# limdil

##### Limiting Dilution Analysis

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

- Keywords
- regression

##### Usage

`limdil(response,dose,tested=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
- 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

A binomial generalized linear model is fitted 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.

##### Value

- List with components
CI numeric vector giving estimated frequency and lower and upper limits of Wald confidence interval test.unit.slope numeric vector giving chisquare likelihood ratio test statistic and p-value for testing the slope of the offset equal to one

##### References

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.

##### Examples

```
Dose <- c(50,100,200,400,800)
Responses <- c(2,6,9,15,21)
Tested <- c(24,24,24,24,24)
limdil(Responses,Dose,Tested,test.unit.slope=TRUE)
```

*Documentation reproduced from package statmod, version 1.2.0, License: LGPL version 2 or newer*