Using an Interaction Parameter in Model-Based Phase I Trials for Combination Treatments? A Simulation Study

Abstract

There is growing interest in Phase I dose-finding studies studying several doses of more than one agent simultaneously. A number of combination dose-finding designs were recently proposed to guide escalation/de-escalation decisions during the trials. The majority of these proposals are model-based: a parametric combination-toxicity relationship is fitted as data accumulates. Various parameter shapes were considered but the unifying theme for many of these is that typically between 4 and 6 parameters are to be estimated. While more parameters allow for more flexible modelling of the combination-toxicity relationship, this is a challenging estimation problem given the typically small sample size in Phase I trials of between 20 and 60 patients. These concerns gave raise to an ongoing debate whether including more parameters into combination-toxicity model leads to more accurate combination selection. In this work, we extensively study two variants of a 4-parameter logistic model with reduced number of parameters to investigate the effect of modelling assumptions. A framework to calibrate the prior distributions for a given parametric model is proposed to allow for fair comparisons. Via a comprehensive simulation study, we have found that the inclusion of the interaction parameter between two compounds does not provide any benefit in terms of the accuracy of selection, on average, but is found to result in fewer patients allocated to the target combination during the trial.

Practical recommendations for implementing a Bayesian adaptive phase I design during a pandemic

“…The rest of the parameters of the design, specifically, the prior distribution hyperparameters (i.e., the parameters of the prior distributions for θ ) and the prior estimates of toxicity at each dose, define the properties of the design – i.e., how accurate it is and how participants are allocated in the trials (e.g., conservatively or aggressively). There are two approaches for how the dose-toxicity skeleton and hyperparameters can be defined – they can be elicited from clinicians and/or historical data [ 29 ], or, if there is no available external information, via calibration [ 30 , 31 ] to determine the parameters that result in good operating characteristics over a range of plausible scenarios. Alternatively, there might be a “hybrid” approach where the clinicians can provide some constraints that the calibrated prior parameters should satisfy (e.g., the DLT risk on the starting dose is available but not for other doses).…”

“…For each combination of the prior estimates of DLT risk and hyperparameters, the proportion of correct selections (PCS) was computed for each scenario in Table 2 . Then, the geometric mean of the PCS across four scenarios was found [ 31 ]. The combination of hyperparameters yielding the highest PCS is then selected as the parameters of the operational prior.…”

Backfilling Cohorts in Phase I Dose-Escalation Studies

“…An alternative option considered here is to calibrate the values of these hyper-parameters over a small range of scenarios, to choose the values yielding the best performance across a wide range of settings (see for example Mozgunov et al [6]). We have chosen scenarios 1, 3, 4, 6, 9 and 13 to represent a diverse set of dose-response relationships.…”

A dose‐finding design for dual‐agent trials with patient‐specific doses for one agent with application to an opiate detoxification trial

“…Then the set of hyper-parameters that result in the highest geometric average of accuracy was selected for the subsequent study. 19 The ensuing values of the parameters were tried: μ 0i ¼ À4:00, À3:75, À3:50, À3:25, À3:00 f g , μ 1i ¼ 0:0, 0:05,0:15,0:30,0:40, 0:50 f g ,σ 0i ¼ 0:40, 0:50, 0:60, 0:70,0:80 f g , σ 1i ¼ 0:15, 0:25, 0:35, 0:45,0:55 f g , σ 01,i ¼ À0:10, 0:00, 0:10 f g , σ η ¼ 0:75,1:00,1:25, 1:50, 2:00, 5:00 f g . The values of hyperparameters given in Section 3.3 were found to yield the best performance in terms of the geometric mean of the average proportion of correct target dose recommendation.…”