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The identification of synergistic interactions between combinations of drugs is an important area within drug discovery and development. Pre-clinically, large numbers of screening studies to identify synergistic pairs of compounds can often be ran, necessitating efficient and robust experimental designs. We consider experimental designs for detecting interaction between two drugs in a pre-clinical in vitro assay in the presence of uncertainty of the monotherapy response. The monotherapies are assumed to follow the Hill equation with common lower and upper asymptotes, and a common variance. The optimality criterion used is the variance of the interaction parameter. We focus on ray designs and investigate two algorithms for selecting the optimum set of dose combinations. The first is a forward algorithm in which design points are added sequentially. This is found to give useful solutions in simple cases but can lack robustness when knowledge about the monotherapy parameters is insufficient. The second algorithm is a more pragmatic approach where the design points are constrained to be distributed log-normally along the rays and monotherapy doses. We find that the pragmatic algorithm is more stable than the forward algorithm, and even when the forward algorithm has converged, the pragmatic algorithm can still out-perform it. Practically, we find that good designs for detecting an interaction have equal numbers of points on monotherapies and combination therapies, with those points typically placed in positions where a 50% response is expected. More uncertainty in monotherapy parameters leads to an optimal design with design points that are more spread out., (Copyright © 2015 John Wiley & Sons, Ltd.)

Pre-clinical studies may be used to screen for synergistic combinations of drugs. The types of in vitro assays used for this purpose will depend upon the disease area of interest. In oncology, one frequently used study measures cell line viability: cells placed into wells on a plate are treated with doses of two compounds, and cell viability is assessed from an optical density measurement corrected for blank well values. These measurements are often transformed and analysed as cell survival relative to untreated wells. The monotherapies are assumed to follow the Hill equation with lower and upper asymptotes at 0 and 1, respectively. Additionally, a common variance about the dose-response curve may be assumed. In this paper, we consider two models for incorporating synergy parameters. We investigate the effect of different models of biological variation on the assessment of synergy from both of these models. We show that estimates of the synergy parameters appear to be robust, even when estimates of the other model parameters are biased. Using untransformed measurements provides better coverage of the 95% confidence intervals for the synergy parameters than using transformed measurements, and the requirement to fit the upper asymptote does not cause difficulties. Assuming homoscedastic variances appears to be robust. The added complexity of determining and fitting an appropriate heteroscedastic model does not seem to be justified., (Copyright © 2013 John Wiley & Sons, Ltd.)

We describe a dose escalation procedure for a combined phase I/II clinical trial. The procedure is based on a Bayesian model for the joint distribution of the occurrence of a dose limiting event and of some indicator of efficacy (both considered binary variables), making no assumptions other than monotonicity. Thus, the chances of each outcome are assumed to be non-decreasing in dose level. We applied the procedure to the design of a placebo-controlled, sequential trial in rheumatoid arthritis, in each stage of which patients were randomized between placebo and all dose levels that currently appeared safe and non-futile. On the basis of data from a pilot study, we constructed five different scenarios for the dose-response relationships under which we simulated the trial and assessed the performance of the procedure. The new design appears to have satisfactory operating characteristics and can be adapted to the requirements of a range of trial situations., (Copyright © 2012 John Wiley & Sons, Ltd.)

The Cancer Research UK study CR0720-11 is a trial to determine the tolerability and effect on survival of using two agents in combination in patients with advanced pancreatic cancer. In particular, the trial is designed first to identify the most suitable combination of doses of the two agents in terms of the incidence of dose-limiting toxicities. Then, the survival of all patients who have received that dose combination in the study so far, together with additional patients assigned to that dose combination to ensure that the total number is sufficient, will be analysed. If the survival outcomes show promise, then a definitive randomised study of that dose combination will be recommended. The first two patients in the trial will be treated with the lowest doses of each agent in combination. An adaptive Bayesian procedure based only on monotonicity constraints concerning the risks of toxicity at different dose levels will then be used to suggest dose combinations for subsequent patients. The survival analysis will concern only patients who received the chosen dose combination, and will compare observed mortality with that expected from an exponential model based on the known survival rates associated with current treatment. In this paper, the Bayesian dose-finding procedure is described and illustrated, and its properties are evaluated through simulation. Computation of the appropriate sample size for the survival investigation is also discussed., (Copyright © 2012 John Wiley & Sons, Ltd.)

Many formal statistical procedures for phase I dose-finding studies have been proposed. Most concern a single novel agent available at a number of doses and administered to subjects participating in a single treatment period and returning a single binary indicator of toxicity. Such a structure is common when evaluating cytotoxic drugs for cancer. This paper concerns studies of combinations of two agents, both available at several doses. Subjects participate in one treatment period and provide two binary responses: one an indicator of benefit and the other of harm. The word 'benefit' is used loosely here: the response might be an early indicator of physiological change which, if induced in patients, is of potential therapeutic value. The context need not be oncology, but might be any study intended to meet both the phase I aim of establishing which doses are safe and the phase II goal of exploring potential therapeutic activity. A Bayesian approach is used based on an assumption of monotonicity in the relationship between the strength of the dose-combination and the distribution of the bivariate outcome. Special cases are described, and the procedure is evaluated using simulation. The parameters that define the model have immediate and simple interpretation. Graphical representations of the posterior opinions about model parameters are shown, and these can be used to inform the discussions of the trial safety committee., (Copyright © 2011 John Wiley & Sons, Ltd.)

Despite an enormous and growing statistical literature, formal procedures for dose-finding are only slowly being implemented in phase I clinical trials. Even in oncology and other life-threatening conditions in which a balance between efficacy and toxicity has to be struck, model-based approaches, such as the Continual Reassessment Method, have not been universally adopted. Two related concerns have limited the adoption of the new methods. One relates to doubts about the appropriateness of models assumed to link the risk of toxicity to dose, and the other is the difficulty of communicating the nature of the process to clinical investigators responsible for early phase studies. In this paper, we adopt a new Bayesian approach involving a simple model assuming only monotonicity in the dose-toxicity relationship. The parameters that define the model have immediate and simple interpretation. The approach can be applied automatically, and we present a simulation investigation of its properties when it is. More importantly, it can be used in a transparent fashion as one element in the expert consideration of what dose to administer to the next patient or group of patients. The procedure serves to summarize the opinions and the data concerning risks of a binary characterization of toxicity which can then be considered, together with additional and less tidy trial information, by the clinicians responsible for making decisions on the allocation of doses. Graphical displays of these opinions can be used to ease communication with investigators., (Copyright (c) 2010 John Wiley & Sons, Ltd.)

Observation of adverse drug reactions during drug development can cause closure of the whole programme. However, if association between the genotype and the risk of an adverse event is discovered, then it might suffice to exclude patients of certain genotypes from future recruitment. Various sequential and non-sequential procedures are available to identify an association between the whole genome, or at least a portion of it, and the incidence of adverse events. In this paper we start with a suspected association between the genotype and the risk of an adverse event and suppose that the genetic subgroups with elevated risk can be identified. Our focus is determination of whether the patients identified as being at risk should be excluded from further studies of the drug. We propose using a utility function to determine the appropriate action, taking into account the relative costs of suffering an adverse reaction and of failing to alleviate the patient's disease. Two illustrative examples are presented, one comparing patients who suffer from an adverse event with contemporary patients who do not, and the other making use of a reference control group. We also illustrate two classification methods, LASSO and CART, for identifying patients at risk, but we stress that any appropriate classification method could be used in conjunction with the proposed utility function. Our emphasis is on determining the action to take rather than on providing definitive evidence of an association., (Copyright (c) 2008 John Wiley & Sons, Ltd.)