The detection of variation in host susceptibility in dilution counting experiments

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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.
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