apc: Calculate aerobic plate count (APC)
In MPN: Most Probable Number and Other Microbial Enumeration Techniques

Description Usage Arguments Details Value Warnings References See Also Examples

apc calculates the Aerobic Plate Count (APC) point estimate and confidence interval of colony forming units (CFU). Adjusts for too-numerous-to-count (TNTC) plates using the maximum likelihood method of Haas et al. (2014).

1 2	apc(count, amount_scor, amount_tntc = NULL, tntc_limit = 250, conf_level = 0.95)

`count`	A vector of CFU counts in each scorable (countable) plate.
`amount_scor`	A vector of inoculum amounts (in ml) in each scorable plate. See Details section.
`amount_tntc`	A vector of inoculum amounts (in ml) in each TNTC plate.
`tntc_limit`	A vector (or scalar) of the limit above which the plate counts are considered too-numerous-to-count (often 100, 250, or 300). Each plate can potentially have a different value. Default is 250.
`conf_level`	A scalar value between zero and one for the confidence level. Typically 0.95 (i.e., a 95 percent confidence interval).

As an example, assume we start with four plates and 1 ml of undiluted inoculum. For the first two plates we use a 100-fold dilution; for the other two plates we use a 1,000-fold dilution. The first two plates were TNTC with limits of 300 and 250. The other plates had CFU counts of 28 and 20. We now have count = c(28, 20), amount_scor = 1 * c(.001, .001), amount_tntc = 1 * c(.01, .01), and tntc_limit = c(300, 250).

Currently, confidence intervals can only be calculated using the likelihood ratio (LR) approach described in Haas et al. (2014).

A list containing:

APC: The aerobic plate count point estimate in CFU/ml.
conf_level: The confidence level used.
LB: The lower bound of the confidence interval.
UB: The upper bound of the confidence interval.

The likelihood ratio confidence interval assumptions depend on asymptotic theory. Therefore, the confidence interval results will be better with larger experiments.

apc() will fail in certain cases where the TNTC results are extremely unlikely to occur when taking the scorable (countable) plates into consideration. In other words, if the countable plates suggest a low concentration of microbes, then TNTC plates at higher dilution levels are probably due to experimental error. Mathematically, the probability is so small that the likelihood function is essentially zero.

Bacteriological Analytical Manual, 8th Edition, Chapter 3, https://www.fda.gov/food/foodscienceresearch/laboratorymethods/ucm063346.htm

Haas CN, Heller B (1988). "Averaging of TNTC counts." Applied and Environmental Microbiology, 54(8), 2069-2072. https://aem.asm.org/content/54/8/2069

Haas CN, Rose JB, Gerba CP (2014). "Quantitative microbial risk assessment, Second Ed." John Wiley & Sons, Inc., ISBN 978-1-118-14529-6.

mpn for Most Probable Number

#------- "Quantitative Microbial Risk Assessment (Haas et al., 2014) --------

# Table 6.1 (Sample A)
my_count <- c(1, 2, 1, 0, 0, 1, 1, 3, 6, 8, 4)
my_amount_scor <- c(1, 1, 1, 1, 1, 2.5, 2.5, 2.5, 2.5, 5, 5)
apc(my_count, my_amount_scor)  #1.08

# Table 6.1 (Sample B)
my_count <- c(1, 0, 5, 1, 0, 5, 0, 1, 5, 1, 8)
my_amount_scor <- c(1, 1, 1, 1, 1, 2.5, 2.5, 2.5, 2.5, 5, 5)
apc(my_count, my_amount_scor)  #1.08

# Table 6.2
my_count <- c(12, 8, 15, 40, 58)
my_amount_scor <- c(1, 1, 1, 10, 10)
my_amount_tntc <- c(10, 100, 100, 100)
my_tntc_limit <- 100
apc(my_count, my_amount_scor, my_amount_tntc, my_tntc_limit) #~7 (6.03, 7.96)


#----------- "Averaging of TNTC Counts" (Haas & Heller, 1988) ---------------
# Note:
#  Results are slightly different due mostly to differences in how the TNTC
#  portion of the likelihood function is formulated (i.e., incomplete gamma
#  function vs. infinite Poisson sum--see Haas et al. (2014) for details of
#  this mathematical relationship).

my_count <- c(10, 12, 23, 48, 63)
my_amount_scor <- c(1, 1, 1, 5, 5)
my_amount_tntc <- c(5, 10, 10)
my_tntc_limit <- 80
apc(my_count, my_amount_scor, my_amount_tntc, my_tntc_limit)
#Haas & Heller: APC = 13.28 CFU/ml