Improving homeopathic prescribing by applying epidemiological techniques: the role of likelihood ratio

CF Stolper¹, ALB Rutten², RFG Lugten³, RJWM Barthels⁴
Commissie Methode en Validering VHAN (Dutch Association of Homeopathic Physicians); ¹ Heerde, Netherlands; ² Breda, Netherlands; ³ Gouda, Netherlands; ⁴ Drunen, Netherlands

A committee of the Dutch association of homeopathic physicians is trying to validate materia medica by evaluating successful cases. These cases are presented and assessed by a group of experienced homeopathic physicians to provide indications about the prevalence of symptoms related to particular homeopathic medicines. The next logical question is whether epidemiological techniques can be applied to them. We have some ideas concerning the information these data can provide, based on epidemiological theory and limited experimental data. Theoretical investigation suggests that the epidemiological concept of likelihood ratio is well adapted to homeopathy. Researching and applying likelihood ratio will lead to more accurate materia medica and repertory. These considerations already indicate some shortcomings in the representation of rare medicines and the use of grading in the current repertories. Homeopathy 91, 230-238

Introduction

Some epidemiological concepts

First we will give an outline of the opportunities offered to homeopathy by epidemiology. In conventional medicine we are used to assessing diagnostic tests. To assess a diagnostic test we need a gold standard to compare the test with.(1) The gold standard is regarded as the best approximation of the truth. For instance, to assess ultrasonography for diagnosis of gallstones the best standard is the result of laparotomy. After laparotomy we can divide patients in four groups, according to outcome:

a: the test (ultrasonography) is positive and the illness (gallstones) is present: true positive

b: the test is positive and the illness is absent: false positive

c: the test is negative and the illness is present: false negative

d: the test is negative and the illness is absent: true negative

This can be depicted in a 2x2 table (Table 1):

We will use the notation a-d to indicate the possible results of a test.

These values can be assessed for every possible test. For example, we can assess the effectiveness of a drug-detecting dog in a group of travellers where we know who is carrying drugs and who is not (Table 2).

After testing the dog we want to use him. If the dog barks we can estimate the chance that the traveller carries drugs; this is the positive diagnostic value (DV+). If the same dog does not bark how great is the chance that we let the traveller rightfully pass? We define this as the negative diagnostic value (DV-).

The mathematical notation according to the 2x2 table is:

DV+ = a/(a+b)

DV- = d/(c+d)

If, as in the situation where we tested the dog, half of the passengers are carrying drugs, the positive diagnostic value of the dog barking is 95/145 = 66%. If the dog does not bark the chance that the traveller is not carrying drugs is 50/55 = 91%.

What happens if the circumstances are different, e.g. only 50 out of 200 travellers are carrying drugs? The 2x2 table for the same dog is given in Table 3:

In this case the chance of anyone carrying drugs when the dog barks is 47/122 = 39%. If the dogs does not bark the chance of the passenger being clean is 75/78 = 96%. Therefore this dog is not suited for a situation where the probability of a traveller carrying drugs is low, because there are too many false alarms (75 false alarms, only three false negatives).

The usefulness of a test depends on the situation, i.e. the chance of a fact being present before the test is performed (prior-chance). Some tests perform well if the prior-chance is low and badly if the prior-chance is high or vice versa.

In a homeopathic consultation we have a similar situation. We are testing the possibility of a medicine by asking question indicating that medicine. At the beginning of a consultation many medicines are possible, so the prior-chance of a medicine is low. If, at a later stage, our differential diagnosis is confined to, say, four medicines the prior-chance is 25%. So the same question can have a different diagnostic value in different stages of the consultation.

Likelihood ratio

The fact that the diagnostic value is not a constant value but depending on the prior-chance is awkward when we try to compare tests. Therefore, we use another value: the likelihood ratio(LR).(2) The likelihood ratio is a constant that indicates the relation between prior-chance and posterior-chance (the chance after the test). This relation is given by a somewhat complicated formula:

Posterior-chance (+) = (((prior-chance/(1 – prior-chance)) x LR(+)) / (((prior-chance/(1-prior-change))xLR + 1).

Table 4: In this table:
a+c = all the patients that got the medicine with a positive effect
b+d = all the other patients, including the ones that got the medicine without positive effect

Table 5 Belladonna and mild headache. LR+=1.13

Table 6 Belladonna and severe headache. LR+=25

We have shown that the original set-up of the repertory causes diagnostic problems for small medicines that can be solved by the use of LRs. But we need to look more closely at the content of symptom rubrics. We must reconsider the layout of the repertory in the light of LRs.

Misleading entries

If we consider a symptom rubric in the repertory the meaning of each medicine-entrance remains unclear. As we saw in the previous section a plain-type entry of a small medicine can stand for an important symptom. For the same reasons, it is possible that the entry of a large medicine is not justified.

Suppose we have half a million people cured by a homeopathic medicine and that, in this population, we have seen symptoms that occur in 80%, 60%, 40%, 20%, 10%, 1% and 0.1%. In this population Sulphur has acted in 10,000 cases, Aconitum in 4,000 cases and Lat-m. in 100 cases:

Of course these are different symptoms, a 20% symptom for Sulphur is different from a 20% symptom for Aconitum. If we remain in the same column of this table the LR = 1: When the occurrence of a symptom in the whole population is 5,000 (1%) the LR =1 for Lat-m. if the same symptom would occur once in the Lat-m. population (prevalence in the Lat-m.-population=1%). For Aconitum the absolute occurrence has to be 40 to obtain LR+=1 and for Sulphur the occurrence has to be 100. Here, again, we see the difficulty of concepts like ‘symptom frequently confirmed’. Symptoms will be more frequently confirmed for more frequently prescribed medicines.

If the occurrence of a symptom with Aconitum is 20% and in the whole population 10%, LR+=2.

If in this population ‘occasionally seen’ means 100 cases of Sulphur the LR=1 when the symptom has a prevalence of 1% in the whole population and LR+<1 when the symptom has a greater prevalence in the whole population.

Large rubrics (= rubrics with many medicines) stand for symptoms of high prevalence. If such a symptom is occasionally seen in the population of a large medicine like Sulphur the prevalence in the Sulphur-population is lower than the prevalence in the general population. Therefore it is likely that plain-type entries of a medicine with many symptoms in a large rubric stand for a LR=<1. This means that these symptoms cannot be used to include the medicine in our considerations. It does not mean that we can exclude it either! It is hard to define the size of rubrics where we can expect this, but possibly we should discard the plain-type entries of the 20 largest medicines in the 10% largest rubrics.

On the basis of our theoretical analysis we believe that it is possible to translate the qualitative concept ‘important symptom according to §153’ into the quantitative epidemiological concept ‘symptom with likelihood ratio of ..’. We have found some experimental evidence to confirm this idea.

We need to study the consequences for the repertory and our methodology.

We require more accurate data to compare prevalence of a symptom associated with a medicine with the prevalence of the symptom in the rest of the population. The best way to assess the prevalence of a symptom in successful prescriptions is to perform prospective studies, but we would need to do this for an enormous number of symptoms. This means significant organisational problems. Surveys to assess the presence of symptoms in the general population can also be used for the comparison between the medicine and the rest of the population. The design of the prospective study must provide the least possible interference with day-to-day practice.

The weight of the argument

‘The diagnostic ability of a doctor is also based on his capacity to estimate diagnostic data in a correct way’.(11) This is also relevant for the homeopathic prescribers because the value of the symptoms has an important role in the process of finding the similimum. Research into the way doctors estimate symptoms can be done by examination of the process of diagnostic decision making. LR is an useful instrument to describe criteria to select medicines- in a statistical way. Unfortunately doctors don’t think in numbers of LRs.(12) Still they can choose correct medicines. The question is now: how do we clear the relation between successful homeopathy and our chosen research-instrument, the LR?

Ideally, we would put after each medicine in each rubric of the repertory the LR, obtained from prospective research. We would expect the LR of the most homeopathic symptoms to range from 1 to 30. But in our experience it is not very easy to handle these numbers in our diagnostic thinking. Doctors usually think proportional, in categories of probability and not in a linear way. A diagnosis or the choice for a specific medicine is very improbable, possible, probable or very probable. Arguments such as the result of a test, the presence or absence of a symptom, are weak, moderate or strong arguments for or against a specific diagnosis or medicine. What we have to do is to correlate LRs with these weights of arguments. What LR ranges constitute weak, moderate or strong arguments? In clinical experience the difference between LR =1 and LR = 10 is greater than the difference between 10 and 20. A linear scale does not accurately reflect clinical importance. A natural scale in information theories is a logarithmic scale. For the homeopathic practice we propose that a 2-logarithm be used.

The logarithmic representation of LR looks as follows:

As we supposed we expect the LR of most homeopathic symptoms to range from 1 to 30. On a logarithmic scale this is 0-5. The results of our prospective research will give us the possibility to put the log₂-LR behind the medicines in the repertory. At this moment it is difficult to translate log₂-LR’s in weights of arguments. But, in theory it is possible to quantitate the meaning of typefaces by weak (normal), moderate (italic) and strong (bold character) arguments. The range for weak arguments can be log₂ LR 0-1, for good arguments 2-3 and for strong arguments 4 and higher. In the rubric MIND-ANGUISH the notation will be then "anac.(3)" or "ant-t.(1)" or "Bell.(5)",assuming that prospective investigation confirms the same importance of the symptom as the repertory.

Here we have estimated the LR based on intuitive assumptions, more or less based on practice experience. This is the way things have been done for over more than two centuries. We can do better by performing prospective studies (see ‘Towards research’).

Repertorisation is the process of putting different symptom-rubrics alongside each other in a spreadsheet. At present a blank in the repertorisation stands for ‘the medicine not present in that rubric’. This suggests that the symptom does not occur in relation to that medicine. This is inaccurate; a blank should stand for a likelihoodratio close to 1 indicating that the occurrence of the symptom with that medicine is the same as the occurrence with the rest of the (waiting room) population.

Towards research

If we want to perform this by prospective research on LR we will have to evaluate an enormous amount of symptoms. This requires a method that interferes with daily practice as little as possible.

Our first goal is to investigate the possibility of assessing the LR of homeopathic symptoms. Our long-term goal is to update our materia medica and repertory by means of statistical instruments that match the homeopathic methodology.

We will conduct this investigation for ourselves, it will not convince anybody that homeopathy works. We want to assess the best symptoms to include or exclude a certain medicine. The presence and the intensity of many symptoms are judged by clinical experience. We rely on this experience and do not want to standardise each item in the investigation more than necessary. If we want to convince others with this kind of research we risk discouraging patients and practitioners from participating.

Our main concern is the relevance of the likelihoodratio for practical use. We could, say, use elaborate and validated personality tests to assess if a person is jealous and base the likelihoodratio on the outcomes of this test. But when the practitioner uses his clinical expertise (and not the same personality test) during consultations he gets another kind of ‘jealousy’. The instrument (symptom) we investigate to determine the LR must be the same as the instrument used in practice. But it is clear that we have to define our symptoms as accurately as possible, i.e. better than in the current materia medica and repertory for many symptoms.

The gold standard in convincing others (high internal validity) is the randomised controlled clinical Trial (RCT). In such research interference with daily practice is significant. But we are already convinced of the importance of symptoms. We just want to know which symptoms are more important than others. The less interference with daily practice, the more co-operation we get.

Analysis

Which are the constituents of the standard homeopathic consultation that can be used to determine the LR? Homeopathic physicians develop the habit of asking a series of standard questions to get an overview of the patient’s health status and his ‘constitution’. This list of questions (but also observations) depends on personal experience but, generally speaking, there is consensus about the kind of questions that everyone asks during the first consultation.

For our first goal, the usefulness of LR, we can start with symptoms that most physicians regard as basic for the first consultation. If we research the likelihood ratio of a homeopathic symptom prospectively and with more participating physicians everyone should ask every patient included in the investigation the same question. If we take the symptom ‘Desire for coffee’ related to the medicine Angustura as an example the investigation could proceed as follows:

1. We define the symptom ‘Desire for coffee’, e.g. more than 10 cups a day.
2. We ask every patient: "How many cups of coffee do you drink each day?".
3. The answer to this question (interpreted by the physician) and the corresponding patient are coded and stored in a central place.
4. After a certain number of patients have been treated for a certain period the results of all the treatments are evaluated.
5. Now we can calculate the prevalence of ‘Desire for coffee’ in the group that responded to Angustura and the prevalence of the symptom in the rest of the population.
6. This results in the LR.

There is no placebo-control, but a comparison between two groups, ‘Angustura’ and ‘not-Angustura’. For the patient there is no perceptible difference in the treatment whether he is part of this investigation or not. For the doctor there is some extra work in gathering the data.

What does the population we investigate look like? We start from a symptom that we investigate in a number of patients. But of course we can take several symptoms at a time. Now we have to define the groups in the 2x2 diagram like we showed in the paragraph ‘Likelihood ratio and homeopathy’.

Here we have to answer the next questions:

1. What is a positive effect?
2. What about the patients that got more than one medicine?

These problems are still to be resolved. Then there is the size of the population we have to investigate. What can we expect? There are different classes of symptoms like:

A. Rare symptoms confined to one medicine

B. Frequently occurring symptoms belonging to a moderate number of medicines

C. Frequently occurring symptoms occurring to many medicines

And, of course, all possible varieties. An example of group A. could be ‘Nausea from the sound of an organ’ (Physostigma). If we want to investigate this symptom we need to include many patients if we want to see this symptom at all. The ‘B-class symptom’ ‘Nausea from odours’ is not that rare: probably frequently occurring with Colchicum, but perhaps rare in relation to the medicine Eupatorium-perfoliatum. The ‘C-class’ symptom ‘Nausea during headache’ occurs frequently, but in varying degrees with different medicines. If our population is small we can only investigate frequently occurring symptoms related to medicines that are frequently associated with that symptom.

We need to include many patients in such an investigation, especially if we want to assess the LR of rare symptoms. It will be necessary to conduct the research at several centres. Our main concern is a design that causes the least possible interference with daily practice. Enthusiasm will be needed to perform the same investigation over and over again for different sets of symptoms. The doctors participating need to be involved in the implementation of the project, and standardisation must be assured. International agreement and co-operation is needed to bring such a project to fruition. We invite all colleagues who are interested to contact us.

Discussion

The transition from the homeopathic notion of ‘important symptom’ to the modern epidemiological idea of LR has great potential. The task is enormous, in return we get more reliable instruments. Symptoms can be seen as diagnostic instruments and the LR as an indication for optimal use. In future, computer programs may show you the symptoms with the highest LR(+) to confirm that medicine, or the lowest LR(-) to exclude it. This may be a solution to shortcomings of the repertory, e.g. handling rare medicines. Furthermore the new data will be based on empirical evidence instead of estimation.

We think that we can and must develop a scientific identity of our own to improve our method instead of proving it^, . But one question provokes the next one, e.g.: to research LR properly we need better descriptions of symptoms and better definition of our ‘gold standard’, the cure. Can we develop an organisation and sufficient communication to establish this new scientific identity?

Conclusions

1. The likelihoodratio(+) can be used as a mathematical representation of §153 of the Organon. That means that symptoms belonging to medicines are accessible for statistical research. This offers the possibility of giving a more accurate and quantitative description of a symptom, based on empirical data.
2. Little known medicines have few symptoms in the repertory. Probably these symptoms are undervalued. The use of likelihoodratio can correct misrepresentation.
3. It is likely that plain-type entries of a medicine with many symptoms in a large rubric stand for a likelihood ratio =<1. This means that these symptoms cannot be used to include the medicine in our considerations.
4. In future typefaces can indicate the weight of the argument of the symptom in relation with a medicine.
5. We propose a research project on likelihood ratios. International agreement and co-operation is needed.

Literature:

Lex Rutten, MD

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