The detection of variation in host susceptibility in dilution counting experiments

Abstract

Variation in host susceptibility results in flattening of the quantal response curve obtained in dilution counting experiments. This departure from the exponential curve obtained with uniform hosts is found primarily at the lower dilutions, where the infection rates are high. The test proposed by Moran, for the detection of host variability, may easily fail to detect quite appreciable heterogeneity with the numbers of observations that are likely to be available in practice. Examination of the response curves corresponding to various theoretical distributions of susceptibility suggests that detection of heterogeneity is unlikely unless the probability that a particle can initiate infection is distributed with a low mean and considerable positive skewness.The problem is related to that of estimating the standard deviation of a tolerance distribution from quantal response data. This suggests an alternative test, based on the Spearman-Kärber method, which, however, appears to be no better than Moran's test. Both methods provide estimates of the variability of the susceptibility distribution.

The Dose-response Relationship of the Ehrlich Ascites Tumour

“…In this work we have applied the method of probit analysis as described by Finney (1952). Armitage and Spicer (1956) have discussed methods for detecting departures from exponentiality and suggest that probit analysis would be suitable for this purpose and, as our results show, we have found it so.…”

Quantal and graded dose-responses of bluetongue virus: a comparison of their sensitivity as assay methods for neutralizing antibody

“…Deviation of observed quantal dose-response curves from the theoretical oneor-more particle Poisson curve have, however, been observed in some virus-host systems (Bryan & Beard, 1940;Meynell, 1957;Fazekas de St Groth & Cairns, 1952;Armitage & Spicer, 1956). In particular, the slopes have been significantly less than that of the Poisson curve.…”

Another test for heterogeneity of host resistance in dilution assays

“…The mean and variance of T have been calculated, thus enabling a rapid test to be made on the assumption that T is approximately normally distributed. This test has the advantage of being very much faster than the %2-test and also appears, in most cases, to be substantially more powerful (Armitage & Spicer (1956)), since it is so constructed that T is large for one particular kind of divergence from the theoretically expected numbers, namely, that in the direction of a flattening of the graph of Pi against i. …”

“…Another method is based on the Spearman-Karber approach but is shown by Armitage & Spicer (1956) Table 1 in the form of the probabilities of the tails of the distribution in its statistically interesting part. This table was constructed in the following way.…”

“…The power of this test would be difficult to determine in any general situation although the change in the distribution of D for particular numerically specified alternatives of the kind given by Armitage & Spicer (1956) could be found, and this would be worth doing. Furthermore, the correlation coefficient between T and D could be found numerically without much difficulty.…”