that they cannot reasonably impart in postgraduate courses notions which at undergraduate level would be considered absurd and sufficient to fail a student who has not yet taken the first degree.
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Former Professor of Ophthalmology, University of Lund, Sweden