Combining multiple comparisons and modeling techniques in dose-response studies

The analysis of data from dose-response studies has long been divided according to two major strategies: multiple comparison procedures and model-based approaches. Model-based approaches assume a functional relationship between the response and the dose, taken as a quantitative factor, according to a prespecified parametric model. The fitted model is then used to estimate an adequate dose to achieve a desired response but the validity of its conclusions will highly depend on the correct choice of the a priori unknown dose-response model. Multiple comparison procedures regard the dose as a qualitative factor and make very few, if any, assumptions about the underlying dose-response model. The primary goal is often to identify the minimum effective dose that is statistically significant and produces a relevant biological effect. One approach is to evaluate the significance of contrasts between different dose levels, while preserving the family-wise error rate. Such procedures are relatively robust but inference is confined to the selection of the target dose among the dose levels under investigation. We describe a unified strategy to the analysis of data from dose-response studies which combines multiple comparison and modeling techniques. We assume the existence of several candidate parametric models and use multiple comparison techniques to choose the one most likely to represent the true underlying dose-response curve, while preserving the family-wise error rate. The selected model is then used to provide inference on adequate doses.     

Utility‐Based Optimization of Combination Therapy Using Ordinal Toxicity and Efficacy in Phase I/II Trials

Summary An outcome‐adaptive Bayesian design is proposed for choosing the optimal dose pair of a chemotherapeutic agent and a biological agent used in combination in a phase I/II clinical trial. Patient outcome is characterized as a vector of two ordinal variables accounting for toxicity and treatment efficacy. A generalization of the Aranda‐Ordaz model (1981, Biometrika 68 , 357–363) is used for the marginal outcome probabilities as functions of a dose pair, and a Gaussian copula is assumed to obtain joint distributions. Numerical utilities of all elementary patient outcomes, allowing the possibility that efficacy is inevaluable due to severe toxicity, are obtained using an elicitation method aimed to establish consensus among the physicians planning the trial. For each successive patient cohort, a dose pair is chosen to maximize the posterior mean utility. The method is illustrated by a trial in bladder cancer, including simulation studies of the method's sensitivity to prior parameters, the numerical utilities, correlation between the outcomes, sample size, cohort size, and starting dose pair.     

Bonferroni parallel gatekeeping - transparent generalizations, adjusted p -values, and short direct proofs

In the two-step version (Dmitrienko, Tamhane, Wang and Chen, 2006) of the Bonferroni parallel-gatekeeping multiple-testing procedure (MTP): (a) a family F1 of null hypotheses H is used as a gatekeeper for another family F2 in that no H in F2 can be rejected unless at least one H is rejected in F1; (b) a Bonferroni MTP is used for F1 at local multiple-level alpha in the first step; and (c) Holm's (1979) step-down MTP is used in the second step for F2 at a local multiple level that depends on the rejections made in the first step. It is shown in this article that this two-step procedure can be generalized in that any MTP with multiple-level control and available multiplicity-adjusted p -values can be used instead of Holm's MTP in the second step. A further generalization related to what Dmitrienko, Molenberghs, Chuang-Stein and Offen (2005) called modified Bonferroni parallel gatekeeping is also given where in case all H s in F2 are rejected, additional rejections in F1 can be made in a third step at local multiple-level alpha through any MTP that is more powerful than the initial Bonferroni MTP, e.g. Holm's MTP. The proofs that these two generalized Bonferroni parallel-gatekeeping MTPs have multiple-level alpha are short and direct, without closed-testing arguments. Multiplicity-adjusted p -values can easily be calculated for these MTPs. The extensions to several successive gatekeeper families are straightforward. An illustration is given.     

Continual reassessment method for partial ordering

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.     

Multiple Comparisons of Treatments with Stable Multivariate Tests in a Two‐Stage Adaptive Design,Including a Test for Non‐Inferiority

The application of stabilized multivariate tests is demonstrated in the analysis of a two‐stage adaptive clinical trial with three treatment arms. Due to the clinical problem, the multiple comparisons include tests of superiority as well as a test for non‐inferiority, where non‐inferiority is (because of missing absolute tolerance limits) expressed as linear contrast of the three treatments. Special emphasis is paid to the combination of the three sources of multiplicity – multiple endpoints, multiple treatments, and two stages of the adaptive design. Particularly, the adaptation after the first stage comprises a change of the a‐priori order of hypotheses.