Adaptive treatment allocation for comparative clinical studies with recurrent events data

Abstract

In long‐term clinical studies, recurrent event data are sometimes collected and used to contrast the efficacies of two different treatments. The event reoccurrence rates can be compared using the popular negative binomial model, which incorporates information related to patient heterogeneity into a data analysis. For treatment allocation, a balanced approach in which equal sample sizes are obtained for both treatments is predominately adopted. However, if one treatment is superior, then it may be desirable to allocate fewer subjects to the less‐effective treatment. To accommodate this objective, a sequential response‐adaptive treatment allocation procedure is derived based on the doubly adaptive biased coin design. Our proposed treatment allocation schemes have been shown to be capable of reducing the number of subjects receiving the inferior treatment while simultaneously retaining a test power level that is comparable to that of a balanced design. The redesign of a clinical study illustrates the advantages of using our procedure.

Response-adaptive treatment randomization for multiple comparisons of treatments with recurrent event responses

“…The two components in the π i functions provide adequate regulation of allocation proportions, to achieve a balance between allocation according to the allocation targets ρ i (also called the allocation rule) and the avoidance of an over-imbalance of allocation proportions between the G treatments. According to the DBCD design of Hu and Zhang, 9 the allocation function for treatment i is and with this allocation function, both the resulting allocation proportion n i / n and the allocation target estimate ρ ^ i converge to the allocation target ρ i. As stressed by Gao et al, 8 adaptive allocation should not be used when the number of overall recurrent events is unacceptably low, as the resulting estimates may be unreliable. In such circumstances, the assignment remains at Stage 1, under which it follows a balanced design.…”

“…The criterion that is used is that if both prefixtruemin false( k 1 , k 2 , … , k G false) ≥ a and q > G n 0, assignment is conducted via Stage 2. The cutoff value a = 5 was used by Gao et al 8 However, this is a very conservative choice and the commencement of Stage 2 is unnecessarily deferred. In case if one of the treatments is very effective and produces no recurrent event for a very long period of time while the other treatments are yielding a lot of recurrent events, Stage 2 is not able to start under the scheme of Gao et al 8 To remedy this problem, we first lower the cutoff value a to 1 and revise the criterion for the commencement of Stage 2 to (i) q ≥ G n 0 and (ii) prefixtruemin false( k 1 , k 2 , … , k G false) ≥ a or prefixtruemax false( k 1 , k 2 , … , k G false) ≥ a normal′.…”

“…To generate a useful treatment randomization procedure for trials of treatments that elicit recurrent event responses, Gao et al 8 derived a response-adaptive treatment allocation scheme that is based on the doubly adaptive biased coin design (DBCD) framework. DBCD is a target-driven response-adaptive design that is capable of embodying optimal criteria within a randomization process.…”

“…The work of Gao et al 8 is a first attempt to develop a framework that enables the implementation of DBCD in trials with recurrent-event outcomes. However, there are two important limitations of their proposed treatment randomization scheme.…”

“…In addition, the concepts of Type I error rate and test power are no longer unique and have to be understood in a multiple testing environment. Second, Gao et al 8 only investigated a very simple patient arrival function, by assuming that individuals enter a study at a constant rate. This is a very strong assumption which hardly resembles actual clinical studies.…”