| Twenty years ago science seemed simple: If a few Randomised
Controlled Trials (RCTs) give significant results you have scientific
proof that a method works. In 1991 the first meta-analysis of homeopathic
trials showed that proof for homeopathy is as good as for conventional
medicine.1 Coincidence or not, since then RCT is no longer a method
without flaws. There are bad RCTs and positive homeopathic RCTs
must be bad. Why? The same people who demand proof for homeopathy
are convinced that homeopathy cannot work. This conviction is based
on two misconceptions:2
1. Homeopathic doctors expect the same results from a homeopathic
potency of a medicinal substance as from a pharmaceutical dose.
Vandenbroucke states: “Microbiologists know for sure that
infinite dilutions of an antibiotic will never show any effect on
bacterial growth”.
2. Medicines can only work as conventional medicines via chemical
interactions. Vandenbroucke: “Accepting that infinite dilutions
work would subvert more than conventional medicine; it wrecks a
whole edifice of chemistry and physics”. It is amazing how
these convictions have become dogmas. No homeopathic doctor will
expect any effect on bacterial growth from an infinitely diluted
antibiotic. Does the world only consist of chemical interactions?
Based on these convictions positive results of homeopathic research
can only prove fraud by homeopathic doctors. The only good homeopathic
RCT is a negative homeopathic RCT, it will be qualified as good
more easily because quality judgements of RCT are quite subjective.
And beware, any negative result can and will be used against us!
Is it likely that a homeopathic RCT will produce a negative result,
even if the method works? Homeopathy is not a perfect method, we
are uncertain about many entries in our materia medica and repertories.
Furthermore, RCT is based on indications and homeopathic medicines
cannot be prescribed only on indication.
Practice or experiment
RCT is an experiment where you want to optimise the possibility
to discern verum from placebo. Any social circumstance can effect
this possibility. An attractive experimental opportunity is a marathon;
it is limited in time and the same for all participants. So we measure
the effect of homeopathic Arnica or Rhus toxicodendron on muscle
soreness after a marathon. But is this illness? We think that a
homeopathic medicine stimulates the defence mechanisms by a stimulus
that resembles illness. Marathon runners however, are highly trained;
what is there to stimulate? Many of us have the experience that
we must stop a homeopathic medicine after some period because the
complaints become worse again. Then the complaints subside, apparently
the patient is over-stimulated. There have been four high quality
trials testing Arnica for this indication and it appeared
that muscle soreness was less in runners taking placebo (nearly
significant).3, 4, 5, 6 This could be proof for the possibility
of over-stimulation by homeopathic medicines, but to our opponents
it is proof that homeopathy does not work.
Another way to optimise the experiment is to measure the effect
on something that can be easily measured like plantar warts. This
indication was tested for the homeopathic medicines Thuja,
Antimonium crudum and Nitricum acidum in a highly
qualified RCT by Labrecque et al.7 The outcome was negative;
does this mean that homeopathy does not work or that these three
medicines are not the optimal choices? Needless to ask our opponents.
These two indications played an important role in the negative
conclusion of the meta-analysis by Shang et al. The quality
of the trials was good in epidemiological respect, but they reflect
one of the problems of homeopathic research: There are no phase
I and phase II studies paving the way towards a sure outcome, like
in conventional medicine.
Classical homeopathy
Many of us will answer to the examples above that this proves that
we should use classical homeopathy. Unfortunately, there is no evidence
for this at the moment. In the meta-analyses of Linde and Shang
classical homeopathy did not perform better than other forms of
homeopathy.
A clear example is Walach’s trial on chronic headaches, a
very good trial with negative outcome.8 Walach explained that the
discontinuation of conventional prophylactic medicines could have
some effect in both verum and control groups, and that the main
problem in classical homeopathy is the long duration of the consultations.
This might cause an extra placebo effect, so that the verum effect
is less visible, see Figure 1.

One of the main advantages of classical homeopathy is that we can
systematically test hypotheses. Based on a number of symptoms we
choose the most likely medicine. If it does not or partially work
we reanalyse the case and prescribe another medicine. But does RCT
provide us with enough time to test several medicines one after
another? And how reliable are our repertories and materia medicas?
Preparations for RCT
The influence of the questionable quality of our instruments is
shown in a 5 year long preparation for a positive RCT on ADHD.9,
10 This improved the success rate of the first prescription
from 21% to 54% and the effectiveness of the fifth prescription
from 68% to 84% by four consecutive steps modifying the conventional
homeopathic procedure. The first step was to develop and test a
questionnaire. Questions that did not lead to successful prescriptions
were removed from the questionnaire. The next step was called ‘polarity
analysis’. Many homeopathic medicines exhibit both poles of
a symptom: there are thirsty Phosphorus patients and there
are Phosphorus patients without thirst. But the ‘mean
Phosphorus patient’ is thirsty. In Kent’s repertory
Phosphorus is in bold type in the rubric ‘Thirst’
and in plain type in the rubric ‘Thirstless’. Does this
mean that ‘thirstlessness’ pleads for Phosphorus?
No, the explanation follows under the paragraph ‘Bayesian
science’. Analysing and calculating polarities improved the
success-rate. Furthermore, Q-potencies were used because they have
less fluctuation in treatment effect. Figure 2 shows the influence
of the consecutive steps on results of treatment.
Another step necessary to obtain significant results was to insert
a screening phase before the actual trial in order to exclude non-responding
patients from the trial.

These results suggest that every RCT should be prepared in this
fashion. This could take several years. Such a preparation fulfils
the same role as phase I and phase II studies in conventional medicine.
But then there is still the problem that our materia medica and
repertories are largely based on expert opinion instead of scientific
research. This problem resembles conventional diagnostics: we know
from expert opinion that night-sweat could indicate tuberculosis,
but scientific assessment should indicate how strong the indication
is. Here Bayesian science comes to help.11
Bayesian science
In 1763 reverent Thomas Bayes published his theorem describing
the way we learn from experience. He showed how we make valid predictions
about the future from past experiences. Bayesian reasoning has since
invaded every field of science, because it can produce valid conclusions
in real-world phenomena. Now medicine can be assessed without placebo-control
and randomisation, science can be used for improving instead of
proving homeopathy.
From experience to prognosis
The bayesian principle is in fact quite simple: a diagnostic test
is better as it is positive more frequently in people with the disease
than in other people. Hahnemann also made this observation and in
the same fashion he concluded that rare and peculiar symptoms are
the most valuable symptoms. Likelihood ratio (LR) expresses the
relation between the prevalence of the symptom in the population
with the illness and the population without the illness. In the
homeopathic translation: the relation between the prevalence of
the symptom in the population cured by a certain medicine and the
rest of the treated population.

A symptom with a higher LR is more important. Peculiar symptoms
have high LR because they are specific for just a few medicines.
The bayesian formula is as follows:
Posterior odds = LR x prior odds†
If a symptom is as frequent in the population cured by a certain
medicine as in the rest- population LR=1. Such a symptom gives no
indication at all for this medicine. When a medicine is frequently
prescribed, like Phosphorus, we will see a number of patients
who are thirstless. But when this occurs as frequently as in the
rest-population, LR=1 and the symptom is no indication for Phosphorus.
Homeopathic diagnosis
The choice of a homeopathic medicine is usually not based on one
fact (diagnosis). In bayesian perspective we can describe the decision-process
of a homeopathic physician: if we add symptoms, our certainty about
the curative effect of a medicine will grow; if our symptoms are
better (eg if they are peculiar) our certainty will grow faster.
Suppose that the chance that a homeopathic medicine cures is 1%
if there are no symptoms, than our conviction that Rhus toxicodendron
will be curative grows as follows with 3 subsequent symptoms (in
this example odds are translated into chance by the computer):

This is a normal procedure in homeopathy. The patient visits the
doctor because of joint pains. The homeopathic doctor then asks
about circumstances that influence the complaint. If the patient
tells him that the pain is ameliorated by motion, the homeopathic
doctor thinks of Rhus toxicodendron as one of the possibilities.
If further investigation learns that the patient has a definite
desire for cold milk his expectation that Rhus toxicodendron
will help grows. The last symptom, aggravation from wet weather,
is subsequently enough to prescribe this medicine.
A New Repertory
Bayesian thinking is a perfect starting point for scientific update
of the homeopathic method. Homeopathic symptoms can be assessed
as diagnostic instruments, like any other diagnostic test e.g. ultrasonography.
In conventional medicine we seek for the relation between test and
diagnosis, in homeopathy we seek for the relation between symptom
and cure.
Computers make it possible to collect an enormous amount of data
about our prescriptions with a minimal amount of work. Then it is
easy to evaluate which cases were successful and which symptoms
led to these cases.12 And which did not!
† Odds = chance / (1-chance); in words: the chance that something
will happen divided by the chance that it will not happen. Odds
= 1 means: chance is fity-fifty
Type and LR
A correct repertory would indicate the difference between medicine-population
and rest of the population, expressed as LR. A homeopathic medicine
should be present in the rubric when the population responding to
that medicine shows the rubric-symptom clearly more often than the
rest of the population, say more than one and a half times more
often. Table shows a possible schema for translating LR into type
face. Such a schema should be evaluated in due course for correspondence
with actual practice.

The intermediate values represented by Italics are just a rough
estimation; further research must indicate optimal values.
An Example: ‘Fear of death’
The Committee for Methods and Validation‡ of the Dutch homeopathic
doctors association started the first prospective assessment of
six homeopathic symptoms in June 2004. The planned duration is three
years. After two years we have 2266 evaluated prescriptions. One
of the assessed symptoms is ‘Fear of death’. The rubric
‘Fear of death’ contains 103 medicines in Kent’s
repertory. There are 103 patients in our assessment with this symptom.
The prevalence of the symptom in the whole population is 4%. According
to the translation of LR into type proposed above we expect a prevalence
of 6% in the population cured by the medicine before entering the
medicine in the rubric. If the prevalence in the medicine-population
is 12% it can be entered in Italics, and if the prevalence is over
24% it should be entered in bold type.
The results are shown in the next table. The expected prevalence
is the prevalence we expect according to the existing entry in the
repertory; Calcarea carbonica is in bold type, we therefore
expect 24% (=6 times 4%) of the Calcarea patients
to have a fear of death. In table we show the results for this symptom.
We used exact binomial calculations (one-tailed) to calculate P-values,
and calculations via binomial approximation of normal distribution
if (number of patients cured by the medicine)x(expected prevalence
of symptom)>5.

‡ Members: Lex Rutten, Erik Stolper, Roland Lugten, Rob Barthels
The entry of Anacardium should be upgraded, probably
to bold type (p=0.938, the p-value in the table is the probability
that LR>1.5). The bold entry of Calcarea carbonica is
incorrect, plain type might still be correct (p=0.675), but even
that is uncertain. The same goes for Phosphorus (p=0.699).
Lycopodium still might be possible, but plain, not in Italics
(p=0.599). Natrium muriaticum should not be in this rubric.
Preliminary outcome
Interim results after two of the planned three years of investigation
are now available. At this moment we have evaluated 56 LR values
considering six repertory rubrics (‘Diarrhoea from anticipation’,
‘Fear of death’, ‘Herpes lips’, ‘Grinding
teeth in sleep’, ‘Sensitive to injustice’ and
‘Loquacity’). Our results suggest the addition of 20
(35.7% of 56) entries to Kent’s original repertory and the
rubric ‘Sensitive to injustice’ in the RADAR-Synthesis
repertory, version 8.1.40. On the other hand 11 (19.6% of 56) of
our outcome values suggest removal of existing entries in the repertory.
Retrospective Data
There are also retrospective data that give an indication of LR
s of homeopathic symptoms, like van Wassenhoven showed.13
Such data should be handled with more care than prospective research,
but they are more reliable than expert opinion. Retrospective data
can also be obtained by analysing successful cases. In the Netherlands
homeopathic medicines are validated by analysing a number of successful
cases by different practitioners.14 One of the results
was that ‘Loquacity’ is present in only 40% of all successful
cases of Lachesis. So it makes no sense to withhold a patient
Lachesis if he or she is not loquacious. At the moment
about 20 medicines are validated, none of these medicines have their
characteristic symptoms in more than 50% of all cases.
Conclusion
As long as the judges of homeopathic RCTs are convinced of the
impossibility of homeopathy we are in a witch-trial. If the results
are negative the outcome is accepted, if the results are positive
we must have committed fraud. As long as this situation persists
we should not perform any RCT.
Even if the witch-hunt is over we should only do RCT after proper
preparation. Our method has too many weaknesses for optimal results.
We made some suggestions for such preparations.
In the long run we should revise our repertories by scientific
research using Bayes’ method. We have to improve our method
before we can convincingly prove it.
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