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

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 The methodology has typically been applied to the analysis of stem cell assays (Shackleton et al, 2006).

elda and limdil are alternative names for the same function.

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.

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.

Value

limdil produces an object of class limdil with the following components. There are print and plot methods for limdil objects.

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

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 <- limdil(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)
limdil(Responses,Dose,Tested,Group,test.unit.slope=TRUE)

[Package statmod version 1.4.10 Index]