get.decision.obd.kb {Keyboard}R Documentation

Boundary Table and Decision Matrix for Phase I/II Trials.

Description

This function generates a boundary table and decision matrix for single-agent phase I/II trials using Keyboard design.

Usage

get.decision.obd.kb(
  toxicity.low,
  toxicity.moderate,
  toxicity.high,
  efficacy.low,
  efficacy.moderate,
  efficacy.high,
  target.toxicity,
  target.efficacy,
  cohortsize,
  ncohort,
  cutoff.eli.toxicity = 0.95,
  cutoff.eli.efficacy = 0.3
)

Arguments

toxicity.low

The upper boundary for the low toxicity interval.

toxicity.moderate

The upper boundary for the moderate toxicity interval.

toxicity.high

The upper boundary for the high toxicity interval.

efficacy.low

The upper boundary for the low efficacy interval.

efficacy.moderate

The upper boundary for the moderate efficacy interval.

efficacy.high

The upper boundary for the high efficacy interval.

target.toxicity

The target DLT rate.

target.efficacy

The target efficacy rate.

cohortsize

The number of patients in the cohort.

ncohort

The total number of cohorts.

cutoff.eli.toxicity

The cutoff value to eliminate a dose with an unacceptably high toxicity for safety. The default value is 0.95.

cutoff.eli.efficacy

The cutoff value to eliminate a dose with unacceptably low efficacy. The default value is 0.3.

Details

The Keyboard design relies on the posterior distribution of the toxicity and efficacy to guide dosage transition. To determine whether to escalate or de-escalate the dose given the observed data at the current dose and a boundary table by investigators, we identify the interval that has the highest joint unit probability mass, which we refer to as the winner key. The decision corresponding to the winner key is the decision for dose assignment.

The prespecified boundary table is determined by the investigators. The four subintervals for toxicity are low, moderate, high, and unacceptable. Generating these four intervals requires three investigators-provided boundaries, which can be specified as follows:

  1. The low interval for toxicity is (0, toxicity.low); toxicity.low is the upper boundary for the low toxicity interval, which can be specified by using the argument toxicity.low.

  2. The moderate interval for toxicity is (toxicity.low, toxicity.moderate); toxicity.low is the upper boundary for the low toxicity interval, which can be specified by using the argument toxicity.low and toxicity.moderate is the upper boundary for the moderate toxicity interval, which can be specified by using the argument toxicity.moderate.

  3. The high interval for toxicity is (toxicity.moderate, toxicity.high); toxicity.moderate is the upper boundary for the moderate toxicity interval, which can be specified by using the argument toxicity.moderate and toxicity.high is the upper boundary for the high toxicity interval, which can be specified by using the argument toxicity.high.

  4. The unacceptable interval for toxicity is (toxicity.high, 1); toxicity.high is the upper boundary for the high toxicity interval, which can be specified by using the argument toxicity.high.

Similarly, there are four subintervals for efficacy as follows:

  1. The low interval for efficacy is (0, efficacy.low); efficacy.low the upper boundary for the low efficacy interval, which can be specified by using the argument efficacy.low.

  2. The moderate interval for efficacy is (efficacy.low, efficacy.moderate); efficacy.low is the upper boundary for the low efficacy interval, which can be specified by using the argument efficacy.low and efficacy.moderate is the upper boundary for the moderate efficacy interval, which can be specified by using the argument efficacy.moderate.

  3. The high interval for efficacy is (efficacy.moderate, efficacy.high); efficacy.moderate is the upper boundary for the moderate efficacy interval, which can be specified by using the argument efficacy.moderate and efficacy.high is the upper boundary for the high efficacy interval, which can be specified by using the argument efficacy.high.

  4. The superb interval for efficacy is (efficacy.high, 1); efficacy.high is the upper boundary for the high efficacy interval, which can be specified by using the argument efficacy.high.

One could suppose that there are d doses in the trial and the current dose is i. Define the number of patients as n_i, the number of patients who experienced toxicity as x_i and the number of responses as y_i. The trial data can be represented as follows:

D= (n_i, x_i, y_i), i = 1, ..., d

Assuming that the toxicity probability is p_i and the efficacy probability is q_i at dose level i, the probability unit intervals for toxicity and efficacy can be partitioned in to subintervals (a, b) and (c,d). (a, b) is the subinterval for toxicity probability, and (c, d) is the subinterval for efficacy probability. (a, b) x (c,d) is one combination interval. There are 16 combination intervals in total given the 4 subintervals for toxicity rate and the 4 subintervals for efficacy intervals. Investigators would then be required to provide 16 decisions that correspond to these 16 combination intervals. Decision "D" denotes de-escalation, so the next cohort of patients will be treated at the next lower dose level. Decision "E" denotes escalation, so the next cohort of patients will be treated at the next higher dose level. Decision "S" denotes stay, so the next cohort of patients will be treated at the current dose level. The following is an example of a prespecified boundary table with a target toxicity rate of 0.2 and a target efficacy rate of 0.4:

Efficacy.low Efficacy.moderate Efficacy.high Efficacy.superb
(0,0.25) (0.25,0.45) (0.45,0.65) (0.65,1)
Toxicity.low (0,0.15) E E E E
Toxicity.moderate (0.15,0.25) E E E S
Toxicity. high (0.25,0.35) D S S S
Toxicity. unaccpetable (0.35,1.0) D D D D

For example, the combination interval (0.25,0.35) x (0,0.25) corresponds to decision "D". Therefore the next cohort of patients will be treated at the next lower level if the observed toxicity rate of the current dose falls in (0.25,0.35) and the observed efficacy rate falls in (0,0.25).

Bayesian rule is used to calculate the joint unit probability mass (JUPM) for the toxicity and efficacy combination intervals. For a given combination interval, JUPM is calculated as follows:

JUPM_{(a,b)}^{(c,d)} =Pr{p_j \in (a,b), q_j \in (c,d) | D} / (b-a)*(d-c)

Pr{p_j \in (a,b), q_j \in (c,d) | D} is the posterior probability of p_i and q_i falling in the subinterval (a,b) and (c,d). Assume the priors for both p_i and q_i follow independent beta distributions beta(\alpha_p,\beta_p) and beta(\alpha_q,\beta_q) independently. The posterior distributions for p_i and q_i are beta(\alpha_p + x_i,\beta_p + n_i - x_i) and beta(\alpha_q + y_i,\beta_q + n_i - y_i). Using these posterior distributions, calculate the JUPM for all 16 combination intervals and find the winning combination interval (a*,b*) and (c*,d*) with the largest JUPM. The decision that corresponds with this winning combination interval is used to treat the next cohort of patients.

Two dose exclusion rules are applied in the trial design: safety rule and futility rule. Safety rule: if at least 3 patients have been treated at a given dose and the observed data indicate that the probability of the current dose's toxicity rate exceeding the target toxicity rate is more than 95%, then we eliminate the current dose and any higher doses from the trial to avoid exposing future patients to unacceptably toxic doses. The probability threshold can be specified with cutoff.eli.toxicity. When a dose is eliminated, the design recommends the next lower dose for treating the next cohort of patients. If the lowest dose is unacceptably toxic, then the trial terminates early and no dose is selected as the OBD. This corresponds to a dose assignment of "DUT", which means to de-escalate due to unacceptable high toxicity and exclude the current dose and any dose higher than this dose from the trial.

Futility rule: if at least 3 patients have been treated at a given dose and the observed data indicate that the probability of the current dose's efficacy rate exceeding the target efficacy rate is less than 30%, then we eliminate this dose from the trial to avoid exposing future patients to these futile doses. The probability threshold can be specified with cutoff.eli.efficacy. This corresponds to two possible dose assignments: "EUE" and "DUE", which both exclude the current dose from the trial. "EUE" denotes escalation due to unacceptable low efficacy; "DUE" denotes de-escalation due to unacceptable low efficacy.

An attractive feature of the Keyboard design is that its dose escalation and de-escalation rule can be tabulated before implementing the trial. Thus, when conducting the trial, no real-time calculation or model fitting is needed, and we need to count only the number of patients, the number of DLTs, and the number of responses observed at the current dose and the decision to escalate or des-escalate the dose based on the pre-tabulated decision rules.

Value

get.decision.obd.kb() returns a prespecified boundary table and a dose assignment decision matrix:

  1. Prespecified boundary table ($boundary.table)

  2. Decision matrix ($decision.matrix)

Note

This method is adopted from Li et al (2017)

Author(s)

Xiaomeng Yuan, Chen Li, Hongying Sun, Li Tang and Haitao Pan

References

Li DH, Whitmore JB, Guo W, Ji Y. Toxicity and efficacy probability interval design for phase I adoptive cell therapy dose-finding clinical trials. Clinical Cancer Research. 2017; 23:13-20. https://clincancerres.aacrjournals.org/content/23/1/13.long

See Also

Other single-agent phase I/II functions: get.decision.obd2.kb(), get.oc.obd.kb(), get.oc.obd2.kb(), select.obd.kb()

Examples


 toxicity.low <- 0.15
 toxicity.moderate <- 0.25
 toxicity.high <- 0.35
 efficacy.low <- 0.25
 efficacy.moderate <- 0.45
 efficacy.high <- 0.65
 target.toxicity <- 0.20
 target.efficacy <- 0.40
 cohortsize <- 3
 ncohort <- 10

 decision.obd <- get.decision.obd.kb( toxicity.low = toxicity.low,
                 toxicity.moderate= toxicity.moderate,
                 toxicity.high = toxicity.high,
                 efficacy.low = efficacy.low,
                 efficacy.moderate = efficacy.moderate,
                 efficacy.high = efficacy.high,
                 target.toxicity=target.toxicity,
                 target.efficacy=target.efficacy,
                 cohortsize=cohortsize, ncohort=ncohort)
 print(decision.obd)
[Package Keyboard version 0.1.3 Index]