get.decision.obd2.kb {Keyboard}R Documentation

Automatic Boundary and Decision Tables for Phase I/II Trials.

Description

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

Usage

get.decision.obd2.kb(
  target.toxicity,
  target.efficacy,
  cohortsize,
  ncohort,
  cutoff.eli.toxicity = 0.95,
  cutoff.eli.efficacy = 0.3,
  decision = c("E", "E", "S", "S", "S", "S", "D", "D", "D")
)

Arguments

target.toxicity

The target toxicity 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 unacceptable high toxicity for safety. The default value is 0.95.

cutoff.eli.efficacy

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

decision

The pre-specified decision matrix for the 9 combination intervals: (low toxicity, low efficacy),(low toxicity, moderate efficacy),(low toxicity, high efficacy), (moderate toxicity, low efficacy),(moderate toxicity, moderate efficacy),(moderate toxicity, high efficacy),(high toxicity, low efficacy),(high toxicity, moderate efficacy),(high toxicity, high efficacy)

Details

The Keyboard design utilizes the posterior distributions of the toxicity and efficacy to guide dosage transition. To determine whether to escalate or de-escalate given the observed data at the current dose, we must generate a boundary table and a decision matrix. The boundary table requires a lower boundary and an upper boundary for both toxicity and efficacy and a decision matrix, which provides dose escalation or de-escalation suggestions.

A Bayesian toxicity probability interval design from Yuan's group is used to determine the lower and upper boundaries for toxicity based on the target toxicity rate.

The boundaries for efficacy are calculated based on the efficacy failure rate, which is 1-target.efficacy. The efficacy failure rate is defined as 1 - target.efficacy and treated similarly to toxicity. The lower and upper boundaries for efficacy failure are determined using a Bayesian toxicity probability interval design. To compute the lower and upper boundaries for efficacy, we use the following:

efficacy.lower.boundary = 1 - efficacy.failure.upper.boundary

efficacy.upper.boundary = 1 - efficacy.failure.lower.boundary

There are 3 subintervals for toxicity:

  1. The low interval for toxicity is (0, toxicity.lower.boundary).

  2. The moderate interval for toxicity is (toxicity.lower.boundary, toxicity.upper.boundary).

  3. The high interval for toxicity is (toxicity.upper.boundary, 1).

There are 3 subintervals for efficacy:

  1. The low interval for efficacy is (0, efficacy.lower.boundary).

  2. The moderate interval for efficacy is (efficacy.lower.boundary, efficacy.upper.boundary).

  3. The high interval for efficacy is (efficacy.upper.boundary, 1).

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 a subinterval for toxicity probability and (c, d) is a subinterval for efficacy probability. (a, b) x (c,d) is a combination interval. 3 toxicity intervals and 3 efficacy intervals result in 9 combination intervals. Besides the target toxicity rate and the target efficacy rate, a matrix is required that contains 9 decisions for these 9 combination intervals ordered as ((low toxicity, low efficacy),(low toxicity, moderate efficacy),(low toxicity, high efficacy), (moderate toxicity, low efficacy),(moderate toxicity, moderate efficacy),(moderate toxicity, high efficacy),(high toxicity, low efficacy),(high toxicity, moderate efficacy),(high toxicity, high efficacy)). Possible decisions are "E", "D","S". 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.

Shown here is an example of boundary tables designed using this method with a target toxicity rate of 0.2 and a target efficacy rate of 0.4:

Efficacy.low Efficacy.moderate Efficacy.high
(0,0.27) (0.27,0.52) (0.52,1)
Toxicity.low (0,0.16) E E S
Toxicity.moderate (0.16,0.24) S S S
Toxicity. high (0.24,1) D D D

For example, the interval combination (0, 0.16) x (0.27,0.52) corresponds to a decision "S". This means that the next cohort of patients will be treated at the current dose level if the observed toxicity rate of current dose falls in (0, 0.16) and the observed efficacy rate falls in (0.27,0.52) .

Suppose that there are d doses in the trial and that 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 shown as follows:

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

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} are the posterior probabilities of p_i and q_i falling in the subinterval (a,b) and (c,d). Assume the prior for both p_i and q_i follows independent beta distributions beta(\alpha_p,\beta_p) and beta(\alpha_q,\beta_q) respectively. 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*), which achieves the largest JUPM. The decision that corresponds to 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 given the observed data indicate that the probability of the toxicity rate of the current dose exceeding the target toxicity rate is more than 95%, we eliminate the current and any higher dose from the trial to prevent exposing future patients to with unacceptable high toxicity. 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 overly toxic, then the trial terminates early and no dose is selected as the OBD. This corresponds to a dose assignment of "DUT", which means de-escalation due to unacceptable high toxicity and excluding 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", both excluding this dose from the trial. "EUE" denotes escalation due to unacceptable low efficacy and "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 one needs to count only the number of patients, the number of DLTs, and the number of responses observed at the current dose and the desicion to escalate or de-escalate is based on the pre-tabulated decision rules.

Value

get.decision.obd2.kb() returns a prespecified boundary table and a dose assignment decision table:

  1. Boundary table ($boundary.table)

  2. Decision matrix ($decision.matrix)

Author(s)

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

References

Liu S. and Yuan, Y. Bayesian Optimal Interval Designs for Phase I Clinical Trials, Journal of the Royal Statistical Society: Series C. 2015; 64, 507-523.

Yuan Y., Hess K.R., Hilsenbeck S.G. and Gilbert M.R. Bayesian Optimal Interval Design: A Simple and Well-performing Design for Phase I Oncology Trials. Clinical Cancer Research. 2016; 22, 4291-4301.

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.obd.kb(), get.oc.obd.kb(), get.oc.obd2.kb(), select.obd.kb()

Examples


decision.obd2.kb <- get.decision.obd2.kb(target.toxicity=0.2,
           target.efficacy=0.4, cohortsize=3, ncohort=10)
 print(decision.obd2.kb)
[Package Keyboard version 0.1.3 Index]