Abstract
In many rare disease Phase II clinical trials, two objectives are of interest to an investigator: maximising the statistical power and maximising the number of patients responding to the treatment. These two objectives are competing, therefore, clinical trial designs offering a balance between them are needed. Recently, it was argued that response-adaptive designs such as families of multi-arm bandit (MAB) methods could provide the means for achieving this balance. Furthermore, response-adaptive designs based on a concept of context-dependent (weighted) information criteria were recently proposed with a focus on Shannon’s differential entropy. The information-theoretic designs based on the weighted Renyi, Tsallis and Fisher informations are also proposed. Due to built-in parameters of these novel designs, the balance between the statistical power and the number of patients that respond to the treatment can be tuned explicitly. The asymptotic properties of these measures are studied in order to construct intuitive criteria for arm selection. A comprehensive simulation study shows that using the exact criteria over asymptotic ones or using information measures with more parameters, namely Renyi and Tsallis entropies, brings no sufficient gain in terms of the power or proportion of patients allocated to superior treatments. The proposed designs based on information-theoretical criteria are compared to several alternative approaches. For example, via tuning of the built-in parameter, one can find designs with power comparable to the fixed equal randomisation’s but a greater number of patients responded in the trials.
Highlights
Consider a Phase II clinical trial with two independent treatment arms, A1 and A2, associated with unknown efficacy probabilities of a binary response
We extend the response-adaptive procedures based on a information-theoretical criteria and investigate whether other information measures, namely the Renyi, Tsallis and Fisher informations, can provide a better exploration versus exploitation trade-off compared to the previously studied Shannon’s entropy in the settings of clinical trials with a binary endpoint
Based on additional simulations, we have focused on the constrained randomised dynamic programming (CRDP) design with p = 0.9 in line with the original recommendation, since for all values of l it consistently gave an advantage in terms of PCA in return for an good performance in terms of power between the designs
Summary
Consider a Phase II clinical trial with two independent treatment arms, A1 and A2, associated with unknown efficacy probabilities of a binary response. Assume that in the example above, the probabilities P1 and P2 are considered as random variables with Beta distributions B(4, 6) and B(6, 4), and one uses the mean as the point estimate: p1 = 0.4 and p2 = 0.6 Following this strategy, the patient should be assigned to arm A2 as it corresponds to the greater success estimate. The same conclusion can be made with other measures of information, e.g., the Fisher information (Kelbert and Mozgunov, 2015a; Suhov et al, 2016) This approach is expected to lead to a high statistical power, but a low number of patients on the superior treatment as it does not account for the fact that one would like to maximise the number of treated patients. As an alternative to these MAB approaches, a response-adaptive design based on a novel information-theoretical criterion for the arm selection in sequential experiments was proposed (Mozgunov and Jaki, 2020).
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