## A Contribution to The Aetiology of Manic-Depressive Insanity (1940)

*Preliminary Calculations*

In the calculation of the frequency of any character ihich has a different incidence rate at different ages, it is essential to correct for age the total number of the population in which the character is being observed. The various methods of doing this, particularly for psychiatric disorders, will not be discussed at length here. There are, as far as I know, only three methods,^{1} Weinberg a shorter method, Strömgren s method, and Weinberg’s method of calculation of morbidity by a morbidity table. One cannot assert of any of these three methods that it is absolutely correct; each one has its advantages and its objections. The last method, which lowically pehaps is the most satisfactory, can be used only with a comparatively large material and in my material will not be found of great assistance. einberg's shorter method is, as Weinberg himself emphasizes, a comparatively crude procedure. One assumes a particular life period as the danger period for the outbreak of the illness, and from the sum‑total of people observed subtracts the number of those vho have never entered on this danger period and half the number of those who have entered on it, but have not yet completely lived through it. The number left forms the corrected total of the population against which the frequency of the character is to be calculated. In the case of manic‑depressive insanity, the period of 20 ‑ 50 has been assumed till now as the danger period of the illness. The method would be free from all objection if the following conditions were fulfilled: Firstly, the assumed danger period must accurately correspond to the real danger period, and secondly, during this danger period there must either be both a uniform distribution of the risk of illness, and a uniform distribution of the number of persons observed, or else distributions of risk of illness and of numbers observed whose irregularities compensate for each other. There is, of course, a further possibility that neither the first nor the second of the above conditions is fulfilled, but that the deviations or errors of both compensate for each other.

It cannot therefore be excluded as a possibility that, working on the assumption of a danger period of 20 ‑ 50 (although first illnesses occur, of course, both before and after this period, and although, as has been seen from Table 1, the danger period would seem to be more accurately represented by the period 50 ‑ 60), one may nevertheless arrive at an approximately correct result. It is clear, however, that one cannot be sure of this until the results have been checked by other and more exact methods. Veinberg, when he introduced this method in the case of schizophrenia, carried out these checks with the aid of his own more complex method and found that, when one assumed for schizophrenia a danger period of 17 ‑ 40, approximately the same result was obtained by his shorter as by his longer method. For this reason I have not considered it desirable, in making use of Weinberg's shorter method, to apply correction, as is sometimes done, in some such way as the following, i.e. allowing a person of the age of 21 a weight of 1/30, one of 22 a weight of 2/30, etc. I have thought it more desirable to employ the method in unaltered form, as has been the custom in previous works of this kind from the Forschungsanstalt in Munich.

For an exact description of Strömgren's method of correcting population values, Strömgren's original paper must be referred to. It will be sufficient to show how the method is employed in the present case. The material for the calculations is provided by Table 1. The figures of columns 4 and 8 are added together serially, so that for every year one has a figure which represents not only that part of the risk of falling 111 with a manic-depressive psychosis to be assigned to that year alone, but also that part of the risk which has already been outlived in all previous years. At the end one attains a number which represents the total danger of becoming manic‑depressive. This is then made equivalent to 10. Accordingly, if one now divides all the numbers obtained in the way described by the final sum, one obtains for every year an expression in the form of a percentage for that part of the risk which has been encountered up to that point. As a matter of convenience, these numbers are then diminished at each year by one‑half of the additional percentage for that year, in order to obtain a figure for the risk encountered. up to the middle of the year and not up to its end. The results of these calculations are given in columns 5 and 9 of Table 1, and it is these figures we use for the calculation of the corrected population value. An example will make this clear. In order to calculate the corrected total of male children (which will act as the divisor in the calculation of the frequency of manic‑depressives among the male children of manic‑depressives), the number of male children under the age of 1 will be multiplied by 0, of those of 1 years by 0.00029, of those of 14 years by 0.00087, and so on up to those of 74, whose number will be multiplied by 0.99807, and those of 75 and over, whose number is included unaltered. One will notice that in columns 5 and. 9 of Table 1 the 5O, point of survival of risk is attained by the male arid the female at the ages of 48 and. 46 respectively. From this it may be expected that we shall obtain higher figures for the frequency of manic‑depressives among the children by the Strmgren method than by Weinberg' a shorter method.

Weinberg's method of calculation by means of a morbidity table is carried out as follows. The material is divided into convenient age groups and the chance of surviving the particular period represented. by each age group without developing the character investigated is calculated. By this means one obtains a series of probabilities covering the whole of the life span; and these probabilities may be all multiplied together to provide a figure which represents the total chance of survival without showing the character in the population investigated. This fraction, subtracted from unity, gives an expression for the frequency of the character. As has already been said, a really large material is necessary for this calculation, and I have used it in the present material only for all children taken together.

(1) *Z. ges. Neurol. Psychiat*. (1935). 153 : 784. This method is in principle the same as that formulated by me and adapted to the calculation of psychiatric risks in a total population, that of England and Wales. (‘The Incidence of Mental Disorder’. *Ann. Eugen*. (1935). 6 11 : 172)