bgtCI: Confidence Intervals for One Proportion in Binomial Group...
In binGroup: Evaluation and Experimental Design for Binomial Group Testing

Description Usage Arguments Details Value Author(s) References See Also Examples

Calculates the point estimate, the exact Clopper-Pearson and Blaker CI, the Score test derived Wilson and Agresti-Coull CI, the asymptotic second-order corrected interval fo Cai and the Wald CI for a single binomial proportion estimated from a binomial group testing trial. Assumes equal group sizes, an assay method classifying a group as positive if at least one unit in the group is positive, individuals units randomly assigned to the groups.

1 2	bgtCI(n, s, y, conf.level = 0.95, alternative = "two.sided", method = "CP")

`n`	integer, specifying the number of groups (i.e. assays i.e. observations)
`s`	integer, specifying the common size of groups i.e. the number of individual units in each group
`y`	integer, specifying the number of positive groups
`conf.level`	nominal confidence level of the interval
`alternative`	character string defining the alternative hypothesis, either 'two.sided', 'less' or 'greater' where 'less' gives the only an upper bound with confidence level=conf.level 'greater' gives the only a lower bound with confidence level=conf.level and 'two.sided' gives a two-sided confidence interval with confidence level=conf.level
`method`	character string defining the method for CI calculation, where: `"CP"` is Clopper-Pearson, an exact tail interval showing symmetric coverage probability (inversion of two one-sided tests), `"Blaker"` is the Blaker interval, an exact interval, inversion of one two.sided test, therefore defined only two.sided, but shorter than the two-sided Clopper-Pearson CI. Both guarantee to contain the true parameter with at least conf.level*100 percent probability, `"AC"` is the Agresti-Coull (generalized Agresti-Coull) interval, asymptotic method, `"Score"` is Wilson Score, asymptotic method derived from inversion of the Score test, `"SOC"` is the second order corrected interval, asymptotic method for one-sided problems (for details see Cai, 2005), and `"Wald"` the Wald interval, which cannot be recommended.

This function allows the computation of confidence intervals for binomial group testing as described in Tebbs & Bilder (2004) and Schaarschmidt (2007). If an actual confidence level greater or equal to that specified in the conf.level argument shall always be guaranteed, the exact method of Clopper-Pearson (method="CP") can be recommended for one-sided and the improved method of Blaker (2000) (method="Blaker") can be recommended for two-sided hypotheses. If a mean confidence level close to that specified in the argument conf.level is required, but moderate violation of this level is acceptable, the Second-Order corrected (method="SOC"), Wilson Score (method="Score") or Agresti-Coull (method="AC") might be used (Brown, Cai, DasGupta, 2001; Cai 2005).

A list containing:

`conf.int`	a confidence interval for the proportion
`estimate`	the point estimator of the proportion

Frank Schaarschmidt

Blaker H (2000). Confidence curves and improved exact confidence intervals for discrete distributions. The Canadian Journal of Statistics 28 (4), 783-798.

Brown LD, Cai TT, DasGupta A (2001). Interval estimation for a binomial proportion. Statistical Science 16 (2), 101-133.

Cai TT (2005). One-sided confidence intervals in discrete distributions. Journal of Statistical Planning and Inference 131, 63-88.

Schaarschmidt F (2007). Experimental design for one-sided confidence intervals or hypothesis tests in binomial group testing. Communications in Biometry and Crop Science 2 (1), 32-40. http://agrobiol.sggw.waw.pl/cbcs/

Tebbs JM & Bilder CR (2004). Confidence interval procedures for the probability of disease transmission in multiple-vector-transfer designs. Journal of Agricultural, Biological and Environmental Statistics, 9 (1), 75-90.

pooledBin for asymptotic confidence intervals and bgtvs for an exact confidence interval when designs with different group sizes are used

bgtTest: for hypothesis tests in binomial group testing

# See the example in Tebbs and Bilder (2004)
# the two.sided 95-percent 
# Clopper-Pearson as default method:

bgtCI(n=24,y=3,s=7)
bgtCI(n=24,y=3,s=7,conf.level=0.95,
 alternative="two.sided", method="CP")

# other methods:
# Blaker CI is exact but shorter
# than Clopper-Pearson, only two.sided

bgtCI(n=24,y=3,s=7, alternative="two.sided",
 method="Blaker")

# the asymptotic Wilson CI might even
# be shorter: 

bgtCI(n=24,y=3,s=7, alternative="two.sided",
 method="Score")

# one-sided confidence intervals:

bgtCI(n=24,y=3,s=7, alternative="less", method="CP")

# Wilson Score interval is less conservative 
bgtCI(n=24,y=3,s=7, alternative="less", method="Score")

# the second-order corrected CI is even shorter
# in this situation:
bgtCI(n=24,y=3,s=7, alternative="less", method="SOC")