A logistic dose-ranging method for phase I clinical investigations trials

Response-adaptive clinical trials: case studies in the medical literature

The past 15 years has seen many pharmaceutical sponsors consider and implement adaptive designs (AD) across all phases of drug development. Given their arrival at the turn of the millennium, we might think that they are a recent invention. That is not the case. The earliest idea of an AD predates Bradford Hill's MRC tuberculosis study, appearing in Biometrika in 1933. In this paper, we trace the development of response-ADs, designs in which the allocation to intervention arms depends on the responses of subjects already treated. We describe some statistical details underlying the designs, but our main focus is to describe and comment on ADs from the medical research literature. Copyright © 2016 John Wiley & Sons, Ltd.

Dimension of model parameter space and operating characteristics in adaptive dose-finding studies

Adaptive, model-based, dose-finding methods, such as the continual reassessment method, have been shown to have good operating characteristics. One school of thought argues in favor of the use of parsimonious models, not modeling all aspects of the problem, and using a strict minimum number of parameters. In particular, for the standard situation of a single homogeneous group, it is common to appeal to a one-parameter model. Other authors argue for a more classical approach that models all aspects of the problem. Here, we show that increasing the dimension of the parameter space, in the context of adaptive dose-finding studies, is usually counter productive and, rather than leading to improvements in operating characteristics, the added dimensionality is likely to result in difficulties. Among these are inconsistency of parameter estimates, lack of coherence in escalation or de-escalation, erratic behavior, getting stuck at the wrong level, and, in almost all cases, poorer performance in terms of correct identification of the targeted dose. Our conclusions are based on both theoretical results and simulations. Copyright © 2016 John Wiley & Sons, Ltd.

Stochastic Approximation and Modern Model-based Designs for Dose-Finding Clinical Trials

In 1951 Robbins and Monro published the seminal paper on stochastic approximation and made a specific reference to its application to the "estimation of a quantal using response, non-response data". Since the 1990s, statistical methodology for dose-finding studies has grown into an active area of research. The dose-finding problem is at its core a percentile estimation problem and is in line with what the Robbins-Monro method sets out to solve. In this light, it is quite surprising that the dose-finding literature has developed rather independently of the older stochastic approximation literature. The fact that stochastic approximation has seldom been used in actual clinical studies stands in stark contrast with its constant application in engineering and finance. In this article, I explore similarities and differences between the dose-finding and the stochastic approximation literatures. This review also sheds light on the present and future relevance of stochastic approximation to dose-finding clinical trials. Such connections will in turn steer dose-finding methodology on a rigorous course and extend its ability to handle increasingly complex clinical situations.

Phase I Studies of Chemotherapeutic Agents in Cancer Patients: A Review of the Designs

I review the designs available for Phase I dose-finding studies of chemotherapeutic agents in cancer patients. The designs are based on the assumption that both efficacy and toxicity increase with dose, and thus attempt to minimize the number of patients treated at low doses, and also to minimize the chance that patients will be treated at excessively toxic or lethal doses. The designs fall into two classes: rule-based and model-guided. Rule-based designs can always determine a reasonable maximum tolerable dose based on observed toxicity, but when model assumptions are not satisfied, many model-guided designs will not.

Improved up-and-down designs for phase I trials

We consider several designs from the family of up-and-down rules for the sequential allocation of dose levels to subjects in a dose-response study. We show that an up-and-down design can be improved by using more information than the most recent response. For example, the k-in-a-row rule uses up to the k most recent responses. We introduce a new design, the Narayana rule, which uses a local estimate of the probability of toxicity calculated from all previous responses. For the Narayana rule, as the sample size gets large, the probability of assignment goes to zero for dose levels not among the two (or three) closest to the target. Different estimators of the target dose are compared. We find that the isotonic regression estimator is superior to other estimators for small to moderate sample sizes.

Adaptive dose finding for phase I clinical trials of drugs used for chemotherapy of cancer

Phase I clinical trials of cancer chemotherapy drugs are intended to determine the maximum tolerable dose (MTD). Thestandard method employed is a rule-based dose-escalation scheme in which escalation depends on the number of patients at a dose level that have dose-limiting toxicity (DLT). The MTD is thus defined in terms of the rules and a series of dose levels selected for sampling. For some trials it is desirable to have a more precise definition of the MTD, and to determine the MTD more accurately than possible with the rule-based schemes. Continuous reassessment methods (CRMs) define the MTD to be the dose at which a fixed fraction of patients experience DLT, and thus appear suited to these trials. It is shown, however, that these methods can have failure modes that in fact make them unattractive. An alternative data-driven dose-finding method is described that combines the robustness of the rule-based methods and with features of CRMs. The method has two stages. In the first stage, doses are escalated by a factor of 1.5. In the second stage, which begins at the first instance of DLT, a two-parameter logistic dose-response model estimates the MTD from the DLT experience of all patients. The model is initialized by setting the dose (d10) at which 10 per cent of patients would experience DLT to half the dose at which the first DLT was observed, and the dose (d90) at which 90 per cent would experience DLT to ten times d10. Weights are assigned such that the information at d10 and d90 is equivalent to that of one patient at each of the two doses. Cohorts of three patients are treated in both stages, and the dose for a new cohort in the second stage is the estimated MTD. The only prior information required to specify the design completely is the dose which will be given to the first cohort. Two stopping rules are investigated; among the requirements for these are that at least three (or four) DLTs be observed and at least nine patients be treated in the second stage. Simulations show that a coefficient of variation of approximately 0.4 on a target DLT probability of 0.3 is obtained over a wide variation in dose-response characteristics of the study drug. The performance of the new method is compared to that of rule-based methods.

A two-stage dose selection strategy in phase I trials with wide dose ranges

At early stages of drug development, the maximum tolerated dose (MTD) must be determined in order to have a range of doses that can be safely administered in humans. This is necessary before the compound can be tested in phase II clinical trials to find the optimal dose in terms of clinical outcome. Although heavily criticized, traditional dose escalation methods are still widely used to estimate the MTD. The recently developed Continual Reassessment Method (CRM) and Logistic Dose Ranging Strategy (LDRS) offer advantages compared to the traditional approach, including improved estimation of the MTD. However, the CRM utilizes a prior distribution that must be specified before having any data from the current trial. The LDRS requires the use of hypothesized data through a seed data set established before the start of the trial. When a wide dose range needs to be tested, the assumed information (prior distribution or seed data set) can have a great impact on dosages used during the trial and on the final estimates of the MTD. This paper combines the LDRS and the traditional dose escalation procedure to suggest a practical two-stage method that provides reliable estimates through relatively easy computation, and yet requires almost no prior information.