toxbdry {clinfun}

Stopping rule for toxicity/futility monitoring

Description

Computes a stopping rule and its operating characteristics for toxicity monitoring based repeated significance testing.

Usage

toxbdry(pLo, pHi, n, cP0=0.1, cP1=0.9, ngrid=6, niter=10, delta=0,
          priority=c("null","alt"))
futilbdry(rLo, rHi, n, size=0.1, power=0.9, ngrid=3, niter=10, delta=0.5)
bdrycross.prob(n, r, ptox)
## S3 method for class 'toxbdry'
print(x, ...)
## S3 method for class 'futilbdry'
print(x, ...)

Arguments

pLo

the toxicity rate that is acceptable.

rLo

baseline (null) response rate.

pHi

the toxicity rate that is too high and hence unacceptable.

rHi

desirable response rate. Stop when it is too unlikely.

n

vector of times (sample size) when toxicty/response is monitored.

r

vector of maximum acceptable toxicities (non-responders for futility) corresponding to n.

ptox

the toxicity rates for which the operating characteristics are calculated. For futility this is the non-response rate.

cP0

boundary crossing probability under pLo i.e. type I error or the probability of declaring a treatment with toxicity rate pLo unacceptable.

cP1

boundary crossing probability under pHi i.e. power or the probability of declaring a treatment with toxicity rate pHi unacceptable.

size

probability of calling drug effective if response rate is rLo.

power

probability of calling drug effective if response rate is rHi.

ngrid

the number of toxicity rates from pLo to pHi for which the operating characteristics are computed.

niter

the number of iterations run to obtain the boundary.

delta

power determining the shape of the boundary. Should be between 0 (default) and 0.5.

priority

the error threshold to prioritize when the max sample size is too small to have both error thresholds satisfied. Default is the null i.e. error under pLo.

x

object returned by the function toxbdry.

...

additional arguments to print.

Details

The shape parameter delta is used to determine the stopping boundary with 0 corresponding to the Pocock boundary where the same significance level is used for all looks and 0.5 corresponding to the O'Brien-Fleming boundary which has smaller probability of stopping at early looks.

Default value of delta for toxicity monitoring is 0; value between 0.1 and 0.2 is a reasonable choice to make it less likely to stop early. Default values of delta for futility stopping is 0.5.

For toxicity monitoring two sets of probabilities - pstop and pcross - are given which correspond to probability of stopping early and probability of declaring the treatment too toxic with the full complement of study subjects accrued and treated.

For futility monitoring instead two sets of probabilities - pstop and peffective - are given corresponding to the probability of stopping early for futility and probability of finishing the trial and declaring it a success. Note that peffective is the complement of pcross in toxicity monitoring.

The futility boundary can have a -1 in earlier looks which means that even zero responses is not sufficient for stopping at that look.

The exact calculations in this function are done along the lines of the method in Chapter 12 of Jennison and Turnbull (2000). Ivanova, Qaqish and Schell (2005) have an illustrative paper.

Value

the function returns a list with:

looks

when toxicty is monitored - same as input n.

lo.bdry

lower boundary is a vector of maximum acceptable number of toxicities corresponding the number of subjects in n. The boundary crossing probability for this is slightly above cP0.

hi.bdry

upper boundary is a vector of maximum acceptable number of toxicities corresponding the number of subjects in n. The boundary crossing probability for this is slightly below cP0.

bdry.oc

the operating characteristics i.e the toxicity rate, the probability of crossing, stopping (i.e. cross before the last observation) and the expected sample size for both the low (lo) and high (hi) boundaries.

bdry.alpha

the alpha levels for testing at each look for the two boundaries.

stopping for toxicity is done when the number of toxicities exceeds the boundary i.e. the boundary gives the maximum acceptable number.

References

Jennison C and Turnbull BW. (2000). Group Sequential Methods with Applications to Clinical Trials. Chapman and Hall/CRC

Ivanova A, Qaqish BF and Schell MJ. (2005). Continuous Toxicity Monitoring in Phase II Trials in Oncology. Biometrics 61, 540-545.

Examples

  toxbdry(0.2, 0.35, c(20,40,60,75))
  toxbdry(0.2, 0.3, c(20,40,60,75), cP0=0.15, cP1=0.8)
  # continuous monitoring
  toxbdry(0.1, 0.3, 2:30)
  # prioritize cP1 error threshold
  toxbdry(0.1, 0.3, 2:25, priority="alt")