title: Dose-finding design for multi-drug combinations.
abstract: BACKGROUND
  Most of the current designs used for Phase I dose finding trials in oncology will either involve only a single cytotoxic agent or will impose some implicit ordering among the doses. The goal of the studies is to estimate the maximum tolerated dose (MTD), the highest dose that can be administered with an acceptable level of toxicity. A key working assumption of these methods is the monotonicity of the dose-toxicity curve.
  
  
  OBJECTIVE
  Here we consider situations in which the monotonicity assumption may fail. These studies are becoming increasingly common in practice, most notably, in phase I trials that involve combinations of agents. Our focus is on studies where there exist pairs of treatment combinations for which the ordering of the probabilities of a dose-limiting toxicity cannot be known a priori.
  
  
  METHODS
  We describe a new dose-finding design which can be used for multiple-drug trials and can be applied to this kind of problem. Our methods proceed by laying out all possible orderings of toxicity probabilities that are consistent with the known orderings among treatment combinations and allowing the continual reassessment method (CRM) to provide efficient estimates of the MTD within these orders. The design can be seen to simplify to the CRM when the full ordering is known.
  
  
  RESULTS
  We study the properties of the design via simulations that provide comparisons to the Bayesian approach to partial orders (POCRM) of Wages, Conaway, and O'Quigley. The POCRM was shown to perform well when compared to other suggested methods for partial orders. Therefore, we comapre our approach to it in order to assess the performance of the new design.
  
  
  CONCLUSIONS
  A limitation concerns the number of possible orders. There are dose-finding studies with combinations of agents that can lead to a large number of possible orders. In this case, it may not be feasible to work with all possible orders.
  
  
  CONCLUSIONS
  The proposed design demonstrates the ability to effectively estimate MTD combinations in partially ordered dosefinding studies. Because it relaxes the monotonicity assumption, it can be considered a multivariate generalization of the CRM. Hence, it can serve as a link between single and multiple-agent dosefinding trials.
authors.affiliation: Department of Mathematics and Computer Science, Hampden-Sydney College, Hampden-Sydney, Virginia 23943, USA. nwages@hsc.edu
authors.forename: Nolan A
authors.initials: NA
authors.lastname: Wages
authors.forename: Mark R
authors.initials: MR
authors.lastname: Conaway
authors.forename: John
authors.initials: J
authors.lastname: O'Quigley
mesh_terms: D000971:Antineoplastic Combined Chemotherapy Protocols / Q000633:toxicity*; D001499:Bayes Theorem; D017321:Clinical Trials, Phase I as Topic / Q000379:methods* / Q000706:statistics & numerical data; D003198:Computer Simulation; D004305:Dose-Response Relationship, Drug; D064420:Drug-Related Side Effects and Adverse Reactions; D006801:Humans; D020714:Maximum Tolerated Dose; D012107:Research Design