| Title: | Estimate Sample Size to Detect Bacterial Contamination in a Product Lot |
| Version: | 1.0.0 |
| Description: | Estimates the sample size needed to detect microbial contamination in a lot with a user-specified detection probability and user-specified analytical sensitivity. Various patterns of microbial contamination are accounted for: homogeneous (Poisson), heterogeneous (Poisson-Gamma) or localized(Zero-inflated Poisson). Ida Jongenburger et al. (2010) <doi:10.1016/j.foodcont.2012.02.004> "Impact of microbial distributions on food safety". Leroy Simon (1963) <doi:10.1017/S0515036100001975> "Casualty Actuarial Society - The Negative Binomial and Poisson Distributions Compared". |
| License: | Unlimited |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.1 |
| VignetteBuilder: | knitr |
| Suggests: | knitr, rmarkdown |
| Imports: | graphics, stats, grDevices |
| NeedsCompilation: | no |
| Packaged: | 2022-10-16 18:30:56 UTC; MFerguso |
| Author: | Martine Ferguson 
[aut, cre] |
| Maintainer: | Martine Ferguson <martine.ferguson@fda.hhs.gov> |
| Repository: | CRAN |
| Date/Publication: | 2022-10-17 12:00:05 UTC |
Calculate the sample size necessary to detect contamination above target level
Description
The n() function calculates the sample size,n, necessary to detect contamination above a target level, G, in a product lot, where the probability of a single sample unit being above the target level is calculated by the msamp function p(). The total cost, cost_tot, associated with sample size is also output.
Usage
n(
C,
w,
G,
Sens,
D = c("homogeneous", "heterogeneous", "localized"),
r = NULL,
f = NULL,
prob_det = 0.9,
samp_dollar,
lot_dollar
)
Arguments
C |
suspected lot contamination (CFU/g) |
w |
weight of single sample unit (g) |
G |
target value to detect (CFU/g) |
Sens |
sensitivity of the analytical test (%) |
D |
distribution of the bacteria in the product lot: "homogeneous", "heterogeneous", or "localized" |
r |
for the heterogeneous case only, the degree of heterogeneity. r > 0 |
f |
for the localized case, r is further specified. 0 < f < 1 |
prob_det |
desired probability of detecting bacterial contamination above the target level in the product lot. Set to 0.9 by default |
samp_dollar |
cost per sample unit in $ |
lot_dollar |
fixed cost (if any) of sampling the lot in $ |
Details
Refer to vignette for details.
Value
A list containing:
n: The sample size
p: The probability of a single sample unit being contaminated above the target level
cost_tot: The total cost associated with sampling of n samples
Examples
#A sample of 25 grams (w=25) is collected and analyzed using an analytical
#test with sensitivity of 90% (Sens=.9), to detect at least 5 CFU's/g (G=5).
#The suspected or postulated level of contamination in the lot is 4 CFU's/g (C=4).
#The desired probability of picking at least one sample unit contaminated above the target
#level is 0.9 (prob_det=0.9), the cost of a single sampling unit is $100 (samp_dollar=100),
#and the fixed cost for sampling the entire lot is $200 (lot_dollar=200).
#homogeneous case
n(C=4,w=25,G=5,Sens=.9,D="homogeneous",r=NULL,f=NULL,prob_det=0.9,samp_dollar=100,lot_dollar=200)
# n=376, total cost=$37,722
#heterogeneous case
n(C=4,w=25,G=5,Sens=.9,D="heterogeneous",r=10,f=NULL,prob_det=0.9,samp_dollar=100,lot_dollar=200)
# n=12, total cost=$1,319
#localized case
n(C=4,w=25,G=5,Sens=.9,D="localized",r=NULL,f=.3,prob_det=0.9,samp_dollar=100,lot_dollar=200)
# n=1,254 , total cost=$125,541
Calculate the probability of a single sample being contaminated
Description
The p() function calculates the probability of a single sample unit, with weight w, and postulated contamination, C, being contaminated above a target level, G.
Usage
p(
C,
w,
G,
Sens,
D = c("homogeneous", "heterogeneous", "localized"),
r = NULL,
f = NULL
)
Arguments
C |
suspected lot contamination (CFU/g) |
w |
weight of single sample unit (g) |
G |
target value to detect (CFU/g) |
Sens |
sensitivity of the analytical test (%) |
D |
distribution of the bacteria in the product lot: "homogeneous", "heterogeneous", or "localized" |
r |
for the heterogeneous case only, the degree of heterogeneity. r > 0 |
f |
for the localized case, r is further specified. 0 < f < 1 |
Details
Refer to vignette for details.
Value
A numeric value: the probability of a single sample unit being contaminated above target level.
Examples
#A sample of 25 grams (w=25) is collected and analyzed using an analytical
#test with sensitivity of 90% (Sens=.9), to detect at least 5 CFU's/g (G=5).
#The suspected or postulated level of contamination in the lot is 4 CFU's/g (C=4)
#homogeneous case
p(C=4,w=25,G=5,Sens=.9,D="homogeneous",r=NULL,f=NULL)
# 0.006117884
#heterogeneous case-- dispersion, r, is postulated as 2
p(C=4,w=25,G=5,Sens=.9,D="heterogeneous",r=2,f=NULL)
# 0.2576463
#localized case -- 30% of the lot is postulated to be contaminated
p(C=4,w=25,G=5,Sens=.9,D="localized",r=NULL,f=.3)
# 0.001835365
Plots the relation between the probability of detection and the sample size, n
Description
The plotn() function examines the effect of increasing the probability of detection on the sample size, n, where the probability of a single sample unit being contaminated above the target limit is calculated from the msamp function p()
Usage
plotn(
C,
w,
G,
Sens,
D = c("homogeneous", "heterogeneous", "localized"),
r = NULL,
f = NULL
)
Arguments
C |
suspected lot contamination (CFU/g) |
w |
weight of single sample unit (g) |
G |
target value to detect (CFU/g) |
Sens |
sensitivity of the analytical test (%) |
D |
distribution of the bacteria in the product lot: "homogeneous", "heterogeneous", or "localized" |
r |
for the heterogeneous case only, the degree of heterogeneity. r > 0 |
f |
for the localized case, r is further specified. 0 < f < 1 |
Details
Refer to vignette for details.
Value
A plot, of recordedplot class. The probability of detection is on the y-axis and the sample size n is on the x-axis. Overlaid at intersecting red dashed lines is the sample size for probability of detection (prob_det) = 0.9.