Sample sizes required to estimate the protective efficacy of a vaccine when there is an unequal allocation of individuals across the vaccine and placebo groups

The effectiveness of a vaccine is measured by means of protective vaccine efficacy, defined by V E = 1 - A R V A R U , where A R V and A R U are, respectively, the disease attack rates in the vaccinated and the unvaccinated population. For each of the cohoret and case-control designs, methods have been presented in the literature for calculating the required sample size when the desired width of the confidence interval and the probability of coverage are pre-specified, where an equal number of individuals were assumed to be allocated to the vaccine and placebo group. In this article, we present a method for calculating the required sample size with a specified degree of precision when there is an unequal allocation of individuals across the two groups. The sample size required to achieve a desired power for the relevant level α test has also been explored, keeping the unequal allocation proportion in mind. The fraction of individuals allocated to the placebo group (ρ ) can be so chosen that the total sample size or the expected number of people developing the disease or some other criteria of interest is minimized.

How to Use and Interpret the Results of a Platform Trial: Users' Guide to the Medical Literature

Platform trials are a type of randomized clinical trial that allow simultaneous comparison of multiple intervention groups against a single control group that serves as a common control based on a prespecified interim analysis plan. The platform trial design enables introduction of new interventions after the trial is initiated to evaluate multiple interventions in an ongoing manner using a single overarching protocol called a master (or core) protocol. When multiple treatment candidates are available, rapid scientific therapeutic discoveries may be made. Platform trials have important potential advantages in creating an efficient trial infrastructure that can help address critical clinical questions as the evidence evolves. Platform trials have recently been used in investigations of evolving therapies for patients with COVID-19. The purpose of this Users' Guide to the Medical Literature is to describe fundamental concepts of platform trials and master protocols and review issues in the conduct and interpretation of these studies. This Users' Guide is intended to help clinicians and readers understand articles reporting on interventions evaluated using platform trial designs.

Randomised trials at the level of the individual

In global health research, short-term, small-scale clinical trials with fixed, two-arm trial designs that generally do not allow for major changes throughout the trial are the most common study design. Building on the introductory paper of this Series, this paper discusses data-driven approaches to clinical trial research across several adaptive trial designs, as well as the master protocol framework that can help to harmonise clinical trial research efforts in global health research. We provide a general framework for more efficient trial research, and we discuss the importance of considering different study designs in the planning stage with statistical simulations. We conclude this second Series paper by discussing the methodological and operational complexity of adaptive trial designs and master protocols and the current funding challenges that could limit uptake of these approaches in global health research.

A natural lead-in approach to response-adaptive allocation for continuous outcomes

Response-adaptive (RA) allocation designs can skew the allocation of incoming subjects toward the better performing treatment group based on the previously accrued responses. While unstable estimators and increased variability can adversely affect adaptation in early trial stages, Bayesian methods can be implemented with decreasingly informative priors (DIP) to overcome these difficulties. DIPs have been previously used for binary outcomes to constrain adaptation early in the trial, yet gradually increase adaptation as subjects accrue. We extend the DIP approach to RA designs for continuous outcomes, primarily in the normal conjugate family by functionalizing the prior effective sample size to equal the unobserved sample size. We compare this effective sample size DIP approach to other DIP formulations. Further, we considered various allocation equations and assessed their behavior utilizing DIPs. Simulated clinical trials comparing the behavior of these approaches with traditional Frequentist and Bayesian RA as well as balanced designs show that the natural lead-in approaches maintain improved treatment with lower variability and greater power.

A response-adaptive randomization procedure for multi-armed clinical trials with normally distributed outcomes

We propose a novel response‐adaptive randomization procedure for multi‐armed trials with continuous outcomes that are assumed to be normally distributed. Our proposed rule is non‐myopic, and oriented toward a patient benefit objective, yet maintains computational feasibility. We derive our response‐adaptive algorithm based on the Gittins index for the multi‐armed bandit problem, as a modification of the method first introduced in Villar et al. (Biometrics, 71, pp. 969‐978). The resulting procedure can be implemented under the assumption of both known or unknown variance. We illustrate the proposed procedure by simulations in the context of phase II cancer trials. Our results show that, in a multi‐armed setting, there are efficiency and patient benefit gains of using a response‐adaptive allocation procedure with a continuous endpoint instead of a binary one. These gains persist even if an anticipated low rate of missing data due to deaths, dropouts, or complete responses is imputed online through a procedure first introduced in this paper. Additionally, we discuss how there are response‐adaptive designs that outperform the traditional equal randomized design both in terms of efficiency and patient benefit measures in the multi‐armed trial context.

Response-adaptive designs for binary responses: How to offer patient benefit while being robust to time trends?

Response‐adaptive randomisation (RAR) can considerably improve the chances of a successful treatment outcome for patients in a clinical trial by skewing the allocation probability towards better performing treatments as data accumulates. There is considerable interest in using RAR designs in drug development for rare diseases, where traditional designs are not either feasible or ethically questionable. In this paper, we discuss and address a major criticism levelled at RAR: namely, type I error inflation due to an unknown time trend over the course of the trial. The most common cause of this phenomenon is changes in the characteristics of recruited patients—referred to as patient drift. This is a realistic concern for clinical trials in rare diseases due to their lengthly accrual rate. We compute the type I error inflation as a function of the time trend magnitude to determine in which contexts the problem is most exacerbated. We then assess the ability of different correction methods to preserve type I error in these contexts and their performance in terms of other operating characteristics, including patient benefit and power. We make recommendations as to which correction methods are most suitable in the rare disease context for several RAR rules, differentiating between the 2‐armed and the multi‐armed case. We further propose a RAR design for multi‐armed clinical trials, which is computationally efficient and robust to several time trends considered.

Is the classical Wald test always suitable under response-adaptive randomization?

The aim of this paper is to analyze the impact of response-adaptive randomization rules for normal response trials intended to test the superiority of one of two available treatments. Taking into account the classical Wald test, we show how response-adaptive methodology could induce a consistent loss of inferential precision. Then, we suggest a modified version of the Wald test which, by using the current allocation proportion to the treatments as a consistent estimator of the target, avoids some degenerate scenarios and so it should be preferable to the classical test. Furthermore, we show both analytically and via simulations how some target allocations may induce a locally decreasing power function. Thus, we derive the conditions on the target guaranteeing its monotonicity and we show how a correct choice of the initial sample size allows one to overcome this drawback regardless of the adopted target.