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Overview

Giardia is a flagellated protozoan parasite of vertebrates. It attaches noninvasively to the small intestinal wall and absorbs nutrients (Miliotis & Bier 2003). Cysts are intermittently excreted in the stools of infected people; they are infectious immediately. Giardiasis often presents with diarrhea and flatulence, with foul-smelling foamy stools (Miliotis and Bier 2003). It can often last for 6 to 10 weeks or more without treatment; furthermore, the disease may appear to resolve, only to return later (Miliotis & Bier 2003). Partial immunity appears to develop, and infections are often asymptomatic (Miliotis & Bier 2003). Immunity is incomplete and appears to apply more to symptomatic disease than actual infection (Valentiner-Branth et al. 2003).

The taxonomy of the genus Giardia is somewhat unclear. There have been a variety of species names assigned to pathogenic Giardia in humans, including G. intestinalisG. enterica, and G. lamblia. The currently accepted name is G. duodenalis (Monis et al. 2009). Although it has been commonly considered a zoonosis, recent evidence indicates that G. duodenalis assemblages A and B (with B sometimes referred to as G. enterica) are more specific to humans (Monis et al. 2009). Dose response relationships vary depending on assemblage and host. It is difficult to distinguish Giardia assemblages morphologically; molecular methods are required (Monis et al. 2009).

Summary of Data

Rendtorff (1954) conducted a series of feeding studies in adult male prisoners. The dose response model that best fits these data is an exponential model with an ID50 of 35 cysts. Essentially the same model fit was obtained by Rose et al. (1991). This model has been found to be consistent with results from an epidemiological study in France of diarrhea and drinking water quality (Zmirou-Navier et al. 2006).

Erlandsen et al. (1969) experimentally infected wild beavers and muskrats with human-derived Giardia cysts. Giardia was much less potent in these experiments (compared to Rendtorff (1954)). This illustrates the necessity of considering assemblage and host when applying a Giardia dose response model.

Another dataset describing Giardia dose response in humans during an outbreak at a ski resort in Colorado has been published (Istre et al. 1984). However, dose is described subjectively as glasses of water consumed, and the concentration of cysts in the water was not measured, so it is not possible to tie the response directly to the numbers of cysts consumed.

Recommendations

For most risk applications in humans, the model fit to experiment 46 is preferable. However, the other models may be useful for describing zoonotic Giardia infection.

Exponential and betapoisson model.jpg

ID # of Doses Agent Strain Dose Units Host type Μodel Optimized parameters Response type Reference
46 8 From an infected human Cysts human exponential
k = 1.99E-02
LD50/ID50 = 3.48E+01

infection The experimental transmission of human intestinal protozoan parasites. II. Giardia lamblia cysts given in capsules
47 4 From infected humans Cysts beaver beta-Poisson a = 1.37E-01

LD50/ID50 = 1.46E+04
N50 = 1.46E+04
infection Cross-species transmission of Giardia spp.: inoculation of beavers and muskrats with cysts of human, beaver, mouse, and muskrat origin
48 5 From infected humans Cysts muskrat exponential
k = 3.68E-06
LD50/ID50 = 1.89E+05

infection Cross-species transmission of Giardia spp.: inoculation of beavers and muskrats with cysts of human, beaver, mouse, and muskrat origin
Best Fit
Experiment ID:
46
# of Doses:
8
Agent Strain:
From an infected human
Dose Units:
Cysts
Host type:
human
Μodel:
exponential
Optimized parameters:
k = 1.99E-02
LD50/ID50 = 3.48E+01

Reference:
Dose response data [1]
Dose Infected Non-infected Total
1 0 5 5
10 2 0 2
25 6 14 20
100 2 0 2
1E+04 3 0 3
1E+05 3 0 3
3E+05 3 0 3
1E+06 2 0 2

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 8.37 -0.000469 7 3.84 
1
14.1 
0.301
Beta Poisson 8.37 6 12.6 
0.212
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

 

Optimized k parameter for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 1.99E-02 8.50E-03 1.05E-02 1.26E-02 2.92E-02 3.29E-02 3.71E-02
ID50/LD50/ETC* 3.48E+01 1.87E+01 2.11E+01 2.38E+01 5.49E+01 6.60E+01 8.15E+01
*Not a parameter of the exponential model; however, it facilitates comparison with other models.

 

Parameter histogram for exponential model (uncertainty of the parameter)

Exponential model plot, with confidence bounds around optimized model

Experiment ID:
47
# of Doses:
4
Agent Strain:
From infected humans
Dose Units:
Cysts
Host type:
beaver
Μodel:
beta-Poisson
Optimized parameters: a = 1.37E-01

LD50/ID50 = 1.46E+04
N50 = 1.46E+04
Reference:
Dose response data [3]
Dose Infected Non-infected Total
48 0 6 6
454 2 4 6
4460 1 2 3
550000 2 1 3

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 22.5 21.3 3 3.84 
3.97e-06
7.81 
5.14e-05
Beta Poisson 1.22 2 5.99 
0.544
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.

 

Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 1.37E-01 1.34E-02 2.24E-02 4.22E-02 3.39E+00 2.21E+02 2.14E+03
N50 1.46E+04 5.09E+02 8.20E+02 1.06E+03 1.71E+08 8.25E+11 1.62E+18

 

Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.

beta Poisson model plot, with confidence bounds around optimized model

Experiment ID:
48
# of Doses:
5
Agent Strain:
From infected humans
Dose Units:
Cysts
Host type:
muskrat
Μodel:
exponential
Optimized parameters:
k = 3.68E-06
LD50/ID50 = 1.89E+05

Reference:
Dose response data [2]
Dose Infected Non-infected Total
30 0 8 8
300 0 7 7
3E+04 0 6 6
125000 2 1 3
5E+05 4 1 5

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 2.49 0.0417 4 3.84 
0.838
9.49 
0.646
Beta Poisson 2.45 3 7.81 
0.484
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

 

Optimized k parameter for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 3.68E-06 1.13E-06 1.35E-06 1.88E-06 9.60E-06 9.60E-06 9.60E-06
ID50/LD50/ETC* 1.89E+05 7.22E+04 7.22E+04 7.22E+04 3.68E+05 5.14E+05 6.14E+05
*Not a parameter of the exponential model; however, it facilitates comparison with other models.

 

Parameter histogram for exponential model (uncertainty of the parameter)

Exponential model plot, with confidence bounds around optimized model