Ephraim A (1890-1894)
Uber die Bedeutung de statistischen Methode für die Medicin [On the relevance of the statistical method for medicine]. Volkmann’s Sammlung Klinische Vortraege N.F. Innere Medicin 24:706-716. Leipzig: Breitkopf and Härtel.
Email to someoneTweet about this on TwitterShare on FacebookPin on PinterestShare on LinkedIn

Title page(s)


Key passage(s)




“One would think that therapy should be the field of medical thinking in which the relation between causes and effects must be most easily detectable… Reality teaches us, however, as is well known, that the contrary is the case: in no field of medicine do the opinions of doctors agree less than in therapeutics. Views are contested, not only on the utility of particular medicines in particular diseases, on the general purpose of particular medicines and therapeutic methods, but even on the value of the whole of internal therapy. When we enquire into the reasons for this truly remarkable and regrettable phenomenon, we ultimately find them, in agreement with Rosenbach, in the lack of observational material.

This is certainly not to suggest that there are too few cases of disease in the world, or that doctors have had too little opportunity to observe them, but rather that the therapeutic observations made hitherto have not been reviewed and employed in a way that enables us to deduce general laws from them, in other words, that we have no statistics of therapy.

Before justifying this conclusion, let me first consider some objections to the significance of statistics in therapy. These can be made with apparent justification and, in fact, some authors have made them partly consciously, on the basis of principles, and partly unconsciously. These objections are generally of three types.

One type of objection stresses the practical worthlessness of statistics…
The second objection made against the use of statistical methods in therapy is no less than that it is unscientific. “Statistics destroy the true medical art and true observation, substituting a uniform, blind and mechanical routine for the action of the spirit and individual genius of the practitioner,”as was declared by one of the most eminent French doctors of this century. Indeed, one hears often enough today of empiricism being despised and presented as being in opposition to a scientific view. Yet we are rarely taught the essence of such rational therapy.

A further [third] reservation… about the position stated at the beginning of this article can be found in [the claim] that a therapy based on statistics does not meet the fundamental requirement that a treatment should be individualised. It is said to be wrong to consider the sum of the cases of a disease as a homogeneous mass, as statistics necessarily do. Each case of disease is said to be unique, an individuality that has to be considered and observed as such if we are to succeed in finding the most appropriate treatment for each case.

Even if one agrees with the above reservations, it should be pointed out that all these objections hold not only for statistics but, in the same way, for the simple (unmethodical) experience that has been our principal guide since time immemorial. But that is not so, [in that] experience is unreliable: even if it has been acquired as perfectly as possible, it is all too easily misleading because the observations on which it is based can never be regarded as fully objective and complete. Statistics, however, can never yield incorrect results if they are soundly based, and conclusions deduced correctly. [On the other hand], what do we gain from learning that a particular medicine is useful in certain circumstances -“frequently”, “from time to time”, or “often”, when we know that this “frequently” is often equivalent to “rather seldom”.  It is impossible to obtain a clear view of the efficacy of a medicine from such abstract expressions, which mainly result from observers using wholly subjective approaches. What is needed here is a methodically controlled experience, [that is] statistics. These alone show us the totality of our observations; allow us to organise them according to particular criteria that seem appropriate; and then to exhibit clearly, if this is at all possible, the interdependence of the observed phenomena. To substantiate the efficacy of mercury in syphilis, or quinine in malaria, or of iron in chlorosis one may not need statistics, although they will probably also yield surprises in these examples. But the most recent debates about the results of various procedures proposed to prevent childbed fever show, for example, how indispensable statistics can be. It would be ridiculous if we presented the results of these procedures saying that this disease occurred after one procedure “rarely”, and after another “very rarely”, etc. For it is precisely and exclusively the numerical proportion, the statistical evidence, that allows an insight into the true efficacy of each procedure… The whole difficulty therefore lies in the counting, namely, to deal with two things: what shall we count? and how many cases have to be counted?

Concerning the first of these two points, it is well known that one can only count things that are alike. This likeness does not actually need to be present in all respects, but is required only in respect of the point relevant to the reason for counting. We may well add loaves and knives together when we are determining the number of objects present, but not when assessing the quantity of food. In the same way, we also have to consider with every statistical counting in medicine that two cases of disease can be completely alike in origin, but, as one knows, quite opposite in terms of their curability. If one wants to determine the effect of a medicine by statistical examination, one will therefore have to count only those cases that are alike in curability, that is, prognosis…

The second question – “how many cases have to be counted to obtain a reliable result?” – does not permit a simple answer. The importance of and need for such an answer can be illustrated by noting that we observe often enough a higher mortality of newborn girls than of boys within a particular family circle. This contradicts statistical experience based on large numbers. We can have statistical results that are only contradictory because they are based on series of numbers differing in size. It now becomes clear that the reliability of a result increases with the size of the series; the so called law of large numbers teaches us that for every kind of phenomenon you need a certain number of observations to yield a constant numerical proportion…

Indispensable as it is, the fulfilment of all these requirements can only be achieved with difficulty. However, failure to fulfil them leads to those incorrect therapeutic statistical results that confront our eyes every day. For if we see again and again that medicines are recommended with reference to seemingly conclusive evidence, which are then revealed to be ineffective upon further application, we shall find the explanation of this remarkable inconsistency in the neglect of one of the above- mentioned conditions. The inefficacy of creolin against cholera and the large list of medicines recently recommended against diphtheria, despite the extraordinary number of cases of these diseases being cured by their application according to their eulogists, is explained just by the fact that not all of these cases have been cholera or diphtheria. The statistical evidence about the cold water treatment of abdominal typhus is unreliable because this disease shows very large variation in prognosis, so one needs a truly extraordinary large number of observations to evaluate a treatment for this disease. Rightly, the copious statistical evidence about the efficacy of treatments for erysipelas has recently been shaken by pointing out that the frequency of spontaneous cure of this disease is massively larger than the eulogists of one or another of the recommended treatments for it has seemed to assume.

That the difficulties resulting from the above are occasionally easily overcome is proven by the numerous teachings which we owe to statistics, particularly in the field of surgery and gynaecology. Even if one accepts that these difficulties cluster in the field of internal diseases, because of the larger variability of these conditions, the all-to-frequent claim that these difficulties are insurmountable cannot be maintained. Rather, a purposeful examination based on abundant material will be able to overcome such difficulties. Anyone who believes that all the barriers to progress that impede statistical investigation are insurmountable should realise that he thereby renounces all reliable therapeutic knowledge. For, as we believe to have shown above, its reliability is guaranteed only by the results of statistical research.”

Translation by Ulrich Tröhler