Reports and notes of the Public Health Laboratories, Cairo. No. 1, 1917.

Date:
1918
Catalogue details

Licence: In copyright

Credit: Reports and notes of the Public Health Laboratories, Cairo. No. 1, 1917. Source: Wellcome Collection.

    28/144 (page 16)
    — 16— can we ascertain to any reasonable degree of approximation how many cases we have thus left behind 2. Now, if we have a known large number of red and white counters in a’ bag and Wwe wish to know, without the exertion of counting them all, what approximately is the number of red or of white counters, we may take out a hundred at random and find the proportion of reds and whites among these and assume legitimately that this proportion holds for the whole number. Many processes in bacteriology and pathology, as well as in other sciences, have this form of opera- tion as their basis, e.g. the enumeration of B. coli in water or of the polymorphonuclear leucocytes in the blood. Now, there is obviously no reason why we should not reverse the process and derive the part from the whole instead of the whole from the part. If among 1,188 blood-cultures we find a certain proportion of positive to negative results, and if from the 1,188 we,select a sufficiently large number on any basis whatever, provided it is one which will not itself influence this proportion, we shall expect to find among the selected cases the same proportion of positive to negative results. If, on the other hand, there is some factor at work which influences this proportion, we can, if we know the direction in which the proportion is influenced, derive the values which would have existed had this factor not been at work. Of the 1,188 blood-cultures there was approximately one positive to every four negative results (see above, 19 per cent). é. Now, we may take a suitable series for our purpose, and such a series may be one opnectiae of all the cases in which a blood-culture and at least three specimens of faeces or urine were examined ; we find that in such a series there were 463 cases (groups I and III, Table I). We find also that of these 463 cases, in all of which a blood-culture was examined, that in thirty-six the blood-culture _ was positive, 7.e. in this series the proportion was thirty-six positive to 427 negative blood-cultures, approximately 1 ; 12 as compared with the 1:4 of the whole series. This, then, has been the result of the tendency to stop the examination of cases with a positive blood-culture, since there is no other factor apparent which would have affected the proportion in this particular series, ‘There- fore we may assume that but for this tendency approximately three times as many positive blood- cultures would have been included among these cases as are actually found there. (?) Now, for the purpose of ascertaining the proportion of positive blood-cultures among cases found positive by the examination of the feeces or urine, excluding of course all cases found positive by the blood-culture only, we find that of eighty-seven such cases fifteen gave a positive blood- culture and seventy-two a negative, giving a proportion of positive blood-cultures of 17 per cent, — from which, on the basis of the above reasoning, we may derive a proportion of forty-five positive to seventy-two negative cultures, or a proportion of positive cultures of 38 per cent. The results for the cultures taken at different periods’ of the illness, as actually found and as calculated with a view to excluding the reducing factor, are set forth in Table ITI. TABLE III. Observed. Calculated to eliminate Reducing Factor. Period. was Cases. Positive. Esa Cases. Positive. Positives : per Cent. per Cent. All cases De VISE Ry See a a 15 La, 117 Wiest Week Chee SRP 1S: 11 6 54 23 Second week Pe Pinte, ote: 27 4 15 35 2 as 31 hater RPh Stolen reg 9 i, 27 J TE (Q) This may be expressed algebraically thus :-— ‘ . _, Apart from the factor under consideration, there would have’ been 463 + 2 cases, consisting of 427 negative and 36 * we positing sifice