# elda

0th

Percentile

##### Extreme Limiting Dilution Analysis

Fit single-hit model to a dilution series using complementary log-log binomial regression.

Keywords
regression
##### Usage
elda(response, dose, tested=rep(1,length(response)), group=rep(1,length(response)), observed=FALSE, confidence=0.95, test.unit.slope=FALSE)
limdil(response, dose, tested=rep(1,length(response)), group=rep(1,length(response)), observed=FALSE, confidence=0.95, test.unit.slope=FALSE)
##### Arguments
response
numeric of integer counts of positive cases, out of tested trials
dose
numeric vector of expected number of cells in assay
tested
numeric vector giving number of trials at each dose
group
vector or factor giving group to which the response belongs
observed
logical, is the actual number of cells observed?
confidence
numeric level for confidence interval
test.unit.slope
logical, should the adequacy of the single-hit model be tested?
##### Details

elda and limdil are alternative names for the same function. limdil was the older name before the publication Hu and Smyth (2009). This function is an implementation of maximum likelihood analysis of limiting dilution data with added features to accommodate small sample sizes (Hu and Smyth, 2009). In particular, the function accommodates gracefully situations where 0% or 100% of the assays give positive results, which is why we call it "extreme" limiting dilution analysis. The methodology has been applied to the analysis of stem cell assays (Shackleton et al, 2006). A binomial generalized linear model is fitted for each group with cloglog link and offset log(dose). If observed=FALSE, a classic Poisson single-hit model is assumed, and the Poisson frequency of the stem cells is the exp of the intercept. If observed=TRUE, the values of dose are treated as actual cell numbers rather than expected values. This doesn't changed the generalized linear model fit but changes how the frequencies are extracted from the estimated model coefficient (Hu and Smyth, 2009). The confidence interval is a Wald confidence interval, unless all the responses are zero or at the maximum value, in which case Clopper-Pearson intervals are computed. If group takes several values, then separate confidence intervals are computed for each group. In this case it also possible to test for non-equality in frequency between the groups. These functions produce objects of class "limdil". There are print and plot methods for "limdil" objects.

##### Value

• An object of class "limdil" with the following components:
• CInumeric vector giving estimated frequency and lower and upper limits of Wald confidence interval of each group
• test.differencenumeric vector giving chisquare likelihood ratio test statistic and p-value for testing the difference between groups
• test.slope.waldnumeric vector giving wald test statistics and p-value for testing the slope of the offset equal to one
• test.slope.lrnumeric vector giving chisquare likelihood ratio test statistics and p-value for testing the slope of the offset equal to one
• test.slope.scorelnumeric vector giving score test statistics and p-value for testing multi-hit alternatives
• test.slope.scorenumeric vector giving score test statistics and p-value for testing heterogeneity
• responsenumeric of integer counts of positive cases, out of tested trials
• testednumeric vector giving number of trials at each dose
• dosenumeric vector of expected number of cells in assay
• groupvector or factor giving group to which the response belongs
• num.groupnumber of groups

##### References

Shackleton, M., Vaillant, F., Simpson, K. J., Stingl, J., Smyth, G. K., Asselin-Labat, M.-L., Wu, L., Lindeman, G. J., and Visvader, J. E. (2006). Generation of a functional mammary gland from a single stem cell. Nature 439, 84-88. http://www.nature.com/nature/journal/v439/n7072/abs/nature04372.html Hu, Y, and Smyth, GK (2009). ELDA: Extreme limiting dilution analysis for comparing depleted and enriched populations in stem cell and other assays. Journal of Immunological Methods 347, 70-78. http://dx.doi.org/10.1016/j.jim.2009.06.008

A webpage interface to this function is available at http://bioinf.wehi.edu.au/software/elda.

• elda
• limdil
• limdil.class
##### Examples
# When there is one group
Dose <- c(50,100,200,400,800)
Responses <- c(2,6,9,15,21)
Tested <- c(24,24,24,24,24)
out <- elda(Responses,Dose,Tested,test.unit.slope=TRUE)
out
plot(out)

# When there are four groups
Dose <- c(30000,20000,4000,500,30000,20000,4000,500,30000,20000,4000,500,30000,20000,4000,500)
Responses <- c(2,3,2,1,6,5,6,1,2,3,4,2,6,6,6,1)
Tested <- c(6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6)
Group <- c(1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4)
elda(Responses,Dose,Tested,Group,test.unit.slope=TRUE)
Documentation reproduced from package statmod, version 1.4.14, License: LGPL (>= 2)

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