elda                 package:statmod                 R Documentation

_E_x_t_r_e_m_e _L_i_m_i_t_i_n_g _D_i_l_u_t_i_o_n _A_n_a_l_y_s_i_s

_D_e_s_c_r_i_p_t_i_o_n:

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

_U_s_a_g_e:

     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)

_A_r_g_u_m_e_n_t_s:

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?

_D_e_t_a_i_l_s:

     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.

_V_a_l_u_e:

     '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

_A_u_t_h_o_r(_s):

     Yifang Hu and Gordon Smyth

_R_e_f_e_r_e_n_c_e_s:

     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. <URL:
     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. <URL: http://dx.doi.org/10.1016/j.jim.2009.06.008>

_E_x_a_m_p_l_e_s:

     # 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)

