Bayesian hierarchical EMAX model for dose‐response in early phase efficacy clinical trials

Abstract

A primary goal of a phase II dose-ranging trial is to identify a correct dose before moving forward to a phase III confirmatory trial. A correct dose is one that is actually better than control. A popular model in phase II is an independent model that puts no structure on the dose-response relationship. Unfortunately, the independent model does not efficiently use information from related doses.One very successful alternate model improves power using a pre-specified dose-response structure. Past research indicates that EMAX models are broadly successful and therefore attractive for designing dose-response trials. However, there may be instances of slight risk of nonmonotone trends that need to be addressed when planning a clinical trial design. We propose to add hierarchical parameters to the EMAX model. The added layer allows information about the treatment effect in one dose to be "borrowed" when estimating the treatment effect in another dose. This is referred to as the hierarchical EMAX model. Our paper compares three different models (independent, EMAX, and hierarchical EMAX) and two different design strategies. The first design considered is Bayesian with a fixed trial design, and it has a fixed schedule for randomization. The second design is Bayesian but adaptive, and it uses response adaptive randomization. In this article, a randomized trial of patients with severe traumatic brain injury is provided as a motivating example. 3123 3124 GAJEWSKI ET AL.whereby individual doses are considered independent and for analysis purposes are individually compared to each other and to control. This pairwise independent model has no structure between doses. From the Bayesian framework when using a flat prior, this independent model has similar properties to several Fisher's exact tests for categorical data. 1 This lack of structure between the doses can have inefficiencies when there is smoothness to the dose-response curve. This can result in lower power for identification of the correct dose, as well as wider intervals relative to alternative model strategies. The risk of assuming a relationship is the misspecification of the model, potentially leading to poor inferences.Alternatively, with the addition of assumptions regarding the dose response relationship into the modeling framework (ie, response improves with increasing dose up to some threshold), there can be improved precision in the estimation of the efficacy at each dose, leading to better dose selection and better go/no-go decision. There are many options for the functional form of models that one can choose for inferences, including, but not limited to, EMAX, logistic, double logistic, exponential, normal dynamic linear, and quadratic. 2 While all of these models have their particular benefits and drawbacks depending on the true functional form, the EMAX model with "Hill" parameter close to 1.0 * has been shown to provide good empirical fit for designing and analyzing dose-response data across a wide range of pharmaceutical studies. 3 The impressive empiri...

Comparison of hierarchical EMAX and NDLM models in dose-response for early phase clinical trials

“…This is a phase II Bayesian clinical trial for selecting the best dose of hyperbaric oxygen treatment, which produces the greatest improvement in the rate of good neurological outcome versus standard of care for subjects with severe traumatic brain injury (TBI). A second goal of this phase II trial is to determine whether there is any hyperbaric treatment that has at least a 50% probability of demonstrating improvement in the rate of good neurological outcome versus a standard treatment in a subsequent phase III confirmatory trial, assuming 500 in the control and 500 in the arm treated with the selected optimal dose regimen of hyperbaric oxygen (Gajewski et al, 2019). The allocation of this phase II trial has a fixed allocation of 20% subjects to control and equal allocation of the 80% to the seven active arms.…”

“…Table 1 summarizes the eight treatment arms involved in the trial. Dose strength as defined in Table 1 is the daily oxygen toxicity units per 100 (OTU/100) (Gajewski et al, 2019).…”

“…To identify the best dose, several statistical models have been proposed. Specifically, we are going to compare three statistical models using an illustrative example, the HOBIT trial (Gajewski et al, 2019). Then, simulation is used to investigate operating characteristics of different designs of the HOBIT trial with the goal to select the treatment arm which is most likely to perform better than the control arm.…”

“…However, there is at least one compound found in Thomas et al (2014) in which the monotonicity assumption did not hold. Therefore, to address the risk of nonmonotonicity Gajewski et al (2019) present the Bayesian hierarchical EMAX model. The hierarchical EMAX has an additional random effect hyperprior to support a more adjustable and flexible model.…”

“…In the past, however, the normal dynamic linear model (NDLM) has been a useful model to explore a nonmonotonic dose-response relationship in that the efficacy at the current dose depends on the efficacy of the previous dose(s). While previous research has compared the EMAX to the hierarchical EMAX (Gajewski et al, 2019) and the EMAX to the NDLM (Liu et al, 2019), the hierarchical EMAX has not been directly compared to the NDLM. More specifically, in previous research it has been found that under monotonicity the EMAX is better than hierarchical EMAX and NDLM; but under nonmonotonicity the hierarchical EMAX and NDLM are better than EMAX.…”