Bayesian interim analysis for prospective randomized studies: reanalysis of the acute myeloid leukemia HOVON 132 clinical trial

Randomized controlled trials (RCTs) are the gold standard to establish the benefit-risk ratio of novel drugs. However, the evaluation of mature results often takes many years. We hypothesized that the addition of Bayesian inference methods at interim analysis time points might accelerate and enforce the knowledge that such trials may generate. In order to test that hypothesis, we retrospectively applied a Bayesian approach to the HOVON 132 trial, in which 800 newly diagnosed AML patients aged 18 to 65 years were randomly assigned to a “7 + 3” induction with or without lenalidomide. Five years after the first patient was recruited, the trial was negative for its primary endpoint with no difference in event-free survival (EFS) between experimental and control groups (hazard ratio [HR] 0.99, p = 0.96) in the final conventional analysis. We retrospectively simulated interim analyses after the inclusion of 150, 300, 450, and 600 patients using a Bayesian methodology to detect early lack of efficacy signals. The HR for EFS comparing the lenalidomide arm with the control treatment arm was 1.21 (95% CI 0.81–1.69), 1.05 (95% CI 0.86–1.30), 1.00 (95% CI 0.84–1.19), and 1.02 (95% CI 0.87–1.19) at interim analysis 1, 2, 3 and 4, respectively. Complete remission rates were lower in the lenalidomide arm, and early deaths more frequent. A Bayesian approach identified that the probability of a clinically relevant benefit for EFS (HR < 0.76, as assumed in the statistical analysis plan) was very low at the first interim analysis (1.2%, 0.6%, 0.4%, and 0.1%, respectively). Similar observations were made for low probabilities of any benefit regarding CR. Therefore, Bayesian analysis significantly adds to conventional methods applied for interim analysis and may thereby accelerate the performance and completion of phase III trials.


SUPPLEMENTAL METHODS
Bayesian inference is a method of statistical inference using Bayes theorem to update a probability distribution of a parameter when new information is obtained.Three key concepts need to be considered including (1) the prior distribution (prior), (2) the likelihood, and (3) the posterior probability.The prior is a probability distribution that represents the prior knowledge before seeing any data.The prior can be based on previously observed data or expert opinion.
Non-informative priors can be used when no prior data or expert opinion is available.The likelihood is the probability density of the newly observed data.The posterior probability is a probability distribution based on the prior distribution combined with the likelihood of newly observed data.The posterior probability represents the updated belief of an event or hypothesis given the available evidence (Figure S6).
The commensurate prior is a Bayesian approach for dynamic borrowing (downweighing of information) proposed by Hobbs et al., which has been extended by incorporating a spike and slab prior. 1 This method centers the priors for the current data's model parameters on the corresponding parameters for the historical data, and assumes a distribution for the difference in model parameters between the current and historical data.Spike-and-slab prior distributions are used to model the variances of these parameters for the current data, conditional on the parameters of the historical data. 2 The follow-up times were censored at 60 days after the start of the second chemotherapy cycle of the last enrolled HO132 patient in the respective interim analysis.To ensure a comparable follow-up time with the HO132 (maximum follow-up time, 10, 16, 22, 28 months at interim analysis 1, 2, 3 and 4 cut-off, respectively), an analysis window from date of registration to the maximum follow-up time was applied to the HO102 control treatment arm at each simulated interim analysis, respectively.The median follow-up time was 7, 10, 12 and 16 months at each simulated interim analysis, respectively.Bayesian inference is a method of statistical inference using Bayes theorem to update a probability distribution of a parameter when new information is obtained.Three key concepts need to be considered including (1) the prior distribution (prior), (2) the likelihood, and (3) the posterior probability.The prior is a probability distribution that represents the prior knowledge before seeing any data.The prior can be based on previously observed data or expert opinion.Non-informative priors can be used when no prior data or expert opinion is available.The likelihood is the probability density of the newly observed data.The posterior probability is a probability distribution based on the prior distribution combined with the likelihood of newly observed data.The posterior probability represents the updated belief of an event or hypothesis given the available evidence.The blue bell shape in the figure depicts the posterior distribution of the HR between arms for event free survival with the median HR.The benefit threshold is set at the assumed treatment effect of HR=0.87.The arrows indicate left of the benefit threshold the probability for HR<0.87,showing the evidence for the targeted benefit of the experimental treatment arm and right of the benefit threshold the probability for HR>0.87.

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Interim The blue bell shape in the figure depicts the posterior distribution of the HR between arms for event free survival with the median HR.The benefit threshold is set at the assumed treatment effect of HR=1.00.The arrows indicate left of the benefit threshold the probability for HR<1.00,showing the evidence for the targeted benefit of the experimental treatment arm and right of the benefit threshold the probability for HR>1.00.

Figure S1 Figure S2 Figure S3 Figure S4 Figure S5 Figure S6
Figure S1Priors of HO132 control treatment arm EFS log hazard rate.

Figure S7
Figure S7Estimation of the probability for specified treatment (HR<0.87)effects by Bayesian analysis of event free survival comparing lenalidomide treatment versus control treatment with informative prior.

Figure S9 Figure S10
Figure S9 Comparison of lenalidomide treatment versus control treatment by Bayesian analysis of MRD negative patients in CR with informative prior.The blue bell shape in the figure depicts the posterior distribution of the treatment difference between arms for MRD negative patients in CR with the median treatment difference.The benefit threshold is set at no difference or zero.The arrow to the left of the benefit threshold indicates less MRD negativity in the lenalidomide treatment arm compared to the control treatment arm, thus showing the evidence favoring the control treatment arm.The arrow to the right of the benefit threshold indicates more MRD negativity in the lenalidomide treatment arm compared to the control treatment arm, thus showing the evidence favoring the lenalidomide treatment arm.A negative median indicates less MRD negativity in the lenalidomide treatment arm compared to the control treatment arm.

Table S1
Results of the interim-analyses.

Table S2
Results of the interim-analyses without external data.