exact2x2 (version 1.4.0)

binomMeld.test: Melded Binomial Confidence Intervals and Tests

Description

Creates tests to compare two binomials, giving confidence intervals for either the difference in proportions, the rate ratio, or the odds ratio. The 95 percent confidence intervals have been shown to guarantee nominal coverage by extensive numerical calculations. It has been theoretically proven that the p-values from the one-sided tests on the null hypothesis of equality match Fisher's exact p-values.

Usage

binomMeld.test(x1, n1, x2, n2, nullparm = NULL, 
    parmtype = c("difference", "oddsratio", "ratio"), 
    conf.level = 0.95, conf.int=TRUE, 
    alternative = c("two.sided", "less", "greater"), 
    eps = 10^-8)

Arguments

x1

number of events in group 1

n1

sample size in group 1

x2

number of events in group 2

n2

sample size in group 2

nullparm

value of the parameter of interest at null, default of NULL gives 0 for parmtype='difference' and 1 for parmtype='ratio' or 'oddsratio'

parmtype

type of parameter of interest, one of "difference", "ratio" or "oddsratio" (see details)

conf.level

confidence level

conf.int

logical, calculate confidence intervals?

alternative

alternative hypothesis, one of "two.sided", "less", or "greater" (see details)

eps

small number used to adjust numeric integration (see note)

Value

• An object of class 'htest'. A list with elements
• statistic
  proportion of events in group 1
• parameter
  proportion of events in group 2
• p.value
  p-value
• conf.int
  confidence interval
• estimate
  estimate of g(p1,p2) by plugging in sample proportions, i.e., unconditional MLE
• null.value
  value of g(p1,p2) under null
• alternative
  type of alternative hypothesis
• method
  description of test
• data.name
  character explicit description of data

Details

Assume X1~ Binomial(n1,p1) and X2~Binomial(n2,p2). We want to test hypotheses on a function of p1 and p2. The functions are given by parmtype: difference tests p2-p1, ratio tests p2/p1, and odds ratio tests p2(1-p1)/(p1(1-p2)). Let g(p1,p2) be one of the three functions. So when alternative is "less" we test H0: g(p1,p2) >= nullparm vs. H1: g(p1,p2)

References

Fay, MP, Proschan, MA, and Brittain, E (2014) Combining One Sample Confidence Procedures for Inferences in the Two Sample Case (to appear in Biometrics).

Examples

# Note the p-value for all tests of equality 
# (Null Hypthesis: true prop 1=true prop 2)
# are the same, and equal to the 
# Fisher's exact (central) p-value
binomMeld.test(3,5,1,8,parmtype="difference")
binomMeld.test(3,5,1,8,parmtype="ratio")
# note that binomMeld.test gives the unconditional MLE 
# for the odds ratio, while fisher.test and exact2x2 
# gives the conditional MLE for the odds ratio
# (also fisher.test gives the odds ratio defined as 
#  the inverse of how it is defined in binomMeld.test)
binomMeld.test(3,5,1,8,parmtype="oddsratio")
exact2x2(matrix(c(1,8-1,3,5-3),2,2),tsmethod="central")