Generation of contaminated lots with variability in prevalence and concentration

The function Lot2LotGen() generates a matrix of contaminated lots from information on the parameters of a beta distribution (alpha, beta) representing the between-lot variability in prevalence; the parameters of a normal distribution (mean, sd) representing the total variability in the microbial concentration in the contaminated units (log10 CFU/g); and the proportion of such total variance assigned to between-lot variance. Every row of the matrix corresponds to a production lot, broken down in units or portions, which are the columns of the matrix.

Usage

Lot2LotGen(
  nLots,
  sizeLot,
  unitSize,
  betaAlpha,
  betaBeta,
  C0MeanLog,
  C0SdLog,
  propVarInter,
  Poisson = FALSE,
  ...
)

Arguments

nLots: Number of lots sampled or size of the Monte Carlo simulation (scalar).
sizeLot: Number of units or portions produced in a lot (scalar).
unitSize: Weight (g) of single unit or portion from a lot (scalar).
betaAlpha: Parameter alpha of the beta distribution representing the between-batch variability in prevalence (scalar).
betaBeta: Parameter beta of the beta distribution representing the between-batch variability in prevalence (scalar).
C0MeanLog: Mean parameter (log10 CFU/g) of the normal distribution representing the total variability in the microbial concentration of contaminated units (scalar or vector).
C0SdLog: Standard deviation parameter (log10 CFU/g) of the normal distribution representing the total variability in the microbial concentration of contaminated units (scalar or vector).
propVarInter: proportion of the total variance (\(C0\_sdLog10^2\)) attributed to between-lot variance. The remaining (1-propVarInter) is the proportion of within-lot variance.
Poisson: need to be defined
...: Other options used to control LotGen()

Value

A list of four elements:

N: (CFU) A matrix of size nLots lots by sizeLot units representing the microbial numbers in the units or portions from contaminated lots;
ProbUnitPos: Probability that the lot is contaminated (a lot is considered contaminated if at least one unit or portion is contaminated) (vector);
P: Mean prevalence of contaminated lots (scalar);
betaGen: True prevalence of contaminated units in the lots (sampled from the beta distribution) (vector).

Note

This function requires that the variability in the prevalence of L. monocytogenes between lots is represented by a beta distribution. To determine the parameters of such a beta distribution, a beta-binomial distribution was fitted to survey data (compiled in Table 3.21 of WHO (2022) , consisting of positive samples and total sample size. The beta-binomial was fitted through a Markov-Chain Monte Carlo approach, with gamma(0.01, 0.01) as priors for both parameters, and assuming that every data source (a published paper) represents a different lot. The parameters of the beta distribution were determined at: betaAlpha=0.5112 and betaBeta=9.959. The mean (C0MeanLog=1.023 log10 CFU/g) and standard deviation (C0SdLog=0.3267 log10\ CFU/g) of the normal distribution representing the overall variability in L. monocytogenes were obtained using data from Jeyaletchumi (2011) (3.0 MPN/g, 3.6 MPN/g in freshly harvested vegetables), Magdovitz et al. (2021) (21, 36 and 75 MPN/g in corn and peas arriving at the frozen food facility), and Kuan et al. (2017) (3.0 MPN/g in bulk carrots at retail). The algorithm decomposes at the log10 level the total variance in concentration into between-lot variance and within-lot variance according to the proportion propVarInter.

References

Team RC (2022). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/. WHO (2022). “A Roadmap for the Development of Risk Assessment Models of Listeria monocytogenes in Selected Produce and Seafood Products.” World Health Organization. Jeyaletchumi PTRSPMCLCRSFMGCYKMNYNKMP (2011). “Evaluation of Listeria spp. and Listeria monocytogenes in selected vegetable farms.” Journal of Tropical Agriculture and Food Science, 39(2), 255-266. Magdovitz BF, Gummalla S, Garren D, Thippareddi H, Berrang ME, Harrison MA (2021). “Prevalence of Listeria species and Listeria monocytogenes on raw produce arriving at frozen food manufacturing facilities.” Journal of Food Protection, 84(11), 1898-1903. Kuan CH, Rukayadi Y, Ahmad SH, Wan C, Radzi M, Thung TY, Premarathne J, Chang WS, Loo YY, Tan CW, Ramzi OB, Fadzil SNM, Kuan CS, Yeo SK, Nishibuchi M, Radu S (2017). “Comparison of the microbiological quality and safety between conventional and organic vegetables sold in Malaysia.” Frontiers in Microbiology, 8, 1433.

Author

Vasco Cadavez vcadavez@ipb.pt and Regis Pouillot rpouillot.work@gmail.com

Examples


dat <- Lot2LotGen(
  nLots = 50,
  sizeLot = 100,
  unitSize = 500,
  betaAlpha = 0.5112,
  betaBeta = 9.959,
  C0MeanLog = 1.023,
  C0SdLog = 0.3267,
  propVarInter = 0.7
)

print(dat$P)
#> [1] 0.7103589
summary(c(dat$N))
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>     0.0     0.0     0.0   417.9     0.0 59206.0