Bayesian hybrid dose-finding design in phase I oncology clinical trials

In oncology, dose escalation is often carried out to search for the maximum tolerated dose (MTD) in phase I clinical trials. We propose a Bayesian hybrid dose-finding method that inherits the robustness of model-free methods and the efficiency of model-based methods. In the Bayesian hypothesis testing framework, we compute the Bayes factor and adaptively assign a dose to each cohort of patients based on the adequacy of the dose-toxicity information that has been collected thus far. If the data observed at the current treatment dose are adequately informative about the toxicity probability of this dose (e.g. whether this dose is below or above the MTD), we make the decision of dose assignment (e.g. either to escalate or to de-escalate the dose) directly without assuming a parametric dose-toxicity curve. If the observed data at the current dose are not sufficient to deliver such a definitive decision, we resort to a parametric dose-toxicity curve, such as that of the continual reassessment method (CRM), in order to borrow strength across all the doses under study to guide dose assignment. We examine the properties of the hybrid design through extensive simulation studies, and also compare the new method with the CRM and the '3 + 3' design. The simulation results show that our design is more robust than parametric model-based methods and more efficient than nonparametric model-free methods.     

The continual reassessment method and its applications: a Bayesian methodology for phase I cancer clinical trials

We discuss the continual reassessment method (CRM) and its extension with practical applications in phase I and I/II cancer clinical trials. The CRM has been proposed as an alternative design of a traditional cohort design and its essential features are the sequential (continual) selection of a dose level for the next patients based on the dose-toxicity relationship and the updating of the relationship based on patients' response data using Bayesian calculation. The original CRM has been criticized because it often tends to allocate too toxic doses to many patients and our proposal for overcoming this practical problem is to monitor a posterior density function of the occurrence of the dose limiting toxicity (DLT) at each dose level. A simulation study shows that strategies based on our proposal allocate a smaller number of patients to doses higher than the maximum tolerated dose (MTD) compared with the original method while the mean squared error of the probability of the DLT occurrence at the MTD is not inflated. We present a couple of extensions of the CRM with real prospective applications: (i) monitoring efficacy and toxicity simultaneously in a combination phase I/II trial; (ii) combining the idea of pharmacokinetically guided dose escalation (PKGDE) and utilization of animal toxicity data in determining the prior distribution. A stopping rule based on the idea of separation among the DLT density functions is discussed in the first example and a strategy for determining the model parameter of the dose-toxicity relationship is suggested in the second example.     

Escalation with overdose control for phase I drug‐combination trials

Dose finding for combined drugs has grown rapidly in oncology drug development. The escalation with overdose control (EWOC) method is a popular model‐based dose‐finding approach to single‐agent phase I clinical trials. When two drugs are combined as a treatment, we propose a two‐dimensional EWOC design for dose finding on the basis of a four‐parameter logistic regression model. During trial conduct, we continuously update the posterior distribution of the maximum tolerated dose (MTD) combination to find the most appropriate dose combination for each cohort of patients. The probability that the next assigned dose combination exceeds the MTD combination can be controlled by a feasibility bound, which is based on a prespecified quantile level of the MTD distribution such as to reduce the possibility of overdosing. We determine dose escalation, de‐escalation, or staying at the same doses by searching the MTD combination along the rows and columns in a two‐drug combination matrix, respectively. We conduct simulation studies to examine the performance of the two‐dimensional EWOC design under various practical scenarios, and illustrate it with a trial example. Copyright © 2013 John Wiley & Sons, Ltd.     

A dose‐finding approach based on shrunken predictive probability for combinations of two agents in phase I trials

We develop a novel dose‐finding method for two‐agent combination phase I trials on the basis of the shrunken predictive probability of toxicity. In this method, a shrinkage logistic regression model that allows distinct shrinkage multipliers for the coefficients of the main effects of two agents and their interaction on the probability of toxicity constructs the toxicity outcome. We also propose dose‐escalation/de‐escalation decision rules on the basis of the shrunken predictive probability of toxicity. Simulation studies under various patterns of monotonic dose‐response relationships for combinations of two agents demonstrated that the proposed method performed no worse than the existing two dose‐finding methods we selected. Copyright © 2013 John Wiley & Sons, Ltd.     

AN EXTENSION OF THE CONTINUAL REASSESSMENT METHODS USING A PRELIMINARY UP-AND-DOWN DESIGN IN A DOSE FINDING STUDY IN CANCER PATIENTS,IN ORDER TO INVESTIGATE A GREATER RANGE OF DOSES

In a phase I clinical trial in cancer patients, the drug involved had one known main adverse effect, which also occurs spontaneously in cancer patients with a fairly high frequency. Experiments in rats have shown marked effects of the drug on tumour growth in high doses, but also dose-dependent toxicity. Consequently, the aim of the study was to determine a dose with a prespecified, acceptable rate of toxicity. As a traditional design could result in inaccurate conclusions, use of the continual reassessment method (CRM) was considered. Twelve dose levels were chosen, allocating to the first patient the lowest, but safe, dose. It is likely that the target dose is far above that, and that CRM then would escalate too fast, skipping certain levels. To ensure that all dose levels inferior to the target dose was tried, some combined methods were proposed: (1) an extension of the design, combining the CRM with a preliminary up-and-down design in order to reach the neighbourhood of the target dose during a successive escalation, and (2) a restriction on the CRM of never escalate more than a single dose level. Simulations showed the extended CRM to be superior by making it possible to investigate a greater range of doses using fewer patients, and to provide more accurate estimates.     

Bridging continual reassessment method for phase I clinical trials in different ethnic populations

Accumulating evidence shows that the conventional one‐size‐fits‐all dose‐finding paradigm is problematic when applied to different ethnic populations. Because of inter‐ethnic heterogeneity, the dosage established in a landmark trial for a certain population may not be generalizable to a different ethnic population, and a follow‐up bridge trial is often needed to find the maximum tolerated dose for the new population. We propose the bridging continual reassessment method (B‐CRM) to facilitate dose finding for such follow‐up bridge trials. The B‐CRM borrows information from the landmark trial through a novel estimate of the dose‐toxicity curve and accommodates the inter‐ethnic heterogeneity using the Bayesian model averaging approach. Extensive simulation studies show that the B‐CRM has desirable operating characteristics with a high probability to select the target dose. This article focuses on ethnic heterogeneity, but the proposed method can be directly used to handle other types of patient heterogeneity, for example, patient subgroups defined by prognostic factors or biomarkers. The software to implement the B‐CRM design is available for free download at http://odin.mdacc.tmc.edu/~yyuan/ . Copyright © 2015 John Wiley & Sons, Ltd.     

Some practical improvements in the continual reassessment method for phase I studies

The Continual Reassessment Method (CRM) is a Bayesian phase I design whose purpose is to estimate the maximum tolerated dose of a drug that will be used in subsequent phase II and III studies. Its acceptance has been hindered by the greater duration of CRM designs compared to standard methods, as well as by concerns with excessive experimentation at high dosage levels, and with more frequent and severe toxicity. This paper presents the results of a simulation study in which one assigns more than one subject at a time to each dose level, and each dose increase is limited to one level. We show that these modifications address all of the most serious criticisms of the CRM, reducing the duration of the trial by 50–67 per cent, reducing toxicity incidence by 20–35 per cent, and lowering toxicity severity. These are achieved with minimal effects on accuracy. Most important, based on our experience at our institution, such modifications make the CRM acceptable to clinical investigators.     

Using the time‐to‐event continual reassessment method in the presence of partial orders

The time‐to‐event continual reassessment method (TITE‐CRM) was proposed to handle the problem of long trial duration in Phase 1 trials as a result of late‐onset toxicities. Here, we implement the TITE‐CRM in dose‐finding trials of combinations of agents. When studying multiple agents, monotonicity of the dose–toxicity curve is not clearly defined. Therefore, the toxicity probabilities follow a partial order, meaning that there are pairs of treatments for which the ordering of the toxicity probabilities is not known at the start of the trial. A CRM design for partially ordered trials (PO‐CRM) was recently proposed. Simulation studies show that extending the TITE‐CRM to the partial order setting produces results similar to those of the PO‐CRM in terms of maximum tolerated dose recommendation yet reduces the duration of the trial. Copyright © 2012 John Wiley & Sons, Ltd.     

Dose finding with drug combinations in cancer phase I clinical trials using conditional escalation with overdose control

We present a Bayesian adaptive design for dose finding of a combination of two drugs in cancer phase I clinical trials. The goal is to estimate the maximum tolerated dose (MTD) as a curve in the two‐dimensional Cartesian plane. We use a logistic model to describe the relationship between the doses of the two agents and the probability of dose limiting toxicity. The model is re‐parameterized in terms of parameters clinicians can easily interpret. Trial design proceeds using univariate escalation with overdose control, where at each stage of the trial, we seek a dose of one agent using the current posterior distribution of the MTD of this agent given the current dose of the other agent. At the end of the trial, an estimate of the MTD curve is proposed as a function of Bayes estimates of the model parameters. We evaluate design operating characteristics in terms of safety of the trial design and percent of dose recommendation at dose combination neighborhoods around the true MTD curve. We also examine the performance of the approach under model misspecifications for the true dose–toxicity relationship. Copyright © 2014 John Wiley & Sons, Ltd.     

Dose escalation trial designs based on a molecularly targeted endpoint

Traditional phase I dose-finding studies for chemotoxic agents base dose escalation on toxicity, with escalation continuing until unacceptable toxicity is observed. Recent development of molecularly targeted agents that have little or no toxicity in the therapeutic dose range has raised questions over the best study designs for phase I studies. Two types of designs are proposed and evaluated in this paper. In these designs, escalation is based on a binary response that indicates whether or not the agent has had the desired effect on the molecular target. One design is developed to ensure that if the true target response rate is low there will be a high probability of escalating and if the true target response rate is high there will be a low probability of escalating. The other design is developed to continue to escalate as long as the true response rate is increasing and to stop escalating when the response rate plateaus or decreases. A limited simulation study is performed and the designs are compared with respect to the dose level at the end of escalation and the number of patients treated on study.     

A Bayesian hierarchical nonlinear model for assessing the association between genetic variation and drug cytotoxicity

Non‐tumor cell‐based model systems have recently gained interest in pharmacogenetic research as a hypothesis generating tool. The hypotheses generated from these model systems can be followed up in functional studies, or tested in individuals taking the same investigational agents. The current cellular phenotypes (e.g. cytotoxicity) of interest in these studies are based on the effects of an individual dosage of a drug on the cell lines, or a summary of results at many dosages of a drug (e.g. dose that inhibits 50 per cent of cell growth, GI 50 ). A more complete analysis of the impact of genetic variation on all aspects of the dose–response curve may lend additional insight into the pharmacogenomics of a particular drug. This paper illustrates the use of a Bayesian hierarchical nonlinear model for the analysis of pharmacogenomic data with cytotoxicity endpoints. The model is illustrated with cytotoxicity and expression data collected on cell lines from a pharmacogenomic study of the drug gemcitabine. By completing an analysis based on the entire dose–response curve, we were able to detect additional genes that affect not only the GI 50, but also the slope of the curve, which reflects the therapeutic index of the drug. Simulation studies also demonstrate that in comparison with the analyses based on the commonly used summary measure GI 50, investigation of the impact of genetic variation on all aspects of the cytotoxicity dose–response curve is more informative, and more powerful with respect to detecting the effect of gene expression on cytotoxicity. Copyright © 2009 John Wiley & Sons, Ltd.     

An evaluation of phase I clinical trial designs in the continuous dose-response setting

Both traditional phase I designs and the increasingly popular continual reassessment method (CRM) designs select an estimate of maximum tolerable dose (MTD) from among a set of prespecified dose levels. Although CRM designs use an implied dose-response model to select the next dose level, in general it is neither assumed nor necessary that this model be tied to the actual dose of a drug. In contrast, in our two-stage design the fitting of a dose-response model after data have been collected is a necessary feature of the design, and the MTD is not constrained to be one of the prespecified dose levels. We conducted a simulation study to evaluate the performance of the two-stage design, two likelihood-based CRM designs, and two traditional designs in estimating the MTD in situations where one assumes that an explicit dose-response model exists. Under a wide variety of dose-response settings, we examined the bias and precision of estimates, and the fraction of estimates that were extremely high or low. We also studied the effect of adding a model fitting step at the end of a traditional design or a CRM design. The best performance was achieved using the two-stage and CRM designs. Although the CRM designs generally had smaller bias, the two-stage design yielded equal or somewhat smaller precision in some cases. The addition of a model-fitting step slightly improved the precision of the CRM estimates and decreased the percentage of extreme estimates. Allowing interpolation between doses for updating during CRM did not improve overall performance.     

The continual reassessment method: comparison of Bayesian stopping rules for dose-ranging studies

The continual reassessment method (CRM) provides a Bayesian estimation of the maximum tolerated dose (MTD) in phase I clinical trials and is also used to estimate the minimal efficacy dose (MED) in phase II clinical trials. In this paper we propose Bayesian stopping rules for the CRM, based on either posterior or predictive probability distributions that can be applied sequentially during the trial. These rules aim at early detection of either the mis-choice of dose range or a prefixed gain in the point estimate or accuracy of estimated probability of response associated with the MTD (or MED). They were compared through a simulation study under six situations that could represent the underlying unknown dose-response (either toxicity or failure) relationship, in terms of sample size, probability of correct selection and bias of the response probability associated to the MTD (or MED). Our results show that the stopping rules act correctly, with early stopping by using the two first rules based on the posterior distribution when the actual underlying dose-response relationship is far from that initially supposed, while the rules based on predictive gain functions provide a discontinuation of inclusions whatever the actual dose-response curve after 20 patients on average, that is, depending mostly on the accumulated data. The stopping rules were then applied to a data set from a dose-ranging phase II clinical trial aiming at estimating the MED dose of midazolam in the sedation of infants during cardiac catheterization. All these findings suggest the early use of the two first rules to detect a mis-choice of dose range, while they confirm the requirement of including at least 20 patients at the same dose to reach an accurate estimate of MTD (MED). A two-stage design is under study.     

An evaluation of phase I cancer clinical trial designs

Phase I clinical trials are designed to identify an appropriate dose for experimentation in phase II and III studies. I present the results from a simulation study to evaluate the performance of nine phase I designs involving the standard design, the two-stage modified Storer's design, the two-stage Korn's design, the one-stage modified continual reassessment method (CRM) designs, and the two-stage modified CRM designs. I compare the performance of the above phase I designs in terms of the following criteria: (i) the proportion of the recommended maximum tolerated dose (MTD) at each dose level; (ii) the proportion of patients treated at each dose level; (iii) the average number of patients to complete the trial; (iv) the probability of toxicity observed; and (v) the average number of cohorts to complete the trial. In general, the one-stage modified CRM II and CRM III designs perform well compared with the other designs considered in this study. The one-stage modified CRM II and III designs require much fewer numbers of cohorts than do the two-stage modified CRM II and III designs. The one-stage modified CRM II and III designs avoid the criticisms of the original CRM by reducing the average number of cohorts and toxicity incidences, while estimating the MTD more accurately than does the standard design. © 1998 John Wiley & Sons, Ltd.     

Three-dose-cohort designs in cancer phase I trials

Traditional designs for phase I clinical trials assign the same dose to patients in the same cohort. In this paper, we present a new class of designs for cancer phase I trials which initially rapidly escalate by allowing multiple doses (usually 3) to be assigned to each cohort of patients. The class of designs, called the LMH-CRM (an extension of the continual reassessment method (CRM) by administering different percentiles of the maximum tolerated dose (MTD), denoted 'low', 'medium', 'high'), is proven to be consistent and coherent (a commonsense property of phase I trials for dose escalation and de-escalation). Three designs (slow, moderate and fast) are derived based on different dose-escalation restrictions. Simulation results show that moderate and fast LMH-CRM combine the advantages of the CRM with one patient per cohort and three patients per cohort: it accurately estimates the MTD; controls overall toxicity rates; and is time efficient.     

A comparison of model choices for the continual reassessment method in phase I cancer trials

Determination of the maximum tolerated dose (MTD) is the main objective of phase I trials. Trials are typically carried out with restricted sample sizes. Model‐based approaches proposed to identify the MTD (including the Continual Reassessment Method or CRM) suppose a simple model for the dose‐toxicity relation. At this early stage of clinical development, the true family of models is not known and several proposals have been done. Asymptotic convergence of the recommendation to the true MTD can be obtained with a one‐parameter model even in case of model misspecification. Nevertheless, operating characteristics with finite sample sizes can be largely affected by the choice of the model. In this paper, we evaluate and compare several models in a simulation framework. This framework includes a large class of dose‐toxicity relations against which to test the competing models, an ‘optimal’ method that provides efficient non‐parametric estimates of the probability of dose limiting toxicity to serve as a benchmark and as a graphic representation. In particular we explore the use of a one‐parameter versus a two‐parameter model, we compare the power and the logistic models and finally we investigate the impact of dose recoding on the operating characteristics. Comparisons are carried out with both a likelihood approach and a Bayesian approach for model estimations. We show that average performances of a one‐parameter model are superior and that the power model has good operating characteristics. Some models can speed up dose escalation and lead to more aggressive designs. We derive some behavior related to the choice of model and insist on the use of simulations under several scenarios before the initiation of each new trial in order to determine the best model to be used. Copyright © 2009 John Wiley & Sons, Ltd.     

Mixed‐effects Gaussian process functional regression models with application to dose–response curve prediction

We propose a new semiparametric model for functional regression analysis, combining a parametric mixed‐effects model with a nonparametric Gaussian process regression model, namely a mixed‐effects Gaussian process functional regression model. The parametric component can provide explanatory information between the response and the covariates, whereas the nonparametric component can add nonlinearity. We can model the mean and covariance structures simultaneously, combining the information borrowed from other subjects with the information collected from each individual subject. We apply the model to dose–response curves that describe changes in the responses of subjects for differing levels of the dose of a drug or agent and have a wide application in many areas. We illustrate the method for the management of renal anaemia. An individual dose–response curve is improved when more information is included by this mechanism from the subject/patient over time, enabling a patient‐specific treatment regime. Copyright © 2012 John Wiley & Sons, Ltd.     

A copula-based model for multivariate non-normal longitudinal data: analysis of a dose titration safety study on a new antidepressant

A new model for multivariate non-normal longitudinal data is proposed. In a first step, each longitudinal series of data corresponding to a given response is modelled separately using a copula to relate the marginal distributions of the response at each time of observation. In a second step, at each observation time, the conditional (on the past) distributions of each response are related using another copula describing the relationship between the corresponding variables. Note that there is no need to consider the same family of distributions for these response variables. The technique is illustrated in a dose titration safety study on a new antidepressant. The haemodynamic effect on diastolic blood pressure, systolic blood pressure and heart rate is studied. These three responses are measured repeatedly over time on ten healthy volunteers during the dose escalation. The available covariates are sex and the concentration of drug in the plasma at time of measurement.     

Impact of microscopic disease extension,extra-CTV tumour islets,incidental dose and dose conformity on tumour control probability

The impact of microscopic disease extension (MDE), extra-CTV tumour islets (TIs), incidental dose and dose conformity on tumour control probability (TCP) is analyzed using insilico simulations in this study. MDE in the region in between GTV and CTV is simulated inclusive of geometric uncertainties (GE) using spherical targets and spherical dose distribution. To study the effect of incidental dose on TIs and the effect of dose–response curve (DRC) on tumour control, islets were randomly distributed and TCP was calculated for various dose levels by rescaling the dose. Further, the impact of dose conformity on required PTV margins is also studied. The required PTV margins are ~2 mm lesser than assuming a uniform clonogen density if an exponential clonogen density fall off in the GTV–CTV is assumed. However, margins are almost equal if GE is higher in both cases. This shows that GE has a profound impact on margins. The effect of TIs showed a bi-phasic relation with increasing dose, indicating that patients with islets not in the beam paths do not benefit from dose escalation. Increasing dose conformity is also found to have considerable effect on TCP loss especially for larger GE. Further, smaller margins in IGRT should be used with caution where uncertainty in CTV definition is of concern.     

Mathematical models of complex dose-response relationships: implications for experimental design in psychopharmacologic research.

We develop a mathematical model to account for the complex relationship between drug dose and clinical response in psychopharmacologic research. The model specifies relationships among drug dose, drug bioavailability, pharmacokinetic factors, course moderators, clinical response and the heterogeneity of the disorder, and allows for the derivation of results that have implications for experimental design in psychopharmacologic research. These results form the basis for computer simulations which indicate that random assignment to two fixed doses is more powerful and less sensitive to heterogeneity than assignment to clinically determined doses. Fixed dose designs, however, tend to overestimate the magnitude of drug bioavailability-clinical response relationships. Clinically determined dose designs are useful in some experimental situations; their effectiveness is enhanced by systematically reducing the clinically determined dose. Larger dose reductions improve the ability to detect bioavailability-clinical response relationships.