binGroup-package {binGroup} | R Documentation |
In this package, confidence intervals for the estimation of one binomial proportion from binomial group testing are provided. Additional to estimation, there are a number of functions for experimental design in the one-sample problem, based on the bias of the point estimate, the power of a test or the expected width of confidence intervals.
Frank Schaarschmidt
Maintainer: Frank Schaarschmidt <schaarschmidt@biostat.uni-hannover.de>
Key references are:
Hepworth G (1996). Exact confidence intervals for proportions estimated by group testing. Biometrics 52, 1134-1146.
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/
Swallow WH (1985). Group testing for estimating infection rates and probabilities of disease transmission. Phytopathology Vol.75, N.8, 882-889.
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, Vol.9, N.1, 75-90.
For further details, see:
Schaarschmidt, F. (2005). Group testing - design and analysis. Thesis Fachbereich Gartenbau, Universitaet Hannover. http://www.biostat.uni-hannover.de/research/thesis
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 2001, Vol.16, No.2, 101-128.
Cai, TT (2005). One-sided confidence intervals in discrete distributions. Journal of Statistical Planning and Inference 131: 63-88.
# # # 1) # Confidence intervals for designs with equal group size (pool size): # ?bgtCI # 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") # # # 2) # Confidence intervals for designs with unequal group size (pool size): # ?bgtvs # The examples of Hepworth (1996), table 5 are: bgtvs(n=c(2,3), s=c(5,2), Y=c(0,0)) bgtvs(n=c(2,3), s=c(5,2), Y=c(0,1)) # ... # # # 3) # For experimental design based on the bias of the point estimate, # ?estDesign ### Compare Table 1 in Swallow(1985), p.885: estDesign(n=10, smax=100, p.tr=0.001) estDesign(n=10, smax=100, p.tr=0.01) # # # 4) # For experimental design based on the power in a hypothesis test, # ?nDesign # ?sDesign ## We want to show that a proportion is smaller ## 0.005 (i.e. 0.5 per cent) with a power ## of 0.80 (i.e. 80 per cent) if the unknown proportion ## in the population is 0.003 (i.e. 0.3 per cent), ## thus we want to detect a delta of 0.002. ## The Clopper Pearson CI shall be used. ## The maximal group size because of limited ## sensitivity of assay might be s=20 and we ## can only afford to perform maximally 100 assays: nDesign(nmax=100, s=20, delta=0.002, p.hyp=0.005, alternative="less", method="CP", power=0.8) ## We want to show that a proportion is smaller ## than 0.005 (i.e. 0.5 ## power of 0.80 (i.e. 80 ## in the population is 0.003 (i.e. 0.3 ## delta = 0.002 shall be detected. A 95-per-cent ## Clopper-Pearson CI (corresponding to an exact test) ## shall be used. The maximal number of groups might ## be 30 where the assay sensitivity is not limited ## until groupsize s = 100. sDesign(smax=100, n=30, delta=0.002, p.hyp=0.005, alternative="less", method="CP", power=0.8) ## We might accept to detect delta=0.004, ## i.e. we accept to reject H0: p>=0.005 with ## power 80 per cent when the true proportion is 0.001: sDesign(smax=100, n=30, delta=0.004, p.hyp=0.005, alternative="less", method="CP", power=0.8) # # # # For experimental design based on the expected width of confidence intervals, # ?bgtWidth # There is a minimal expected CI length, if # group size s is increased (fixed other parameters) # the corresponding group size might be chosen: bgtWidth(n=20, s=seq(from=1, to=200, by=10), p=0.01, alternative="less", method="CP" )