The skeleton does not have to be related to the actual doses or the probabilities of DLTs at the actual doses, but rather is selected to yield good operating characteristics of the CRM as described in Lee and Cheung [
12]. It has been shown by several authors [
12,
13] that CRM designs are robust and efficient with the implementation of “reasonable” skeletons. O’Quigley and Zohar [
13] define a “reasonable” skeleton as one that demonstrates good robustness properties in terms of its operating characteristics. It is relatively straightforward to have an intuitive idea about whether or not a skeleton is “reasonable.” For instance, the “unreasonable” skeleton
α
k
= {0.12, 0.20, 0.21, 0.22, 0.36} would have trouble distinguishing between levels 2, 3 and 4. Similarly, the skeleton
α
k
= {0.01, 0.20, 0.85, 0.90, 0.95} would encourage experimentation at level 2 when targeting a DLT probability of
θ = 0.20. This will likely have poor operating characteristics if the true MTD is any dose other than level 2.
To generate reasonable skeletons, we can rely on the algorithm of Lee and Cheung [
12] to produce adequate spacing between skeleton values at neighboring doses, without having to rely on a clinician’s estimate at every dose level. The algorithm is available as a function,
getprior, within the R package
dfcrm and requires four pieces of information in order to generate the skeleton; the prior MTD (
ν), the target toxicity rate (
θ), the number of dose levels (
K), and a spacing measure (
δ) of the skeleton. The values of
θ and
K are pre-specified. Pan and Yuan [
14] showed that skeletons produced by the algorithm of Lee and Cheung [
12] are invariant to the specification of the prior location of the MTD
ν, indicating that skeletons obtained by using different values of
ν are equivalent. The work conducted in calibrating a skeleton and prior in Bayesian CRM [
12,
15] has been focused on setting the prior MTD to be the median dose, so we lean on this approach in the web application. As for
δ, based on simulation results in Cheung [
9], the optimal range of
δ is [0.04, 0.08] for
θ = 0.20, 0.25 and [0.04, 0.10] for
θ = 0.33. A value of
δ = 0.05 lies in the optimal range for common values of
θ, and thus will result in reasonable skeletons in many practical situations. Using this information, we can generate skeleton values using the
getprior function in R package
dfcrm (i.e
getprior(
δ,
θ,
ν,
k)).