A new dose-finding design for bivariate outcomes

For some drugs, toxicity events lead to early termination of treatment before a therapeutic response is observed. That is, there are three possible outcomes: toxicity (therapeutic response unknown), therapeutic response without toxicity, and no response with no toxicity. The optimal dose is the dose that maximizes the probability of the joint event, response, and no toxicity. The optimal safe dose is the dose, from among the doses with toxicity rate less than the maximum tolerable level, that maximizes the probability of response and no toxicity. We present a new sequential design to maximize the number of subjects assigned in the neighborhood of the optimal safe dose in a dose-finding trial with two outcomes.     

Retrospective analysis of sequential dose-finding designs

The continual reassessment method (CRM) is a dose-finding design using a dynamic sequential updating scheme. In common with other dynamic schemes the method estimates a current dose level corresponding to some target percentile for experimentation. The estimate is based on all included subjects. This continual reevaluation is made possible by the use of a simple model. As it stands, neither the CRM, nor any of the other dynamic schemes, allow for the correct estimation of some target percentile, based on retrospective data apart from the exceptional situation in which the simplified model exactly generates the observations. In this article we focus on the very specific issue of retrospective analysis of data generated by some arbitrary mechanism and subsequently analyzed via the continual reassessment method. We show how this can be done consistently. The proposed methodology is not restricted to that particular design and is applicable to any sequential updating scheme in which dose levels are associated with percentiles via model inversion.     

Dose-Finding Designs for HIV Studies

We present a class of simple designs that can be used in early dose-finding studies in HIV. Such designs, in contrast with Phase I designs in cancer, have a lot of the Phase II flavor about them. Information on efficacy is obtained during the trial and is as important as that relating to toxicity. The designs proposed here sequentially incorporate the information obtained on viral reduction. Initial doses are given from some fixed range of dose regimens. The doses are ordered in terms of their toxic potential. At any dose, a patient can have one of three outcomes: inability to take the treatment (toxicity), ability to take the treatment but insufficient reduction in viral load (viral failure), and ability to take the treatment as well as a sufficient reduction of viral load (success). A clear goal for some class of designs would be the identification of the dose leading to the greatest percentage of successes. Under certain assumptions, which we identify and discuss, we can obtain efficient designs for this task. Under weaker, sometimes more realistic assumptions, we can still obtain designs that have good operating characteristics in identifying a level, if such a level exists, having some given or greater success rate. In the absence of such a level, the designs will come to an early closure, indicating the ineffectiveness of the new treatment.     

Continual reassessment method for ordered groups

We investigate the two-group continual reassessment method for a dose-finding study in which we anticipate some ordering between the groups. This is a situation in which, for either group, we have little or almost no knowledge about which of the available dose levels will correspond to the maximum tolerated dose (MTD), but we may have quite strong knowledge concerning which of the two groups will have the higher level of MTD, if indeed they do not have the same MTD. The motivation for studying this problem came from an investigation into a new therapy for acute leukemia in children. The background to this study is discussed. There were two groups of patients: one group already received heavy prior therapy while the second group had received relatively much lighter prior therapy. It was therefore anticipated that the second group would have an MTD higher or at least as high as the first. Generally, likelihood methods or, equivalently, the use of noninformative Bayes priors, can be used to model the main aspects of the study, i.e., the MTD for one of the groups, reserving more informative Bayes modeling to be applied to the secondary features of the study. These secondary features may simply be the direction of the difference between the MTD levels for the two groups or, possibly, information on the potential gap between the two MTDs.     

Dose-finding with two agents in Phase I oncology trials

We propose an adaptive two-stage Bayesian design for finding one or more acceptable dose combinations of two cytotoxic agents used together in a Phase I clinical trial. The method requires that each of the two agents has been studied previously as a single agent, which is almost invariably the case in practice. A parametric model is assumed for the probability of toxicity as a function of the two doses. Informative priors for parameters characterizing the single-agent toxicity probability curves are either elicited from the physician(s) planning the trial or obtained from historical data, and vague priors are assumed for parameters characterizing two-agent interactions. A method for eliciting the single-agent parameter priors is described. The design is applied to a trial of gemcitabine and cyclophosphamide, and a simulation study is presented.     

Dose-finding based on efficacy-toxicity trade-offs

We present an adaptive Bayesian method for dose-finding in phase I/II clinical trials based on trade-offs between the probabilities of treatment efficacy and toxicity. The method accommodates either trinary or bivariate binary outcomes, as well as efficacy probabilities that possibly are nonmonotone in dose. Doses are selected for successive patient cohorts based on a set of efficacy-toxicity trade-off contours that partition the two-dimensional outcome probability domain. Priors are established by solving for hyperparameters that optimize the fit of the model to elicited mean outcome probabilities. For trinary outcomes, the new algorithm is compared to the method of Thall and Russell (1998, Biometrics 54, 251-264) by application to a trial of rapid treatment for ischemic stroke. The bivariate binary outcome case is illustrated by a trial of graft-versus-host disease treatment in allogeneic bone marrow transplantation. Computer simulations show that, under a wide rage of dose-outcome scenarios, the new method has high probabilities of making correct decisions and treats most patients at doses with desirable efficacy-toxicity trade-offs.     

Dose-finding evaluation of once-daily treatment with olodaterol,a novel long-acting β2-agonist,in patients with asthma: results of a parallel-group study and a crossover study

Background

Olodaterol is a novel, inhaled long-acting β₂-agonist (LABA) with >24-hour duration of action investigated in asthma and chronic obstructive pulmonary disease.

Methods

Two multicentre studies examined the efficacy and safety of 4 weeks’ once-daily (QD) olodaterol (2, 5, 10 and 20 μg, with background inhaled corticosteroids) in patients with asthma. One randomised, double-blind, parallel-group study (1222.6; 296 patients) administered treatment in the morning. Pulmonary function tests (PFTs) were performed pre-dose (trough) and ≤3 hours post-dose (weeks 1 and 2), and ≤6 hours post-dose after 4 weeks; primary end point was trough forced expiratory volume in 1 second (FEV₁) response (change from baseline mean FEV₁) after 4 weeks. A second randomised, double-blind, placebo- and active-controlled (formoterol 12 μg twice-daily) incomplete-block crossover study (1222.27; 198 patients) administered QD treatments in the evening. PFTs were performed over a 24-hour dosing interval after 4 weeks; primary end point was FEV₁ area under the curve from 0–24 hours (AUC_0–24) response (change from study baseline [mean FEV₁] after 4 weeks).

Results

Study 1222.6 showed a statistically significant increase in trough FEV₁ response with olodaterol 20 μg (0.147 L; 95 % confidence interval [CI]: 0.059, 0.234; p = 0.001) versus placebo, with more limited efficacy and no evidence of dose response compared to placebo across the other olodaterol doses (2, 5 and 10 μg). Study 1222.27 demonstrated increases in FEV₁ AUC_0–24 responses at 4 weeks with all active treatments (p < 0.0001); adjusted mean (95 % CI) differences from placebo were 0.140 (0.097, 0.182), 0.182 (0.140, 0.224), 0.205 (0.163, 0.248) and 0.229 (0.186, 0.272) L for olodaterol 2, 5, 10 and 20 μg, respectively, and 0.169 (0.126, 0.211) for formoterol, providing evidence of increased efficacy with higher olodaterol dose. Olodaterol was generally well tolerated, with a few events associated with known sympathomimetic effects, mainly with 20 μg.

Conclusions

The LABA olodaterol has >24-hour duration of action. In patients with asthma, evidence of bronchodilator efficacy was demonstrated with statistically and clinically significant improvements in the primary end point of trough FEV₁ response measured in clinics over placebo for the highest administered dose of 20 μg in Study 1222.6, and statistically and clinically significant improvements versus placebo in FEV₁ AUC_0–24 responses at 4 weeks for all doses tested in Study 1222.27, which also exhibited a dose response. Bronchodilator efficacy was seen over placebo for all olodaterol doses for morning and evening peak expiratory flow in both studies. All doses were well tolerated.

Trial registrations

{"type":"clinical-trial","attrs":{"text":"NCT00467740","term_id":"NCT00467740"}}NCT00467740 (1222.6) and {"type":"clinical-trial","attrs":{"text":"NCT01013753","term_id":"NCT01013753"}}NCT01013753 (1222.27).

Electronic supplementary material

The online version of this article (doi:10.1186/s12931-015-0249-8) contains supplementary material, which is available to authorized users.     

A curve-free method for phase I clinical trials

Consider the problem of finding the dose that is as high as possible subject to having a controlled rate of toxicity. The problem is commonplace in oncology Phase I clinical trials. Such a dose is often called the maximum tolerated dose (MTD) since it represents a necessary trade-off between efficacy and toxicity. The continual reassessment method (CRM) is an improvement over traditional up-and-down schemes for estimating the MTD. It is based on a Bayesian approach and on the assumption that the dose-toxicity relationship follows a specific response curve, e.g., the logistic or power curve. The purpose of this paper is to illustrate how the assumption of a specific curve used in the CRM is not necessary and can actually hinder the efficient use of prior inputs. An alternative curve-free method in which the probabilities of toxicity are modeled directly as an unknown multidimensional parameter is presented. To that purpose, a product-of-beta prior (PBP) is introduced and shown to bring about logical improvements. Practical improvements are illustrated by simulation results.