wilsonCI: Standard unordered-Binomial confidence interval utilities.

In assaforon/cir: Centered Isotonic Regression and Dose-Response Utilities

Standard unordered-Binomial confidence interval utilities.

Description

Standard small-sample Binomial confidence interval utilities, using the methods of Wilson, Agresti-Coull and Jeffrys.

Usage

wilsonCI(phat, n, conf = 0.9, ...)

agcouCI(phat, n, conf = 0.9, ...)

jeffCI(phat, n, conf = 0.9, w1 = 0.5, w2 = w1, ...)

Arguments

phat	numeric vector, point estimates for which an interval is sought
n	integer vector of same length, of pointwise sample sizes
conf	numeric in (0,1), the confidence level
...	pass-through for compatibility with a variety of calling functions
w1, w2	numeric, weights used in jeffCI only

Details

These functions implement the basic (uncorrected) three intervals which are seen by the consensus of literature as the "safest" off-the-shelf formulae. None of them account for ordering or monotonicity; therefore the cir package default is morrisCI which does account for that, with the 3 unordered formulae used for optional narrowing of the interval at individual points.

Value

A two-column matrix with the same number of rows as length(phat), containing the calculated lower and upper bounds, respectively.

See Also

isotInterval for more details about how forward CIs are calculated, quickInverse for inverse (dose-finding) intervals.

Examples

# Interesting run (#664) from a simulated up-and-down ensemble:
# (x will be auto-generated as dose levels 1:5)
dat=doseResponse(y=c(1/7,1/8,1/2,1/4,4/17),wt=c(7,24,20,12,17))
# The experiment's goal is to find the 30th percentile
slow1=cirPAVA(dat,full=TRUE)
# Default interval (Morris+Wilson); same as you get by directly calling 'quickIsotone'
int1=isotInterval(slow1)
# Morris without Wilson; the 'narrower=FALSE' argument is passed on to 'morrisCI'
int1_0=isotInterval(slow1,narrower=FALSE)
# Wilson without Morris
int2=isotInterval(slow1,intfun=wilsonCI)
# Agresti=Coull (the often-used "plus 2")
int3=isotInterval(slow1,intfun=agcouCI)
# Jeffrys (Bayesian-inspired) is also available
int4=isotInterval(slow1,intfun=jeffCI)

### Showing the data and the intervals
par(mar=c(3,3,4,1),mgp=c(2,.5,0),tcl=-0.25)
plot(dat,ylim=c(0,0.65),refsize=4,las=1,main="Forward-Estimation CIs") # uses plot.doseResponse()

# The true response function; true target is where it crosses the y=0.3 line
lines(seq(0,7,0.1),pweibull(seq(0,7,0.1),shape=1.1615,scale=8.4839),col=4)

lines(int1$ciLow,lty=2,col=2,lwd=2) 
lines(int1$ciHigh,lty=2,col=2,lwd=2) 

lines(int1_0$ciLow,lty=2) 
lines(int1_0$ciHigh,lty=2) 

lines(int2$ciLow,lty=2,col=3) 
lines(int2$ciHigh,lty=2,col=3) 
# Plotting the remaining 2 is skipped, as they are very similar to Wilson.

# Note how the default (red) boundaries take the tighter of the two options everywhere, 
# except for one place (dose 1 upper bound) where they go even tighter thanks to monotonicity 
# enforcement. This can often happen when sample size is uneven; since bounds tend to be 
# conservative it is rather safe to do.

legend('topleft',pch=c(NA,'X',NA,NA,NA),lty=c(1,NA,2,2,2),col=c(4,1,2,1,3),lwd=c(1,1,2,1,1),legend
=c('True Curve','Observations','Morris+Wilson (default)','Morris only','Wilson only'),bty='n')

assaforon/cir documentation built on April 7, 2024, 12:23 p.m.