quickInverse {cir}

Point and Interval Inverse Estimation ("Dose-Finding"), using CIR and IR

Description

Convenience wrapper for point and interval estimation of the "dose" that would generate a target "response" value, using CIR and IR.

Usage

quickInverse(
  y,
  x = NULL,
  wt = NULL,
  target,
  estfun = cirPAVA,
  intfun = morrisCI,
  delta = TRUE,
  conf = 0.9,
  resolution = 100,
  extrapolate = FALSE,
  adaptiveShrink = FALSE,
  starget = target[1],
  adaptiveCurve = 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 percentile dose estimate is needed. See Note.

estfun

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

intfun

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

delta

logical: should intervals be calculated using the delta ("local") method (default, TRUE) or back-drawn directly from the forward bounds? See Details.

conf

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

resolution

numeric: how fine should the grid for the inverse-interval approximation be? Default 100, which seems to be quite enough. See 'Details'.

extrapolate

logical: should extrapolation beyond the range of estimated y values be allowed? Default FALSE. Note this affects only the point estimate; interval boundaries are not extrapolated.

adaptiveShrink

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

starget

The shrinkage target. Defaults to target[1].

adaptiveCurve

logical, should the CIs be expanded by using a parabolic curve between estimation points rather than straight interpolation (default FALSE)? Recommended when adaptive design was used and target is not 0.5.

...

Other arguments passed on to doseFind and quickIsotone, and onwards from there.

Details

The inverse point estimate is calculated in a straightforward manner from a forward estimate, using doseFind. For the inverse interval, the default option (delta=TRUE) calls deltaInverse for a "local" (Delta) inversion of the forward intervals. If delta=FALSE, a second call to quickIsotone generates a high-resolution grid outlining the forward intervals. Then the algorithm "draws a horizontal line" at y=target to find the right and left bounds on this grid. Note that the right (upper) dose-finding confidence bound is found on the lower forward confidence bound, and vice versa. This approach is not recommended, tending to produce CIs that are too wide.

If the data were obtained from an adaptive dose-finding design and you seek to estimate a dose other than the experiment's target, note that away from the target the estimates are likely biased (Flournoy and Oron, 2019). Use adaptiveShrink=TRUE to mitigate the bias. In addition, either provide the true target as starget, or a vector of values to target, with the first value being the true target.

Value

A data frame with 4 elements:

• target The user-provided target values of y, at which x is estimated

• point The point estimates of x

• lowerPPconf,upperPPconf the interval-boundary estimates for a 'PP'=100*conf confidence interval

References

Flournoy N and Oron AP, 2020. Bias Induced by Adaptive Dose-Finding Designs. Journal of Applied Statistics 47, 2431-2442.

See Also

quickIsotone,doseFind,deltaInverse

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
inv1=quickInverse(dat, target=0.3, adaptiveShrink = TRUE, adaptiveCurve = TRUE)
# With old PAVA as the forward estimator, and without the adaptive-design corrections:
inv0=quickInverse(dat, target=0.3, estfun=oldPAVA)


### Showing the data and the estimates
par(mar=c(3,3,1,1), mgp=c(2,.5,0), tcl=-0.25)
plot(dat, ylim=c(0.05,0.55), las=1) # uses plot.doseResponse()

# The true response function; true target is where it crosses the y=0.3 line
lines(seq(1,5,0.1),pweibull(seq(1,5,0.1),shape=1.1615,scale=8.4839),col=4)
abline(h=0.3,col=2,lty=3)
# Plotting the point estimates, as "tick" marks on the y=0.3 line
lines(rep(inv1$point,2),c(0.25,0.35), lwd=1.5) # CIR
lines(rep(inv0$point,2),c(0.25,0.35),lty=2, lwd=1.5) # IR
# You could plot the CIs too, 
# Here's code to plot the CIR 90% CI as a light-green rectangle:
# rect(inv1$lower90conf,0.25,inv1$upper90conf,0.35,col=rgb(0,1,0,alpha=0.3),border=NA)
#  Intervals are plotted and interval options are explored more extensively 
#       in the 'deltaInverse' help page.

legend('topleft',pch=c(NA,'X',NA,NA),lty=c(1,NA,2,1),col=c(4,1,1,1),
	legend=c('True Curve','Observations','IR Estimate','CIR Estimate'),bty='n')