Semiparametric Dose Finding Methods for Partially Ordered Drug Combinations

Drug combination is a critically important therapeutic approach for complex diseases such as cancer and HIV due to its potential for efficacy at lower, less toxic doses and the need to move new therapies rapidly into clinical trials. One of the key issues is to identify which combinations are additive, synergistic, or antagonistic. While the value of multidrug combinations has been well recognized in the cancer research community, to our best knowledge, all existing experimental studies rely on fixing the dose of one drug to reduce the dimensionality, e.g. looking at pairwise two-drug combinations, a suboptimal design. Hence, there is an urgent need to develop experimental design and analysis methods for studying multidrug combinations directly. Because the complexity of the problem increases exponentially with the number of constituent drugs, there has been little progress in the development of methods for the design and analysis of high-dimensional drug combinations. In fact, contrary to common mathematical reasoning, the case of three-drug combinations is fundamentally more difficult than two-drug combinations. Apparently, finding doses of the combination, number of combinations, and replicates needed to detect departures from additivity depends on dose–response shapes of individual constituent drugs. Thus, different classes of drugs of different dose–response shapes need to be treated as a separate case. Our application and case studies develop dose finding and sample size method for detecting departures from additivity with several common (linear and log-linear) classes of single dose–response curves. Furthermore, utilizing the geometric features of the interaction index, we propose a nonparametric model to estimate the interaction index surface by B-spine approximation and derive its asymptotic properties. Utilizing the method, we designed and analyzed a combination study of three anticancer drugs, PD184, HA14-1, and CEP3891 inhibiting myeloma H929 cell line. To our best knowledge, this is the first ever three drug combinations study performed based on the original 4D dose–response surface formed by dose ranges of three drugs.

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Bayesian dose finding in oncology for drug combinations by copula regression

Journal of the Royal Statistical Society Series C (Applied Statistics) ◽

10.1111/j.1467-9876.2009.00649.x ◽

2009 ◽

Vol 58 (2) ◽

pp. 211-224 ◽

Cited By ~ 78

Author(s):

Guosheng Yin ◽

Ying Yuan

Keyword(s):

Drug Combinations ◽

Dose Finding

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Consequences of Performing Parallel Dose Finding Trials in Heterogeneous Groups of Patients

JNCI Cancer Spectrum ◽

10.1093/jncics/pkz013 ◽

2019 ◽

Vol 3 (2) ◽

Author(s):

Bethany Jablonski Horton ◽

John O'Quigley ◽

Mark R Conaway

Keyword(s):

Maximum Tolerated Dose ◽

Dose Finding ◽

Operating Characteristics ◽

Dose Selection ◽

Partially Ordered ◽

Optimal Interval ◽

Multiple Group ◽

Ordered Groups ◽

Toxicity Risk ◽

Dose Recommendations

Abstract Patient heterogeneity, in which patients can be grouped by risk of toxicity, is a design challenge in early phase dose finding trials. Carrying out independent trials for each group is a readily available approach for dose finding. However, this often leads to dose recommendations that violate the known order of toxicity risk by group, or reversals in dose recommendation. In this manuscript, trials for partially ordered groups are simulated using four approaches: independent parallel trials using the continual reassessment method (CRM), Bayesian optimal interval design, and 3 + 3 methods, as well as CRM for partially ordered groups. Multiple group order structures are considered, allowing for varying amounts of group frailty order information. These simulations find that parallel trials in the presence of partially ordered groups display a high frequency of trials resulting in reversals. Reversals occur when dose recommendations do not follow known order of toxicity risk by group, such as recommending a higher dose level in a group of patients known to have a higher risk of toxicity. CRM for partially ordered groups eliminates the issue of reversals, and simulation results indicate improved frequency of maximum tolerated dose selection as well as treating a greater proportion of trial patients at this dose compared with parallel trials. When information is available on differences in toxicity risk by patient subgroup, methods designed to account for known group ordering should be considered to avoid reversals in dose recommendations and improve operating characteristics.

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Isotonic designs for phase I trials in partially ordered groups

Clinical Trials ◽

10.1177/1740774517722760 ◽

2017 ◽

Vol 14 (5) ◽

pp. 491-498 ◽

Cited By ~ 4

Author(s):

Mark Conaway

Keyword(s):

Risk Groups ◽

Cytotoxic Agents ◽

Dose Finding ◽

Fixed Dose ◽

Phase I Trials ◽

Partially Ordered ◽

Ordered Groups ◽

Wide Range ◽

Order Restricted ◽

Increasing Function

Background/aims: Dose-finding trials can be conducted such that patients are first stratified into multiple risk groups before doses are allocated. The risk groups are often completely ordered in that, for a fixed dose, the probability of toxicity is monotonically increasing across groups. In some trials, the groups are only partially ordered. For example, one of several groups in a trial may be known to have the least risk of toxicity for a given dose, but the ordering of the risk among the remaining groups may not be known. The aim of the article is to introduce a method for designing dose-finding trials of cytotoxic agents in completely or partially ordered groups of patients. Methods: This article presents a method for dose-finding that combines previously proposed mathematical models, augmented with results using order restricted inference. The resulting method is computationally convenient and allows for dose-finding in trials with completely or partially ordered groups. Extensive simulations are done to evaluate the performance of the method, using randomly generated dose–toxicity curves where, within each group, the risk of toxicity is an increasing function of dose. Results: Our simulations show that the hybrid method, in which order-restricted estimation is applied to parameters of a parsimonious mathematical model, gives results that are similar to previously proposed methods for completely ordered groups. Our method generalizes to a wide range of partial orders among the groups. Conclusion: The problem of dose-finding in partially ordered groups has not been extensively studied in the statistical literature. The proposed method is computationally feasible, and provides a potential solution to the design of dose-finding studies in completely or partially ordered groups.

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Shift models for dose-finding in partially ordered groups

Clinical Trials ◽

10.1177/1740774518801599 ◽

2018 ◽

Vol 16 (1) ◽

pp. 32-40 ◽

Cited By ~ 3

Author(s):

Bethany Jablonski Horton ◽

Nolan A Wages ◽

Mark R Conaway

Keyword(s):

Maximum Tolerated Dose ◽

Dose Finding ◽

Dose Selection ◽

Continual Reassessment Method ◽

Two Stage ◽

Partially Ordered ◽

Ordered Groups ◽

Continual Reassessment ◽

Meaningful Group ◽

Shift Model

Background Limited options are available for dose-finding clinical trials requiring group-specific dose selection. While conducting parallel trials for groups is an accessible approach to group-specific dose selection, this approach allows for maximum tolerated dose selection that does not align with clinically meaningful group order information. Methods The two-stage continual reassessment method is developed for dose-finding in studies involving three or more groups where group frailty order is known between some but not all groups, creating a partial order. This is an extension of the existing continual reassessment method shift model for two ordered groups. This method allows for dose selection by group, where maximum tolerated dose selection follows the known frailty order among groups. For example, if a group is known to be the most frail, the recommended maximum tolerated dose for this group should not exceed the maximum tolerated dose recommended for any other group. Results With limited alternatives for dose-finding in partially ordered groups, this method is compared to two alternatives: (1) an existing method for dose-finding in partially ordered groups which is less computationally accessible and (2) independent trials for each group using the two-stage continual reassessment method. Simulation studies show that when ignoring information on group frailty, using independent continual reassessment method trials by group, 30% of simulations would result in maximum tolerated dose selection that is out of order between groups. In addition, the two-stage continual reassessment method for partially ordered groups selects the maximum tolerated dose more often and assigns more patients to the maximum tolerated dose compared to using independent continual reassessment method trials within each group. Simulation results for the proposed method and the less computationally accessible approach are similar. Conclusion The proposed continual reassessment method for partially ordered groups ensures appropriate maximum tolerated dose order and improves accuracy of maximum tolerated dose selection, while allowing for trial implementation that is computationally accessible.

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