cir (version 2.1.1)

deltaInverse: Calculate inverse (dose-finding) intervals, using local inversion and the Delta method

Description

Calculate left-bound to right-bound intervals for the dose point estimates, using local slopes at design points (places where observations exist) to invert the forward lower-upper bounds.

Usage

deltaInverse(
  y,
  x = NULL,
  wt = NULL,
  target = NULL,
  estfun = cirPAVA,
  intfun = morrisCI,
  conf = 0.9,
  adaptiveShrink = FALSE,
  starget = target[1],
  parabola = FALSE,
  ...
)

Arguments

y

can be either of the following: y values (response rates), a 2-column matrix with positive/negative response counts by dose, a DRtrace object or a doseResponse object.

x

dose levels (if not included in y).

wt

weights (if not included in y).

target

A vector of target response rate(s), for which the interval is needed. If NULL (default), interval will be returned for the point estimates at design points (e.g., if the forward point estimate at $x_1$ is 0.2, then the first returned interval is for the 20th percentile).

estfun

the function to be used for point estimation. Default cirPAVA.

intfun

the function to be used for initial (forward) interval estimation. Default morrisCI (see help on that function for additional options).

conf

numeric, the interval's confidence level as a fraction in (0,1). Default 0.9.

adaptiveShrink

logical, should the y-values be pre-shrunk towards an experiment's target? Recommended if data were obtained via an adaptive dose-finding design. See DRshrink.

starget

The shrinkage target. Defaults to target[1].

parabola

logical: should the confidence-interval's interpolation between points with observations follow a parabola (TRUE) creating broader intervals between observations, or a straight line (FALSE, default)?

...

additional arguments passed on to quickIsotone

Value

two-column matrix with the left and right bounds, respectively

Details

The Delta method in this application boils down to dividing the distance to the forward (vertical) bounds, by the slope, to get the left/right interval width. Slope estimates are performed by slope. An alternative method (dubbed "global") is hard-coded into quickInverse.

See Also

quickIsotone,quickInverse,isotInterval, slope; DRshrink for the shrinkage fix.

Examples

# NOT RUN {
# 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
quick1=quickIsotone(dat)
invDelta=deltaInverse(dat)

### Showing the data and the estimates
par(mar=c(3,3,4,1),mgp=c(2,.5,0),tcl=-0.25)
# Following command uses plot.doseResponse()
plot(dat,ylim=c(0.05,0.55),refsize=4,las=1,xlim=c(-1,6),main="Inverse-Estimation CIs") 

# 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)
abline(h=0.3,col=2,lty=3) ### The experiment's official target

# Forward CIs; the "global" inverse interval just draws horizontal lines between them
# To get "global" values calculated for you at specific targets, choose 'delta=FALSE' 
# when calling quickInverse()
lines(quick1$lower90conf,lty=2,col=3) 
lines(quick1$upper90conf,lty=2,col=3) 
# Note how for y=0.3, both bounds are infinite (i.e., no intersection with the horizontal line)
# unless one dares to extrapolate outside range of observations.

# Now, the default "local" inverse interval, which is finite for the range of estimated y values.
# In particular, it is finite (albeit very wide) for y=0.3.
lines(invDelta[,1],quick1$y,lty=2)
lines(invDelta[,2],quick1$y,lty=2)

legend('topleft',pch=c(NA,'X',NA,NA),lty=c(1,NA,2,2),col=c(4,1,1,3),legend=
	c('True Curve','Observations','Local Interval (default)','Forward/Global Interval'),bty='n')

# }