binomRRci               package:MCPAN               R Documentation

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

     Simultaneous asymptotic CI for contrasts of binomial proportions,
     assuming that standard normal approximation holds on the log
     scale. Confidence intervals for ratios of (weighted geometric
     means) of proportions are calculated based on differences of
     log-proportions, and normal approximation on the log-scale.

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

     binomRRci(x,...)

     ## Default S3 method:
     binomRRci(x, n, names=NULL,
      type="Dunnett", cmat=NULL,
      alternative="two.sided", conf.level=0.95,
      dist="MVN", ...)

     ## S3 method for class 'formula':
     binomRRci(formula, data,
      type="Dunnett", cmat=NULL,
      alternative="two.sided", conf.level=0.95,
      dist="MVN",...)

     ## S3 method for class 'table':
     binomRRci(x, type="Dunnett",
      cmat=NULL, alternative="two.sided",
      conf.level=0.95, dist="MVN",...)

     ## S3 method for class 'matrix':
     binomRRci(x, type="Dunnett",
      cmat=NULL, alternative="two.sided",
      conf.level=0.95, dist="MVN",...)

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

       x: a numeric vector, giving the number of successes in I
          independent samples, or an object of class '"table"',
          representing the 2xk-table, or an object of class '"matrix"',
          representing the 2xk-table 

       n: a numeric vector, giving the number of trials (i.e. the
          sample size) in each of the I groups (only required if 'x' is
          a numeric vector, ignored otherwise) 

   names: an optional character string, giving the names of the groups/
          sample in 'x', 'n'; if not specified the possible names of x
          are taken as group names (ignored if 'x' is a table or
          matrix)

 formula: a two-sided formula of the style 'response ~ treatment',
          where 'response' should be a categorical variable with two
          levels, while treatment should be a factor specifying the
          treatment levels

    data: a data.frame, containing the variables specified in formula

    type: a character string, giving the name of a contrast method, as
          defined in 'contrMat(multcomp)'; ignored if 'cmat' is
          specified 

    cmat: a optional contrast matrix 

alternative: a single character string, one of "two.sided", "less",
          "greater" 

conf.level: a single numeric value, simultaneous confidence level 

    dist: a character string, '"MVN"' invokes multiplicity adjustment
          via the multivariate normal distribution, '"N"' invokes use
          of quantiles of the univariate normal distribution

     ...: arguments to be passed to binomest, currently only 'success'
          labelling the event which should be considered as success

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

     The interval for the ratio of two independent proportions,
     described in section "Crude Methods using first-order variance
     estimation" in Gart and Nam (1988) are extended to multiple
     contrasts. Confidence intervals are constructed based on contrasts
     for differences of lp=log (x+0.5)/(n+0.5), using quantiles of the
     multivariate normal or normal approximation. Applying the
     exponential functions to the bounds results in intervals for the
     risk ratio. In case that 0 occur in both, the numerator and
     denominator of the ratio, the interval is expanded to [0,Inf], in
     case that only 0s numerator go to the numerator, the lower bound
     is expanded to 0, in case that only 0s go to the denominator, the
     upper bound is expanded to Inf.

     See the examples for different usages.

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

     A object of class "binomRDci", a list containing: 

conf.int: a matrix with 2 columns: lower and upper confidence bounds,
          and M rows

alternative : character string, as input

conf.level: single numeric value, as input

quantile: the quantile used to construct the confidence intervals

estimate: a matrix with 1 column: containing the estimates of the
          contrasts

       x: the observed number of successes in the treatment groups

       n: the number of trials in the treatment groups

       p: the estimated proportions in the treatment groups

 success: a character string labelling the event considered as success

   names: the group names

  method: a character string, specifying the method of interval
          construction

    cmat: the contrast matrix used

_N_o_t_e:

     Note, that all implemented methods are approximate only. The
     coverage probability of the  intervals might seriously deviate
     from the nominal level for small sample sizes and extreme success
     probabilities.

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

     Gart, JJ and Nam,J-m (1988): Approximate interval estimation of
     the ratio of binomial parameters: a review and corrections for
     skewness. Biometrics 44, 323-338.

_S_e_e _A_l_s_o:

     summary.binomRDci for the risk difference, summary.binomORci for
     the odds ratio, plot.sci for plotting

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

     # In simple cases, counts of successes
     # and number of trials can be just typed:

     ntrials <- c(40,20,20,20)
     xsuccesses <- c(1,2,2,4)
     names(xsuccesses) <- LETTERS[1:4]
     ex1D<-binomRRci(x=xsuccesses, n=ntrials,
      type="Dunnett")
     ex1D

     ex1W<-binomRRci(x=xsuccesses, n=ntrials,
      type="Williams", alternative="greater")
     ex1W

     # results can be plotted:
     plot(ex1D, main="Comparisons to control group A")

     # summary gives a more detailed print out:
     summary(ex1W)

     # if data are represented as dichotomous variable
     # in a data.frame one can make use of table:

     data(liarozole)

     head(liarozole)

     # here, it might be important to define which level of the
     # variable 'Improved' is to be considered as success

     binomRRci(Improved ~ Treatment, data=liarozole,
      type="Dunnett", success="y", base=4, alternative="greater")

     # If data are available as a named kx2-contigency table:

     tab<-table(liarozole)
     tab

     binomRRci(tab, type="Dunnett", success="y", base=4, alternative="greater")

     # Performance for extreme cases:

     binomRRci(x=c(0,0,20,5),n=c(20,20,20,20),names=c("A","B","C","D"),
      type="Dunnett", alternative="greater")

