Computes a stopping rule and its operating characteristics for toxicity monitoring based repeated significance testing.
toxbdry(pLo, pHi, n, cP0=0.1, cP1=0.9, ngrid=6, niter=10, delta=0,
priority=c("null","alt"))
bdrycross.prob(n, r, ptox)
# S3 method for toxbdry
print(x, …)the toxicity rate that is acceptable.
the toxicity rate that is too high and hence unacceptable.
vector of times (sample size) when toxicty is moniroted.
vector of maximum acceptable toxicities corresponding to n.
the toxicity rates for which the operating characteristics are calculated.
boundary crossing probability under pLo i.e. type I error or the probability of declaring a treatment with toxicity rate pLo unacceptable.
boundary crossing probability under pHi i.e. power or the probability of declaring a treatment with toxicity rate pHi unacceptable.
the number of toxicity rates from pLo to pHi for which the operating characteristics are computed.
the number of iterations run to obtain the boundary.
power determining the shape of the boundary. Should be between 0 (default) and 0.5.
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.
object returned by the function toxbdry.
additional arguments to print.
the function returns a list with:
when toxicty is monitored - same as input n.
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.
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.
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.
the alpha levels for testing at each look for the two boundaries.
stopping for toxicity is done when the number of toxicities exceeda the boundary i.e. the boundary gives the maximum acceptable number.
Default value of boundary shape corresponds to the Pocock boundary where the same significance level is used for all looks. For a more conservative stopping rule use delta greater than 0 where 0.5 corresponds to the O'Brien-Fleming boundary which is extremely conservative in the early looks. Value between 0.1 and 0.2 is a reasonable compromise.
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.
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.
# NOT RUN {
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")
# }
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