Limiting Dilution Analysis

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

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

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.


  • List with 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.unit.slopenumeric vector giving chisquare likelihood ratio test statistic and p-value for testing the slope of the offset equal to one


Bonnefoix T, Bonnefoix P, Verdiel P, Sotto JJ. (1996). Fitting limiting dilution experiments with generalized linear models results in a test of the single-hit Poisson assumption. J Immunol Methods 194, 113-119. Clopper, C. and Pearson, S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26, 404-413. 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.

  • limdil
# 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)
Group <- c(1,1,1,1,1)

# 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)
Documentation reproduced from package statmod, version 1.3.6, License: LGPL (>= 2)

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