Sequential design methods for binary response variables exist for determination of the concentration or dose associated with the 50% point along the dose-response curve; the up-and-down method of Dixon and Mood is now commonly used in anesthesia research. There have been important developments in statistical methods that (1) allow the design of experiments for the measurement of the response at any point (quantile) along the dose-response curve, (2) demonstrate the risk of certain statistical methods commonly used in literature reports, (3) allow the estimation of the concentration or dose-the target dose-associated with the chosen quantile without the assumption of the symmetry of the tolerance distribution, and (4) set bounds on the probability of response at this target dose. This article details these developments, briefly surveys current use of the up-and-down method in anesthesia research, reanalyzes published reports using the up-and-down method for the study of the epidural relief of pain during labor, and discusses appropriate inferences from up-and-down method studies.

Advances in and limitations of up-and-down methodology: a précis of clinical use, study design, and dose estimation in anesthesia research.

Purpose Human epidermal growth factor (HER) –mediated signaling is critical in many cancers, including subsets of breast and lung cancer. HER family members signal via the phosphatidylinositide 3-kinase (PI3K) –AKT/protein kinase B–mammalian target of rapamycin (mTOR) cascade; mTOR activation is critical for the expression of multiple contributors to tumor growth and invasion. On the basis of preclinical data suggesting synergy of HER2 inhibition and mTOR inhibition in breast and lung cancer models, we conducted a phase I combination study of neratinib, a small-molecule irreversible pan-HER tyrosine kinase inhibitor, and temsirolimus, an mTOR inhibitor, in patients with advanced solid tumors. Patients and Methods This study enrolled patients to dosing combinations of neratinib and temsirolimus. The primary objective was to estimate the toxicity contour of the combination and establish recommended phase II doses. Results Sixty patients were treated on 12 of 16 possible dosing combinations. Diarrhea was the...

Phase I Study of Neratinib in Combination With Temsirolimus in Patients With Human Epidermal Growth Factor Receptor 2–Dependent and Other Solid Tumors

Summary. Much of the statistical methodology underlying the experimental design of phase 1 trials in oncology is intended for studies involving a single cytotoxic agent. The goal of these studies is to estimate the maximally tolerated dose, the highest dose that can be administered with an acceptable level of toxicity. A fundamental assumption of these methods is monotonicity of the dose–toxicity curve. This is a reasonable assumption for single-agent trials in which the administration of greater doses of the agent can be expected to produce dose-limiting toxicities in increasing proportions of patients. When studying multiple agents, the assumption may not hold because the ordering of the toxicity probabilities could possibly be unknown for several of the available drug combinations. At the same time, some of the orderings are known and so we describe the whole situation as that of a partial ordering. In this article, we propose a new two-dimensional dose-finding method for multiple-agent trials that simplifies to the continual reassessment method (CRM), introduced by O’Quigley, Pepe, and Fisher (1990, Biometrics 46, 33–48), when the ordering is fully known. This design enables us to relax the assumption of a monotonic dose–toxicity curve. We compare our approach and some simulation results to a CRM design in which the ordering is known as well as to other suggestions for partial orders.

Continual reassessment method for partial ordering.

Summary. Treating patients with a combination of agents is becoming commonplace in cancer clinical trials, with biochemical synergism often the primary focus. In a typical drug combination trial, the toxicity profile of each individual drug has already been thoroughly studied in single-agent trials, which naturally offers rich prior information. We propose a Bayesian adaptive design for dose finding that is based on a copula-type model to account for the synergistic effect of two or more drugs in combination. To search for the maximum tolerated dose combination, we continuously update the posterior estimates for the toxicity probabilities of the combined doses. By reordering the dose toxicities in the two-dimensional probability space, we adaptively assign each new cohort of patients to the most appropriate dose. Dose escalation, de-escalation or staying at the same doses is determined by comparing the posterior estimates of the probabilities of toxicity of combined doses and the prespecified toxicity target. We conduct extensive simulation studies to examine the operating characteristics of the design and illustrate the proposed method under various practical scenarios.

/pdf/bayesian-dose-finding-in-oncology-for-drug-combinations-by-3w4ke1l5ei.pdf

Bayesian dose finding in oncology for drug combinations by copula regression

Two-agent combination trials have recently attracted enormous attention in oncology research. There are several strong motivations for combining different agents in a treatment: to induce the synergistic treatment effect, to increase the dose intensity with nonoverlapping toxicities, and to target different tumor cell susceptibilities. To accommodate this growing trend in clinical trials, we propose a Bayesian adaptive design for dose finding based on latent 2 x 2 tables. In the search for the maximum tolerated dose combination, we continuously update the posterior estimates for the unknown parameters associated with marginal probabilities and the correlation parameter based on the data from successive patients. By reordering the dose toxicity probabilities in the two-dimensional space, we assign each coming cohort of patients to the most appropriate dose combination. We conduct extensive simulation studies to examine the operating characteristics of the proposed method under various practical scenarios. Finally, we illustrate our dose-finding procedure with a clinical trial of agent combinations at M. D. Anderson Cancer Center.

/pdf/a-latent-contingency-table-approach-to-dose-finding-for-36kwfei4lc.pdf

A Latent Contingency Table Approach to Dose Finding for Combinations of Two Agents

The objective of a Phase I trial with two agents is to find a set of maximum-tolerated dose combinations that yield a prespecified toxicity rate. In this article, we consider the case where several doses of one agent are fixed and the goal is to find the maximum-tolerated dose of the other agent to be used in combination with each of the doses of agent one. We propose a Bayesian design that uses a parsimonious working model for the dose-toxicity relationship. We show that the new design is more effective in identifying the maximum-tolerated combinations than one-dimensional designs applied at each dose level of one of the agents.

Two-dimensional dose finding in discrete dose space.

This paper investigates the design and analysis of dose-finding trials with two agents The set of doses for each agent is fixed in advance The goal of the trial is to find the set of dose combinations with probability of toxicity closest to a pre-specified value For each of the two agents we assume that the probability of toxicity of an agent is non-decreasing with dose when the dose of the other agent is fixed Using this assumption we construct a new non-parametric design that operates on a two-dimensional grid of all possible dose combinations A bivariate isotonic regression estimator of the maximum tolerated combinations is described We conclude that the new design and the bivariate isotonic estimator are superior to the procedure where several independent dose-finding trials are run

A non-parametric approach to the design and analysis of two-dimensional dose-finding trials.

We consider the problem of dose-finding where subjects can be stratified into two populations with possibly different susceptibility to toxicity. The goal is to find the maximally tolerated dose for each population. We propose a non-parametric design for this problem. Toxicity is estimated using the bivariate isotonic regression estimator. The new design is compared with the two-sample continual reassessment method.

Kai Wang

Papers

Two-dimensional dose finding in discrete dose space.

A non-parametric approach to the design and analysis of two-dimensional dose-finding trials.

Bivariate isotonic design for dose-finding with ordered groups