Incorporating historical two‐arm data in clinical trials with binary outcome: A practical approach

Abstract

SUMMARY The feasibility of a new clinical trial may be increased by incorporating historical data of previous trials. In the particular case where only data from a single historical trial are available, there exists no clear recommendation in the literature regarding the most favorable approach. A main problem of the incorporation of historical data is the possible inflation of the type I error rate. A way to control this type of error is the so‐called power prior approach. This Bayesian method does not “borrow” the full historical information but uses a parameter 0 ≤ δ ≤ 1 to determine the amount of borrowed data. Based on the methodology of the power prior, we propose a frequentist framework that allows incorporation of historical data from both arms of two‐armed trials with binary outcome, while simultaneously controlling the type I error rate. It is shown that for any specific trial scenario a value δ > 0 can be determined such that the type I error rate falls below the prespecified significance level. The magnitude of this value of δ depends on the characteristics of the data observed in the historical trial. Conditionally on these characteristics, an increase in power as compared to a trial without borrowing may result. Similarly, we propose methods how the required sample size can be reduced. The results are discussed and compared to those obtained in a Bayesian framework. Application is illustrated by a clinical trial example.

Comments on “Incorporating historical two‐arm data in clinical trials with binary outcome: A practical approach” by Manuel Feißt, Johannes Krisam and Meinhard Kieser

“…Blue circles show the acceptance region for the test without borrowing from historical data, which is symmetrical to the diagonal c = t. Red crosses show the acceptance region using the Feißt et al approach. As also acknowledged in the Discussion of Feißt et al, 1 this acceptance region is shifted "towards the alternative," that is, pairs of (c, t) with smaller values of t for the same c lead to rejection of H 0 , compared to pairs (c, t) that lead to rejection of H 0 without borrowing.…”

“…The clinical trial example from Feißt et al 1 addresses the hypothesis test H 0 : π C = π T vs H 1 : π C 6 ¼ π T , where π C (π T ), denotes the response rate in the current control (treatment) arm. The test should be performed at the α = 0.05 level.…”

“…The probability of H 0 rejection for a pair of true response rates, (π C , π T ), in the current trial is obtained by summation of the probabilities P(c) P(t) (determined from (π C , π T )) over all points (C, T) in the rejection region. Figure 2 shows the probability of H 0 rejection, that is, the power curves, for varying current treatment response rate π T when the current control response rate π C is fixed at 0.23, the value also employed in Feißt et al 1 . Note that qualitatively equivalent graphs are obtained for other choices of π C .…”

Decision rules for identifying combination therapies in open‐entry, randomized controlled platform trials

“…We can specify whether we want to share information on the backbone monotherapy and SoC arms across the study cohorts. Several different methods have been proposed to facilitate adequate borrowing of non‐concurrent (these can be internal or external to the trial) controls 27–32 . We consider four options, all applying to both SoC and backbone monotherapy: (1) no sharing, using only data from the current cohort (see first row of Figure 2), (2) full sharing of all available data, that is, using all data 1‐to‐1 (see second row of Figure 2), (3) only sharing of concurrent data, that is, using concurrent data 1‐to‐1 (see third row of Figure 2), and (4) using a dynamic borrowing approach further described in Appendix A.1, in which the degree of shared data increases with the homogeneity of the observed data in the current cohort and the pooled observed data of all other cohorts, that is, discounting the pooled observed data of other cohorts less, if the observed response rate is similar (see fourth row of Figure 2).…”

“…Several different methods have been proposed to facilitate adequate borrowing of nonconcurrent (these can be internal or external to the trial) controls. [27][28][29][30][31][32] We consider four options, all applying to both SoC and backbone monotherapy: (1) no sharing, using only data from the current cohort (see first row of Figure 2), (2) full sharing of all available data, that is, using all data 1-to-1 (see second row of Figure 2), (3) only sharing of concurrent data, that is, using concurrent data 1-to-1 (see third row of Figure 2), and (4) using a dynamic borrowing approach further described in Appendix A.1, in which the degree of shared data increases with the homogeneity of the observed data in the current cohort and the pooled observed data of all other cohorts, that is, discounting the pooled observed data of other cohorts less, if the observed response rate is similar (see fourth row of Figure 2). Whenever a new cohort enters the platform trial, a key design element is the allocation ratio to the newly added arms (combination therapy, add-on monotherapy, backbone monotherapy and SoC) and whether the allocation ratio of the already ongoing cohorts should be changed as well, for example, randomizing less patients to backbone monotherapy and SoC in case this data is shared across cohorts.…”