Biology Reference
In-Depth Information
(A)
(B)
0
20
40
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80
100
0
10
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Female worm burden
Female worm burden
FIGURE 7.4 The output of a regression model fitted to Ascaris lumbricoides egg
counts (eggs per gram of feces) using a zero-inflated negative binomial (ZINB) distri-
bution. The mean of the negative binomial (NB) component, m, and probability of the
Bernoulli component,
, were modeled as dependent on the female worm burden, x, using
the following relationships: ln(m)
p
d ln(x). The over-
dispersion parameter, k, of the NB component was assumed constant. The fitted mean, m,
and probability,
¼
a
þ
b ln(x); ln[
p
/(1
e p
)]
¼
c
þ
, along with corresponding 95% confidence intervals (CIs) are denoted by
the thick solid and thin dashed lines in (A) and (B), respectively. Maximum likelihood
estimates to 2 significant figures are as follows: NB component, a
p
¼
¼
¼
470, b
0.71, k
1.1;
¼
¼e
Bernoulli component, c
0.33, d
1.3. The value of b is statistically significantly less than 1
e
(95% CI: 0.66
0.76) indicating density-dependent female worm fecundity. In (A) the small
gray circular data points represent the individual egg count data and the large squares
represent the mean egg counts in the following female worm burden groups: 1
e
4; 5
e
8;
9
. In (B) the large square data points represent
the proportion of zero counts in the following worm burden groups: 1; 2; 3; 4; 5
e
11; 12
e
15; 16
e
18; 19
e
22; 23
e
30; 31
e
39; 40
þ
e
6; 7
e
8;
9
e
16; 16
e
32; 33
þ
.
female worm burden, pointing to a density-dependent diagnostic sensi-
tivity ( Figure 7.4 ). 44
Extrapolating individual-level diagnostic sensitivity to the chance of
detecting infection in a randomly sampled individual (moving from an
individual to a population level) indicates that diagnostic sensitivities will
vary considerably among communities with different endemicities
( Figure 7.5 ). Furthermore, sensitivity will decline throughout the course
of an effective control program, potentially leading to overoptimistic
assessment of the achieved reduction in infection and premature cessa-
tion of control.
Regression Models
The preponderance of overdispersion in parasitological data means
that classical regression techniques, which assume normal errors with
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