*! version 1.1.1 30may2013

Title

stlda -- Limiting dilution analysis

Syntax

stlda cellsvar nvar negvar [if] [in] , [stlda_options]

stlda_options

method(methodtype) set the method used for computing confidence intervals; default is method(wald1)

level(#) set the confidence level of the confidence interval; default is level(95)

plot display a graphical summary of the fitted model

cellsvar specifies the variable giving the expected number of cells, or dose, tested at each dilution level.

nvar specifies the variable giving the number of replicate cultures at each dilution level.

negvar specifies the variable giving the number of negative cultures observed at each dilution level.

Description

stlda performs analysis of limiting dilution assays. Point and confidence interval (CI) estimates of the frequency of
biologically active cells are computed. The CI can be constructed by three different methods (see below the method option).
A single-hit model is assumed, which is fitted by maximum likelihood within the framework of generalized linear models (GLM); see
Bonnefoix et al. (1996) for details. Also several goodness-of-fit tests are computed. Besides tests based on deviance and
Pearson chi-squared statistics (as performed, e.g., by L-Calc software, StemCell Technologies), tests of the single-hit hypothesis
(similar to those performed by the ELDA webtool http://bioinf.wehi.edu.au/software/elda) are included. These single-hit
hypothesis tests are defined in the context of an extended GLM which includes a linear term modelling the effect of the dose (see Hu
and Smyth, 2009). In these tests, here implemented using Wald, score and likelihood ratio statistics, the null hypothesis that the
coefficient of the linear term (the slope) of the GLM is equal to one is tested.

Options

method(methodtype) specifies the method of CI construction to be used. The accepted values of methodtype are wald1, wald2
and prlik. Either wald1 or wald2 determine the computation of different versions of Wald CIs. With wald1 the
CI limits are obtained by exponentiating the corresponding limits of a Wald CI for the logarithm of the frequency. With wald2
the CI limits are obtained by a direct application of the Wald method to the frequency estimate, deriving its standard error from the
standard error of the estimate of its logarithm by means of the delta method. When the argument is prlik, a profile likelihood CI
is computed. The default is method(wald1).

level(#) specifies the confidence level of the CI as a percentage. The default is level(95).

plot specifies if a plot with the fitted mean proportion of negative cultures and their confidence intervals is to be
displayed. The plot also shows the observed proportion of negative cultures of the experiment.

Remarks

Note that, although some checking of the correctness of the input variables (i.e., the mandatory variables cellsvar, nvar
and negvar) is done, the order in which they are entered must be respected. If not, either spurious results or an error message
will be generated.

stlda requires that the Stata module -moremata- (Jann, 2005) be installed.

Examples

Load the example dataset (Table III, from Strijbosch et al., 1987):

. use "http://fmwww.bc.edu/repec/bocode/s/stlda"

Analysis using the default options:

. stlda cells n neg

An analysis giving the estimates of Table IV of Strijbosch et al. (1987) (the first group of replicate cultures is omitted):

. stlda cells n neg in 2/L, method(wald2)

A 99% level CI constructed using the profile likelihood method:

. stlda cells n neg, method(prlik) l(99)

The same, but with a plot summarizing the fitted model:

. stlda cells n neg, method(prlik) level(99) plot

Saved results

stlda saves the following in r():

Scalars

r(freq) frequency estimate

r(ci_ll) lower limit of the CI for the frequency

r(ci_ul) upper limit of the CI for the frequency

r(deviance) deviance test statistic

r(p_deviance) p-value of the deviance test

r(pearson) Pearson chi-squared test statistic

r(p_pearson) p-value of the Pearson chi-squared test

r(df) degrees of freedom of the deviance and Pearson chi-squared tests

r(slope) slope estimate

r(wald_slope) statistic of the Wald test for slope

r(p_wald_slope) p-value of the Wald test for slope

r(score_slope) statistic of the score test for slope

r(p_score_slope) p-value of the score test for slope

r(lr_slope) statistic of the likelihood ratio test for slope

r(p_lr_slope) p-value of the likelihood ratio test for slope

Author

Ignacio López de Ullibarri

Department of Mathematics

University of A Coruña, Spain

E-mail: ilu@udc.es

References

Bonnefoix T, Bonnefoix P, Verdiel P and Sotto JJ (1996), Fitting limiting dilution experiments with generalized linear
models results in a test of the single-hit Poisson assumption, Journal of Immunological Methods, 194: 113-119

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

Jann B (2005), moremata: Stata module (Mata) to provide various functions, available from
http://ideas.repec.org/c/boc/bocode/s455001.html

Strijbosch LWG, Buurman WA, Does RJMM and Zinken PH (1987), Limiting dilution assays. Experimental design and statistical
analysis, Journal of Immunological Methods, 97: 133-140