Summary
A study has been made of the distortion introduced by using the multiple-hit (gamma)
model for the construction of population curves where some of the underlying assumptions
are violated. The three violations, over which, because of physiological evidence,
there is greatest occasion for concern, are considered in some detail. These distortions
are that a latent interval exists between hits so that true survival would follow
a gamma distribution shifted to the right; that the probability of responding to an
environmental insult may change with the age of the platelet so that survival would
follow an Erlangian distribution; and that platelet destruction may be governed by
competing processes of differing relative importances. Under fairly general conditions,
the discrepancies between these models (if true) and the “best fit” (minimax) gamma
function of integral order are small (less than 3%) especially when compared with
the kind of experimental errors usually encountered.
It seems then that until such time as very precisely measured data are available,
the multiple-hit model may be used with confidence at least as a device for estimating
the mean.
It is pointed out, however, that the estimation of the number of hits to destruction,
or the mean waiting time between them separately, is likely to be imprecise. Nevertheless,
the estimation of the mean (which is the ratio of the number of hits to the reciprocal
of the waiting time) may still be much more satisfactory than estimates not explicity
defended by rational models. The latter consideration is statistical and will be dealt
with in a later paper in this series.
