AUGUST, 1951 Vol. 76, No. 905 The Precision of the 3-Point Correction Method of Spectrophotometric Assay of Vitamin A BY D. C . M. ADAMSON, W. F. ELVIDGE, N. T. GRIDGEMAN, E. H. HOPKINS, R. E. STUCKEY AND R. J. TAYLOR A seven-laboratory determination of Ei:& a t 328 mp, geometrically corrected for absorption irrelevant to vitamin A, was carried out on each of five oils containing vitamin A. Readings were made in duplicate on photo-electric instruments. From a statistical analysis of the results it is concluded that the limits of error of a determination in duplicate from any one laboratory are about f15 per cent. for P = 0.05. The corresponding figure for gross, i.e., uncorrected, E values is about f2 per cent. THE practice of taking the vitamin-A content of any oil to be directly proportional to its absorption of ultra-violet light at 328mp is moribund, despite the fact that within certain classes of oils and concentrates an empirical relation between the two can be assumed with some degree of confidence and roughly checked by colorimetric reactions; for an analytical method, the interpretation of which depends on extraneous information, does not lend itself to standardisation and so must eventually be laid aside in favour of some more nearly absolute method-even if the new method is technically more complex.Most new methods now being developed, and some already in use, for t.he estimation of vitamin A depend on the elimination of, or allowance for, the ultra-violet absorption due to the presence in the sample of com- pounds other than the vitamin.Knowing the spectrophotometric characteristics of the 445446 ADAMSON, ELVIDGE, GRIDGEMAN, HOPKINS, STUCKEY AND TAYLOR : LVol. 76 pure vitamin ia the particular solvent used, we can then calculate the vitamin-A content of the sample by simple proportion. In practice it is customary to express the result not in percentages (parts per 100) but in International Units per gram (parts per 107/3), the I.U. being 0.3 pg of vitamin A as alcohol.’ The ingenuity and simplicity of one method of allowing for irrelevant absorption have earned it considerable attention. This is the Morton - Stubbs 3-point geometric correction meth0d.~s3s~s6 Its basic assumption is that the irrelevant absorption of most ‘oils and con- centrates is linear at three points in the regions 310 to 313 mp, 325 to 328 mp and 336 to 339 mp.Now it conveniently happens that there are points within the same regions on the absorption curve of vitamin A itself whose ordinakes bear the relation 6:7:6 and this makes for a simple geometry. The exact points chosen and the constants of the correction formula depend upon whether the whole oil or the unsaponifiable fraction is being examined and upon the solvent used. For the whole oil in cyclohexane the formula is- E at 328 mp (corr.) = 7 x E at 328 mp - 2.882 x E at 313 mp - 4.118 x E at 3386 mp. Hence the substitution of the Morton-Stubbs method for the old method involves only the taking of two extra spectrophotometric readings on the same solution and a consequent calculation. The theory of the correction procedure is discussed elsewhere6; the present paper is concerned with its reproducibility, a matter that does not yet seem to have been investigated.EXPERIMENTAL Seven independent laboratories undertook to determine, by photo-electric spectro- photometry, E:& at 313 mp, 328 mp and 338.5 mp, each in duplicate (separate weighings), on five oils, the solvent to be cyclohexane. As a subsidiary investigation, they were asked for complete ultra-violet absorption curves between about 250 mp and 350 mp. This secondary information was mainly for another purpose,6 but in the present context it served to show that none of the five curves conformed to the requirement’ that it should “agree closely with that of the international standard measured under the same conditions and compensated with a solution of the diluent oil,” and in particular that intensities of absorption “in the region 310 to 350mp expressed as decimal factions of the maximum should not differ between sample and standard by more than 0.02.” As these requirements were not met, the curves were presumed to contain irrelevant absorption and to be in need of rectifica- tion.Not all the absorption curves rose to a maximum at exactly 328 mp, but none of the maxima fell outside the critical range 325 to 328 mp. For the sake of simplicity the figure 328 will be used in the remainder of this paper for all the maxima. Four of the samples were- A refined fish-liver oil concentrate, E at 328 mp (gross) . . 16-61 A hake-liver oil, E at 328mp (gross) .... . . - 6.31 = 154.4 - A halibut-liver oil, E at 328mp (gross) . . . . . . - A cod-liver oil, E at 328mp (gross) . . . . .. .. - - 0.628 - The fifth sample was a blend of these oils. Its composition was afterwards revealed as 20 parts of concentrate, 31 parts of halibut-liver oil, 20 parts of hake-liver oil and 30 parts of cod-liver oil. Its gross E at 328 mp could therefore be expected to be 37.11; the average value found was reasonably close, viz., 36.82. REswLTs Before application of the correction formula, the submitted estimates of the gross EiZL at 328mp for the five samples were themselves statistically analysed, and a coefficient of variation of 1.48 for any one estimate in one laboratory emerged. Additionally, the corre- sponding coefficient for estimates at any of the three wavelengths was extracted and found to be 1.26.These are normal values and compare favourably, for instance, with the figure of 1-55 found in a recent investigation of the basic limits of error of photo-electric instruments.7 The mean results in the form of percentage variation per :;ample are shown in Table I. As expected, the individual estimates (not tabulated) show a wider range. Not all the single estimates were available; three of the seven laboratories submitted averages of duplicate estimates only, and this necessitated a The correction formula was then applied to each triad of E estimates. The values in Table I range from 92.3 to 117.2.August, 19511 SPECTROPHOTOMETRIC ASSAY OF VITAMIN A 447 correspondingly restricted estimate of the residual coefficient of variation.of the analysis of variance of the corrected E values are set out in Table 11. The essentials TABLE I ESTIMATES OF CORRECTED Ei& AT 328 mp ARRANGED AS PERCENTAGES OF OVER-ALL AVERAGES, EACH ENTRY BEING THE MEAN OF TWO ESTIMATES Laboratory A . . .. B . . .. c .. . . D . . . . E .. . . F . . . . G .. . . Means .. Concentrate, % . . 93.8 . . 104.8 . . 100.5 . . 100.9 . . 95.7 . . 102.6 . . 101-6 .. 100 Absolute mean E values 138.7 Halibut-liver Hake-liver oil, Oil, % % 117.2 94-9 92.3 104.6 99.0 100.4 98.5 100.5 96.7 97.1 95-9 97.6 100.4 104.9 100 100 15.21 5-62 Cod-liver oil, 97.5 104-9 105.9 104.8 97.1 92.6 97.2 % 100 0.541 Blend, 107.2 111.7 93.5 103.8 93.7 95.4 94.7 34.80 % 100 TABLE I1 ANALYSIS OF VARIANCE OF THE ESTIMATES OF CORRECTED Ei& AT 328 mp Source of Variance D.F.Mean square Between laboratories . . . . .. 6 77-49 Laboratories x oils . . .. .. 24 68.61 Residual error . . .. . . .. 20 161.54 Although the interaction term “laboratories x oils” in Table I1 has a mean square lower than that for the residual error, it will be wise to take it into account inasmuch as it covers more of the experimental data than does the residual term. We may therefore combine the two estimates and hence take the square root of the weighted mean square of 68.61 and 161.54, i.e., 10.5, as the fairest estimate of the residual coefficient of variation. esented in another form as the percentage of irrelevant absorption at 328 mp estimated by correction. Table I11 shows these means. The expected values for the blend are calculated from each laboratory’s findings on the four main oils and the known composition of the blend. The seven laboratories are entered in descending order of agreement between the values found and expected for the blend.The results of the trial may be TABLE I11 ESTIMATES OF PERCENTAGE OF IRRELEVANT ABSORPTION AT 328mp BY THE CORRECTION METHOD Each figure represents the mean of at Laboratory G . . .. c .. .. F . . . . D .. . . E .. .. A . . .. B . . .. Means . . Concentrate, % . . 6.9 . . 10.3 . . 3.6 . . 10.9 . . 11.8 . . 17.0 . . 10.7 . . 10.2 Halibut-liver Hake-liver oil, oil, % 7. 9.6 5.4 13.8 12.1 13.3 10.9 9.7 7.7 13.2 12.6 4.8 17.0 20.3 10.3 10.7 10.9 least two estimates Blend Cod-liver +- 7 oil, Found, Expected, % % % 16.0 11.6 16.7 11.8 13.9 16.3 13.1 14.2 7.1 12.2 6.8 7.5 8.1 7.0 4 4 7.5 7-0 10.9 5-2 10.6 12.0 14.0 12.0 10.2 The distribution of results in Table I11 and, in particular, the results for the blend give further credence to the derived errors.It is interesting to note that analysis of variance of the contents of Table I11 shows no significant difference between samples; if all the oils had in truth contained the same amount of irrelevant absorption (on the “correction” criteria) a distribution such as that now found would occur in 1 in 5 trials of this size. It might strictly be claimed that, as far as these oils are concerned, the gross E value provides448 ADAMSON, ELVIDGE, GRIDGEMAN, HOPKINS, STUCKEY AND TAYLOR [Vol. 76 a measure of the presumptive relative potency that is as good as the corrected value.In fact, however, the tendency for the cod-liver oil figure to be higher, and perhaps to be more consistent, cannot be ignored, especially as there is some evidences to show a fair reliability of the method when applied to this type of oil. DISCUSSION OF RESULTS That this estimate of 106 for the residual coefficient of variation of one result in one laboratory is not unreasonable can be inferred from a theoretical consideration of the influence of observational errors on corrected E values.6 The magnification predicted is of the order of 9.5, so that from the coefficient of variation found for the gross estimates (see above), 1.25, we should expect the coefficient for the corrected values to be nearly 12. I t concerns the variations in the relative readings of the three optical densities from one test solution to another.Inter- laboratory discrepancies in the calibration of instruments and experimental errors in the preparation of test solutions are not directly concerned ; these are factors that operate equally at all three wavelengths, and the calculation of the corrected result involves no magnification of this type of error. In this particular set of results no significant inter-laboratory differences arose (see Tables I and 11). This is unusual; work by the Photo-electric Spectrometry Group, published in part ,’ indicates that , in general, inter-laboratory (more strictly, perhaps, inter-instrument) differences can be represented by a coefficient of variation of about 1.6. If we take the published value of 1.62 and the companion value of 1.55 for the residual coefficient of variation of one result on one test solution, it follows that the standard deviation of any one duplicated assay in one laboratory is- It is important to make clear the meaning of this coefficient., i.e., *Z.O per cent., which means (a) that two-thirds of all such duplicates, each from a different laboratory, will fall within the range 98 to 104 per cent. of the over-all means, and (b) that there is a probability of 2 in 3 that the true result, defined as the mean assay from an infinite number of laboratories, lies within the range 98 to 104 per cent. about any one (duplicate) result. On the same basis, the corresponding deviation for corrected E values can be expected to amroximate to- J( 1.622 + (1.55 : g‘5r), i.e., 1106‘per cent. The value found for this deviation of duplicates in the present investigation (with no significant inter-laboratory differences) is + 7 4 per cent., and this is probably a fair guide (erring, if at all, on the low side) to what can normally be expected. The equivalent P = 0.05 limits of error are +15 per cent. (again for the mean of two estimates from one laboratory). REFER:ENCES 1. 2. 3. 4. -,- , Ibid., 1948, 42, 195. 5. Morton, R. A., J . Pharm. Pharmacol., 1950 2, 129. 6. Gridgeman, N. T., Analyst, 1951, 76, 440. 7. “Report of the Expert Committee on Biological Standardization,” World Health Organisation Morton, R. A., and Stubbs, A. L., Analyst, 1946, 71, 348. -,- , Biochem. J., 1947, 41, 525. Technical Report Series, No. 3, 1950. Edisbury, J . R., Phot. Spect. Group Bull. No. 1, April, 1940, 10. GLAXO LABORATORIES LIMITED, GREENFORD, MIDDIXSEX BOOTS PURE DRUG COMPANY LIMITED, NOTTINGHAM LEVER BROTHERS & UNILEVER LIMITED, SHARNBROOK, BEDFORD, and PORT SUNLIGHT, CHESHIRE THE CROOKES LABORATORIES LIMITED, PARK ROYAL, LONDOS, S.W. 10 THE BRITISH DRUG HOUSES LIMITED, LONDON, N.l, and POOLE, DORSET January, 195 1