Biology Reference
In-Depth Information
who are less frequent in the population, most obviously because of
mortality. This issue has been highlighted in the context of observed age-
intensity profiles for cestode (Diphyllobothrium ditremum) infections of
Arctic char (Salvelinus alpinus).
128
Because the mean of overdispersed
count data underestimates the true population mean to an increasing
degree with declining sample size,
126
smaller observed intensities of
infection in older age groups can be a statistical artifact.
The prevalence of infection for a negative binomial parasite distribution
is given by 1
m,k) is the probability a host has zero
worms given the mean intensity of infection, m, and overdispersion
parameter, k. The relationship between the prevalence, p, and mean
intensity of infection, m, is non-linear, p
e
P(0
j
m,k), where P(0
j
m/k)
k
; prevalence
initially increases rapidlywith increasingmean intensity, before saturating
at a level determined by parameter k. Data on A. lumbricoides worm
counts collated from a variety of communities suggest that the best fit to
the prevalence
¼
1
e
(1
þ
e
intensity relationship is obtained when the value of k is
allowed to increase linearlywith themean.
57
It is noteworthy that although
prevalence is, in general, a less informative index of infection, it is unbiased
by sample size.
126
The zero-inflated negative binomial distribution is a mixture of nega-
tive binomial and Bernoulli (binary) distributions (
Figure 7.1
). This
permits zero counts to arise from either the Bernoulli component or the
count component, which inflates the number of zeros relative to the
negative binomial. Recent analysis of A. lumbricoides egg counts collected
from a community in Bangladesh has demonstrated the superiority of
a zero-inflated negative binomial over its non-zero-inflated counterpart in
describing the data.
44
This is in accordance with another recent analysis of
A. lumbricoides, T. trichiura and hookworm egg counts collected in
northeast Ecuador as part of a study into the ancillary effects on STHs of
long-term mass ivermectin treatments aimed principally at controlling
onchocerciasis.
132
Zero inflation has also been shown in egg counts from
parasites of livestock
133,134
and wildlife,
135
and so empirical evidence is
building to suggest that this is a characteristic feature of fecal egg count
data.
Excess zeros in A. lumbricoides egg count distributions are likely to arise
from two predominant mechanisms: (1) hosts harboring only males
(unfertilized females produce unfertilized and still contribute to positive
counts), and (2) failure of the diagnostic method to detect parasite eggs.
The first mechanism can be accounted for if per host worm counts are
available and stratified by worm sex. That is, if the second mechanism is
unimportant, removal of male-only infection should remove the majority
of excess zeros. The data from Bangladesh indicate that this is not the case,
which is unsurprising given the modest sensitivity of the diagnostic
method. Furthermore, the fraction of zero counts declines with increasing
