arXiv subjects

Pavel Mozgunov

Publications and source records attributed to Pavel Mozgunov.

30 records · Page 2Linked to original sources

arXiv2021

A Comparison of Model-Free Phase I Dose Escalation Designs for Dual-Agent Combination Therapies

It is increasingly common for therapies in oncology to be given in combination. In some cases, patients can benefit from the interaction between two drugs, although often at the risk of higher toxicity. A large number of designs to conduct phase I trials in this setting are available, where the objective is to select the maximum tolerated dose combination (MTC). Recently, a number of model-free (also called model-assisted) designs have provoked interest, providing several practical advantages over the more conventional approaches of rule-based or model-based designs. In this paper, we demonstrate a novel calibration procedure for model-free designs to determine their most desirable parameters. Under the calibration procedure, we compare the behaviour of model-free designs to a model-based approach in a comprehensive simulation study, covering a number of clinically plausible scenarios. It is found that model-free designs are competitive with the model-based design in terms of the proportion of correct selections of the MTC. However, there are a number of scenarios in which model-free designs offer a safer alternative. This is also illustrated in the application of the designs to a case study using data from a phase I oncology trial.

stat.ME↗

arXiv2020

A Seamless Phase I/II Platform Design with a Time-To-Event Efficacy Endpoint for Potential COVID-19 Therapies

In the search for effective treatments for COVID-19, initial emphasis has been on re-purposed treatments. To maximise the chances of finding successful treatments, novel treatments that have been developed for this disease in particular, are needed. In this manuscript we describe and evaluate the statistical design of the AGILE platform, an adaptive randomized seamless Phase I/II trial platform that seeks to quickly establish a safe range of doses and investigates treatments for potential efficacy using a Bayesian sequential trial design. Both single agent and combination treatments are considered. We find that the design can identify potential treatments that are safe and efficacious reliably with small to moderate sample sizes.

stat.AP↗

arXiv2020

Adding flexibility to clinical trial designs: an example-based guide to the practical use of adaptive designs

Adaptive designs for clinical trials permit alterations to a study in response to accumulating data in order to make trials more flexible, ethical and efficient. These benefits are achieved while preserving the integrity and validity of the trial, through the pre-specification and proper adjustment for the possible alterations during the course of the trial. Despite much research in the statistical literature highlighting the potential advantages of adaptive designs over traditional fixed designs, the uptake of such methods in clinical research has been slow. One major reason for this is that different adaptations to trial designs, as well as their advantages and limitations, remain unfamiliar to large parts of the clinical community. The aim of this paper is to clarify where adaptive designs can be used to address specific questions of scientific interest; we introduce the main features of adaptive designs and commonly used terminology, highlighting their utility and pitfalls, and illustrate their use through case studies of adaptive trials ranging from early-phase dose escalation to confirmatory Phase III studies.

stat.AP↗

arXiv2020

Efficient adaptive designs for clinical trials of interventions for COVID-19

The COVID-19 pandemic has led to an unprecedented response in terms of clinical research activity. An important part of this research has been focused on randomized controlled clinical trials to evaluate potential therapies for COVID-19. The results from this research need to be obtained as rapidly as possible. This presents a number of challenges associated with considerable uncertainty over the natural history of the disease and the number and characteristics of patients affected, and the emergence of new potential therapies. These challenges make adaptive designs for clinical trials a particularly attractive option. Such designs allow a trial to be modified on the basis of interim analysis data or stopped as soon as sufficiently strong evidence has been observed to answer the research question, without compromising the trial's scientific validity or integrity. In this paper we describe some of the adaptive design approaches that are available and discuss particular issues and challenges associated with their use in the pandemic setting. Our discussion is illustrated by details of four ongoing COVID-19 trials that have used adaptive designs.

q-bio.QM↗

arXiv2019

Loss Functions in Restricted Parameter Spaces and Their Bayesian Applications

Squared error loss remains the most commonly used loss function for constructing a Bayes estimator of the parameter of interest. However, it can lead to sub-optimal solutions when a parameter is defined in a restricted space. It can also be an inappropriate choice in the context when an extreme overestimation and/or underestimation results in severe consequences and a more conservative estimator is preferred. We advocate a class of loss functions for parameters defined on restricted spaces which infinitely penalize boundary decisions like the squared error loss does on the real line. We also recall several properties of loss functions such as symmetry, convexity, and invariance. We propose generalizations of the squared error loss function for parameters defined on the positive real line and on an interval. We provide explicit solutions for corresponding Bayes estimators and discuss multivariate extensions. {Four} well-known Bayesian estimation problems are used to demonstrate inferential benefits the novel Bayes estimators can provide in the context of restricted estimation.

math.ST↗

arXiv2018

Improving Safety of the Continual Reassessment Method via a Modified Allocation Rule

This paper proposes a novel criterion for the allocation of patients in Phase~I dose-escalation clinical trials aiming to find the maximum tolerated dose (MTD). Conventionally, using a model-based approach the next patient is allocated to the dose with the toxicity estimate closest (in terms of the absolute or squared distance) to the maximum acceptable toxicity. This approach, however, ignores the uncertainty in point estimates and ethical concerns of assigning a lot of patients to overly toxic doses. Motivated by recent discussions in the theory of estimation in restricted parameter spaces, we propose a criterion which accounts for both of these issues. The criterion requires a specification of one additional parameter only which has a simple and intuitive interpretation. We incorporate the proposed criterion into the one-parameter Bayesian continual reassessment method (CRM) and show, using simulations, that it results in the same proportion of correct selections on average as the original design, but in fewer mean number of toxic responses. A comparison to other model-based dose-escalation designs demonstrates that the proposed design can result in either the same mean accuracy as alternatives but fewer number of toxic responses, or in a higher mean accuracy but the same number of toxic responses. We conclude that the new criterion makes the existing model-based designs more ethical without losing efficiency in the context of Phase I clinical trials.

stat.ME↗

arXiv2018

An information-theoretic Phase I/II design for molecularly targeted agents that does not require an assumption of monotonicity

For many years Phase I and Phase II clinical trials were conducted separately, but there was a recent shift to combine these Phases. While a variety of Phase~I/II model-based designs for cytotoxic agents were proposed in the literature, methods for molecularly targeted agents (TA) are just starting to develop. The main challenge of the TA setting is the unknown dose-efficacy relation that can have either an increasing, plateau or umbrella shape. To capture these, approaches with more parameters are needed to model the dose-efficacy relationship or, alternatively, more orderings of the dose-efficacy relationship are required to account for the uncertainty in the curve shape. As a result, designs for more complex clinical trials, for example, trials looking at schedules of a combination treatment involving TA, have not been extensively studied yet. We propose a novel regimen-finding design which is based on a derived efficacy-toxicity trade-off function. Due to its special properties, an accurate regimen selection can be achieved without any parametric or monotonicity assumptions. We illustrate how this design can be applied in the context of a complex combination-schedule clinical trial. We discuss practical and ethical issues such as coherence, delayed and missing efficacy responses, safety and futility constraints.

stat.ME↗

arXiv2018

An information-theoretic approach for selecting arms in clinical trials

The question of selecting the "best" amongst different choices is a common problem in statistics. In drug development, our motivating setting, the question becomes, for example: what is the dose that gives me a pre-specified risk of toxicity or which treatment gives the best response rate. Motivated by a recent development in the weighted information measures theory, we propose an experimental design based on a simple and intuitive criterion which governs arm selection in the experiment with multinomial outcomes. The criterion leads to accurate arm selection without any parametric or monotonicity assumption. The asymptotic properties of the design are studied for different allocation rules and the small sample size behaviour is evaluated in simulations in the context of Phase I and Phase II clinical trials with binary endpoints. We compare the proposed design to currently used alternatives and discuss its practical implementation.

math.ST↗

arXiv2018

A Benchmark for Dose Finding Studies with Continuous Outcomes

An important tool to evaluate the performance of any design is an optimal benchmark proposed by O'Quigley and others (2002, Biostatistics 3(1), 51-56) that provides an upper bound on the performance of a design under a given scenario. The original benchmark can be applied to dose finding studies with a binary endpoint only. However, there is a growing interest in dose finding studies involving continuous outcomes, but no benchmark for such studies has been developed. We show that the original benchmark and its extension by Cheung (2014, Biometrics 70(2), 389-397), when looked at from a different perspective, can be generalised to various settings with several discrete and continuous outcomes. We illustrate and compare the benchmark performance in the setting of a Phase I clinical trial with continuous toxicity endpoint and in the setting of a Phase I/II clinical trial with continuous efficacy outcome. We show that the proposed benchmark provides an accurate upper bound for model-based dose finding methods and serves as a powerful tool for evaluating designs.

math.ST↗

arXiv2018

A review of the deterministic and diffusion approximations for stochastic chemical reaction networks

This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena, such as a deficiency and a bistability. It is advocated that the diffusion approximation can be considered as an alternative theoretical approach to study the reaction networks rather than a simulation shortcut. We discuss two examples in which the diffusion approximation is able to catch qualitative properties of reaction networks that the deterministic model misses. We provide an explicit construction of the original process and the diffusion approximation such that the distance between their trajectories is controlled and demonstrate this construction for the examples. We also discuss the limitations and potential directions of the developments.

math.PR↗

arXiv2015

Limits of Kalman Filter application in heavy tailed problems

In this paper we consider the behavior of Kalman Filter state estimates in the case of distribution with heavy tails .The simulated linear state space models with Gaussian measurement noises were used. Gaussian noises in state equation are replaced by components with alpha-stable distribution with di erent parameters alpha and beta. We consider the case when "all parameters are known" and two methods of parameters estimation are compared: the maximum likelihood estimator (MLE) and the expectation- maximization algorithm (EM). It was shown that in cases of large deviation from Gaussian distribution the total error of states estimation rises dramatically. We conjecture that it can be explained by underestimation of the state equation noises covariance matrix that can be taken into account through the EM parameters estimation and ignored in the case of ML estimation.

math.ST↗

arXiv2015

Asymptotic behaviour of weighted differential entropies in a Bayesian problem

We consider a Bayesian problem of estimating of probability of success in a series of conditionally independent trials with binary outcomes. We study the asymptotic behaviour of differential entropy for posterior probability density function conditional on $x$ successes after $n$ conditionally independent trials, when $n \to \infty$. It is shown that after an appropriate normalization in cases $x \sim n$ and $x$ $\sim n^β$ ($0<β<1$) limiting distribution is Gaussian and the differential entropy of standardized RV converges to differential entropy of standard Gaussian random variable. When $x$ or $n-x$ is a constant the limiting distribution in not Gaussian, but still the asymptotic of differential entropy can be found explicitly. Then suppose that one is interested to know whether the coin is fair or not and for large $n$ is interested in the true frequency. To do so the concept of weighted differential entropy introduced in \cite{Belis1968} is used when the frequency $γ$ is necessary to emphasize. It was found that the weight in suggested form does not change the asymptotic form of Shannon, Renyi, Tsallis and Fisher entropies, but change the constants. The main term in weighted Fisher Information is changed by some constant which depend on distance between the true frequency and the value we want to emphasize. In third part we derived the weighted versions of Rao-Cramér, Bhattacharyya and Kullback inequalities. This result is applied to the Bayesian problem described above. The asymptotic forms of these inequalities are obtained for a particular class of weight functions.

cs.IT↗