  Phase I clinical trials are essential to bringing novel therapies from
chemical development to widespread use. Traditional approaches to dose-finding
in Phase I trials, such as the '3+3' method and the Continual Reassessment
Method (CRM), provide a principled approach for escalating across dose levels.
However, these methods lack the ability to incorporate uncertainty regarding
the dose-toxicity ordering as found in combination drug trials. Under this
setting, dose-levels vary across multiple drugs simultaneously, leading to
multiple possible dose-toxicity orderings. The Partial Ordering CRM (POCRM)
extends to these settings by allowing for multiple dose-toxicity orderings. In
this work, it is shown that the POCRM is vulnerable to 'estimation incoherency'
whereby toxicity estimates shift in an illogical way, threatening patient
safety and undermining clinician trust in dose-finding models. To this end, the
Bayesian model averaged POCRM (BMA-POCRM) is proposed. BMA-POCRM uses Bayesian
model averaging to take into account all possible orderings simultaneously,
reducing the frequency of estimation incoherencies. The effectiveness of
BMA-POCRM in drug combination settings is demonstrated through a specific
instance of estimate incoherency of POCRM and simulation studies. The results
highlight the improved safety, accuracy and reduced occurrence of estimate
incoherency in trials applying the BMA-POCRM relative to the POCRM model.
