A group sequential design and sample size estimation for an immunotherapy trial with a delayed treatment effect

Li, Bosheng; Su, Liwen; Gao, Jun; Jiang, Liyun; Yan, Fangrong

doi:10.1177/0962280220980780

Cited by 5 publications

(9 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Obtain the sum of the elements in every column of R and then store the obtained sum divided by B in a vector r 1 of length K in turn; afterwards, accumulate the vector r 1 in order to obtain another vector r 2 ; the elements of r 1 and r 2 are the stage-wise empirical power and cumulative empirical power, respectively; the final element of r 2 is the empirical power of the whole group sequential trial. 25,26 It is worth noting that the empirical power possesses an overall upward trend with the increase of the maximum sample size, but fluctuates in a narrow interval for a given scenario and a given maximum sample size due to the randomness of the Monte Carlo simulation. 26 According to these phenomena, we designed a search algorithm to determine the required maximum sample size, that is, the least maximum sample size of which the empirical power is robustly larger than or equal to 1 − 𝛽.…”

Section: Empirical Power Calculationmentioning

confidence: 99%

“…25,26 It is worth noting that the empirical power possesses an overall upward trend with the increase of the maximum sample size, but fluctuates in a narrow interval for a given scenario and a given maximum sample size due to the randomness of the Monte Carlo simulation. 26 According to these phenomena, we designed a search algorithm to determine the required maximum sample size, that is, the least maximum sample size of which the empirical power is robustly larger than or equal to 1 − 𝛽. A power function that is calculated by the above simulation procedure plays a role as the objective function of the search algorithm.…”

Section: Empirical Power Calculationmentioning

confidence: 99%

“…Step 3 : Repeat Step 2 for B times and store the obtained results in a

B \times K

‐dimensional matrix R by row. Obtain the sum of the elements in every column of R and then store the obtained sum divided by B in a vector

r_{1}

of length K in turn; afterwards, accumulate the vector

r_{1}

in order to obtain another vector

r_{2}

; the elements of

r_{1}

and

r_{2}

are the stage‐wise empirical power and cumulative empirical power, respectively; the final element of

r_{2}

is the empirical power of the whole group sequential trial 25,26 …”

Section: Mandm Designmentioning

confidence: 99%

See 2 more Smart Citations

M&M: A maximum duration design with the Maxcombo test for a group sequential trial of an immunotherapy with a random delayed treatment effect

et al. 2021

Statistics in Medicine

Self Cite

View full text Add to dashboard Cite

A random delayed treatment effect is expected in a confirmatory clinical trial for an immunotherapy due to the individual heterogeneity of physiological conditions. For this reason, the delay time will be assumed to follow a continuous distribution that is difficult to estimate accurately based on the early-phase data, which hinders the specification of the most powerful weighted log-rank test. Therefore, we propose a simulation-based maximum duration design with a robustly powerful Maxcombo test for a group sequential trial for the immunotherapy with the random delayed treatment effect. The design obtains the group sequential boundaries by a simulation procedure and determines the required maximum sample size using a one-dimensional search in which another simulation procedure is used to calculate empirical power. The simulation researches proved the accuracy of the group sequential boundaries and their robustness against the misspecified maximum sample sizes for large samples and revealed their moderate sensitivity against the misspecified survival distributions under the null hypothesis of no difference. The studies investigated whether the type I error rate would inflate under the "inferior" null hypothesis and evaluated the robustness against different distributions of the delay time in terms of the empirical power among the Maxcombo tests and component weighted log-rank tests.

show abstract

Section: Empirical Power Calculationmentioning

confidence: 99%

Section: Empirical Power Calculationmentioning

confidence: 99%

“…Step 3 : Repeat Step 2 for B times and store the obtained results in a

B \times K

‐dimensional matrix R by row. Obtain the sum of the elements in every column of R and then store the obtained sum divided by B in a vector

r_{1}

of length K in turn; afterwards, accumulate the vector

r_{1}

in order to obtain another vector

r_{2}

; the elements of

r_{1}

and

r_{2}

are the stage‐wise empirical power and cumulative empirical power, respectively; the final element of

r_{2}

is the empirical power of the whole group sequential trial 25,26 …”

Section: Mandm Designmentioning

confidence: 99%

See 1 more Smart Citation

M&M: A maximum duration design with the Maxcombo test for a group sequential trial of an immunotherapy with a random delayed treatment effect

et al. 2021

Statistics in Medicine

Self Cite

View full text Add to dashboard Cite

show abstract

“…Non-proportional hazards (NPH) caused by delayed treatment effect is commonly observed in cancer immunotherapy trials and in other settings. [1][2][3][4] Various proposals for accounting for NPH in the design and analysis of clinical trials have been proposed, including using the average hazard ratio as an alternative measure to replace an assumed common hazard ratio, 5 applying weighted, supremum or composite logrank tests, 6,7 and use of a ''max combo'' combination test. [8][9][10] However, most trials with a time-to-event endpoint continue to be designed and analyzed using methodology appropriate for a proportional hazards (PH) setting, including testing via an unweighted logrank test and estimation of a single hazard ratio, albeit now interpreted as an average hazard ratio over the study period.…”

Section: Introductionmentioning

confidence: 99%

Futility monitoring for randomized clinical trials with non-proportional hazards: An optimal conditional power approach

Wang

George

2023

Clinical Trials

View full text Add to dashboard Cite

Background Standard futility analyses designed for a proportional hazards setting may have serious drawbacks when non-proportional hazards are present. One important type of non-proportional hazards occurs when the treatment effect is delayed. That is, there is little or no early treatment effect but a substantial later effect. Methods We define optimality criteria for futility analyses in this setting and propose simple search procedures for deriving such rules in practice. Results We demonstrate the advantages of the optimal rules over commonly used rules in reducing the average number of events, the average sample size, or the average study duration under the null hypothesis with minimal power loss under the alternative hypothesis. Conclusion Optimal futility rules can be derived for a non-proportional hazards setting that control the loss of power under the alternative hypothesis while maximizing the gain in early stopping under the null hypothesis.

show abstract

“…In previous studies, a piecewise proportional hazards model or a piecewise exponential distribution with a threshold lag function has been employed in immunotherapy trials. [8][9][10][11] However, assuming a smooth transition in the hazard ratio seems more reasonable, given that the effective process of immunotherapy typically consists of three phases: no effect, partial effect, and full effect. 12 Building on this understanding, Ye and Yu 12 proposed a generalized linear lag function to model the three-phased delayed treatment effect and developed a general lag model describing the survival time of patients in immunotherapy trials based on this function.…”

mentioning

confidence: 99%

Group sequential design with maximin efficiency robust test for immunotherapy with generalized delayed treatment effect

Li,

Zhang,

Yang

et al. 2023

Pharmaceutical Statistics

Self Cite

View full text Add to dashboard Cite

The delayed treatment effect is a common feature of immunotherapy, characterized by a gradual onset of action ranging from no effect to full effect. In this study, we propose a generalized delayed treatment effect function to depict the delayed effective process precisely and flexibly. To reduce potential power loss caused by the delayed treatment effect in a group sequential trial, we employ the maximin efficiency robust test, which enhances power robustness across a range of possible delays. We present novel approaches based on the Markov chain method for determining group sequential boundaries, calculating the power function, and estimating the maximum sample size through iterative regressions between the square root of the maximum sample size and the normal quantile of power. Extensive simulation studies validate the effectiveness of our approaches, particularly in balanced trials, demonstrating the validity of group sequential boundaries and the accuracy of maximum sample size estimations. Additionally, we utilize a real trial as an example to compare our considered trial with group sequential trials using the log‐rank and generalized piecewise weighted log‐rank tests. The results show significantly reduced maximum sample sizes, highlighting the economic advantage of our approach.

show abstract

A group sequential design and sample size estimation for an immunotherapy trial with a delayed treatment effect

Cited by 5 publications

References 25 publications

M&M: A maximum duration design with the Maxcombo test for a group sequential trial of an immunotherapy with a random delayed treatment effect

M&M: A maximum duration design with the Maxcombo test for a group sequential trial of an immunotherapy with a random delayed treatment effect

Futility monitoring for randomized clinical trials with non-proportional hazards: An optimal conditional power approach

Group sequential design with maximin efficiency robust test for immunotherapy with generalized delayed treatment effect

Contact Info

Product

Resources

About