elda {statmod}R Documentation

Extreme Limiting Dilution Analysis

Description

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

CI

numeric vector giving estimated frequency and lower and upper limits of Wald confidence interval of each group

test.difference

numeric vector giving chisquare likelihood ratio test statistic and p-value for testing the difference between groups

test.slope.wald

numeric vector giving wald test statistics and p-value for testing the slope of the offset equal to one

test.slope.lr

numeric vector giving chisquare likelihood ratio test statistics and p-value for testing the slope of the offset equal to one

test.slope.scorel

numeric vector giving score test statistics and p-value for testing multi-hit alternatives

test.slope.score

numeric vector giving score test statistics and p-value for testing heterogeneity

response

numeric of integer counts of positive cases, out of tested trials

tested

numeric vector giving number of trials at each dose

dose

numeric vector of expected number of cells in assay

group

vector or factor giving group to which the response belongs

num.group

number of groups

Author(s)

Yifang Hu and Gordon Smyth

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

See Also

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

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)

[Package statmod version 1.4.14 Index]