An Efficient Algorithm to Determine the Optimal Two-Stage Randomized Multinomial Designs in Oncology Clinical Trials

Abstract

Sun et al. (2009) proposed an optimal two-stage randomized multinomial design that incorporates both response rate (RR) and early progression rate (EPR) in designing phase II oncology trials. However, determination of the design parameters in their approach requires evaluating huge numbers of combinations among possible values of design parameters, and thus requires highly intensive computation. In this paper we develop an efficient algorithm to identify the optimal two-stage randomized multinomial designs in phase II oncology clinical trials comparing a treatment arm to a control arm. The proposed algorithm substantially reduces the computation intensity via an approximation method. Some other techniques are also used to further improve its efficiency. Examples show that the proposed algorithm has more than a 90% reduction in computation time while having an acceptably low approximation error. This may enhance usage of the optimal two-stage multinomial design in clinical trials and also make it feasible to extend the design to more complicated scenarios.

Key Words:

• Early progression rate
• Oncology phase II clinical trials
• Response rate
• Two-stage randomized multinomial design

Acknowledgments

This paper is a follow-up

Notes

*N1 is sample size for each arm in stage 1; N2 is sample size for each arm in stage 2; E(N) is the expected total sample size for both arms. For the method of computing expected sample size, please refer to Sun et al. (2009).

**Nmax is the maximum possible number of patients needed for the trial.

^True type I and II error rates are the actual type I and II error rates of the proposed optimal design.

^#Approximation error for computing “true type I error rate” and “true type II error rate.”

*N1 is sample size for each arm in stage 1; N2 is sample size for each arm in stage 2; E(N) is the expected total sample size for both arms. For the method of computing expected sample size, please refer to Sun et al. (2009).

**Nmax is the maximum possible number of patients needed for the trial.

^True type I and II error rates are the actual type I and II errors rates of the proposed optimal design.

^#Approximation error for computing “true type I error rate” and “true type II error rate.”

*N1 is sample size for each arm in stage 1; N2 is sample size for each arm in stage 2; E(N) is the expected total sample size for both arms. For the method of computing expected sample size, please refer to Sun et al. (2009).

**Nmax is the maximum possible number of patients needed for the trial.

^True type I and II error rates are the actual type I and II errors rates of the proposed optimal design.

^#Approximation error for computing “true type I error rate” and “true type II error rate.”

This paper is a follow-up communication to Sun et al. (2009).