327 research outputs found
Sample size determination for equivalence trials
No full textIn clinical practice we are usually interested in showing that an innovative therapy is more effective than a standard one. However, in some cases we have to respond to the different purpose of proving equivalence of two competing treatments (equivalence trials). For example, when a pharmaceutical company is aware that there is not evidence enough for proving superiority of a new treatment, it can decide to go for equivalence. The idea is that the new drug has chances to be approved and put on the market if it guarantees at the same time other advantages, for instance
in terms of safety or costs. In this paper we refer to the setting of equivalence trials, with specific regard to the issue of sample size determination (SSD). First step is to define the so called equivalence interval I, that is a set of values of the parameter of interest indicating a negligible difference between the treatments effects. Hence, we declare success if an interval estimate of θ is entirely included in I. By adapting the metodology presented in Brutti and De Santis (2008) to equivalence trials, we derive two alternative SSD criteria based on Bayesian credible intervals. In particular we consider the so-called two priors approach (see Wang and
Gelfand, 2002): on the one hand pre-experimental information is represented by the analysis prior, on the other hand uncertainty on the target value θ D – that is chosen in the range of equivalence – is modeled by the design prior.
Finally, we also consider a robust version of the above criteria in which the
single analysis prior is replaced by a suitable class of prior distribution. In this work we derive results for the normal model with conjugate priors, illustrating an application, based on a real example by Spiegelhalter et al. (2004)
Sample Size Requirements for Calibrated Approximate Credible Intervals for Proportions in Clinical Trials
No full textIn Bayesian analysis of clinical trials data, credible intervals are widely used for inference on unknown parameters of interest, such as treatment effects or differences in treatments effects. Highest Posterior Density (HPD) sets are often used because they guarantee the shortest length. In most of standard problems, closed-form expressions for exact HPD intervals do not exist, but they are available for intervals based on the normal approximation of the posterior distribution. For small sample sizes, approximate intervals may be not calibrated in terms of posterior probability, but for increasing sample sizes their posterior probability tends to the correct credible level and they become closer and closer to exact sets. The article proposes a predictive analysis to select appropriate sample sizes needed to have approximate intervals calibrated at a pre-specified level. Examples are given for interval estimation of proportions and log-odds
A decision-theoretic approach to sample size determination under several priors
No full textIn this article, we consider sample size determination for experiments in which estimation and design are performed by multiple parties. This problem has relevant applications in contexts involving adversarial decision makers, such as control theory, marketing,and drug testing. We adopt a decision-theoretic perspective, and we assume that a decision on an unknown parameter of a statistical model involves two actors who share the same data and loss function but not the same prior beliefs on the parameter. We aim at determining an appropriate sample size so that the posterior expected loss incurred by one actor taking the optimal action of the other is small. We develop general results for the one-parameter exponential family under quadratic loss and analyze the interactive impact of the prior beliefs of the three different parties on the resulting sample sizes. Relationships with other sample size determination criteria are explored
Classical and Bayesian power functions; their use in clinical trials.
No full textThe most widely used method for sample size determination in clinical trials is based on the power function. This function expresses the probability of rejecting a statistical null hypothesis on the quantity of interest, typically the unknown difference between the effects of two alternative treatments. The standard classical power function, which we will refer to hereafter as the Conditional Frequentist Power function, does not take into account the following: (a) uncertainty on the design value used for the unknown parameter to compute the power; (b) pre-experimental information on the difference of unknown effects, provided, for instance, by previous clinical studies. By taking into account (a) and (b), several extensions of the power function have been proposed: the Predictive Frequentist Power function, the Conditional and Predictive Bayesian Power functions. We review these methods, their relationships with the standard approach and implications
on sample size determination
On the predictive performance of a non-optimal action in hypothesis testing
No full textIn Bayesian decision theory, the performance of an action is measured by its pos- terior expected loss. In some cases it may be convenient/necessary to use a non- optimal decision instead of the optimal one. In these cases it is important to quantify the additional loss we incur and evaluate whether to use the non-optimal decision or not. In this article we study the predictive probability distribution of a relative measure of the additional loss and its use to define sample size determination criteria in a general testing set-up
On the limit distribution of the power function induced by a design prior
No full textThe hybrid frequentist-Bayesian approach to sample size determination is based on the expectation of the power function of a test with respect to a design prior for the unknown parameter value. In clinical trials this quantity is often called probability of success (PoS). Determination of the limiting value of PoS as the number of observa- tions tends to infinity, that is crucial for well defined sample size criteria, has been considered in previous articles. Here, we focus on the asymptotic behavior of the whole distribution of the power function induced by the design prior. Under mild conditions, we provide asymptotic results for the three most common classes of hypotheses on a scalar parameter. The impact of the design parameters choice on the distribution of the power function and on its limit is discussed
Joint control of consensus and evidence in Bayesian design of clinical trials
No full textIn Bayesian inference, prior distributions formalize preexperimental information and uncertainty on model parameters. Sometimes different sources of knowledge are available, possibly leading to divergent posterior distributions and inferences. Research has been recently devoted to the development of sample size criteria that guarantee agreement of posterior information in terms of credible intervals when multiple priors are available. In these articles, the goals of reaching consensus and evidence are typically kept separated. Adopting a Bayesian performance-based approach, the present article proposes new sample size criteria for superiority trials that jointly control the achievement of both minimal evidence and consensus, measured by appropriate functions of the posterior distributions. We develop both an average criterion and a more stringent criterion that accounts for the entire predictive distributions of the selected measures of minimal evidence and consensus. Methods are developed and illustrated via simulation for trials involving binary outcomes. A real clinical trial example on Covid-19 vaccine data is presented
Bayesian Set Estimation with Alternative Loss Functions: Optimality and Regret Analysis
No full textDecision-theoretic interval estimation requires the use of loss functions that, typically, take into account the size and the coverage of the sets. We here consider the class of monotone loss functions that, under quite general conditions, guarantee Bayesian optimality of highest posterior probability sets. We focus on three specific families of monotone losses, namely the linear, the exponential and the rational losses whose difference consists in the way the sizes of the sets are penalized. Within the standard yet important set-up of a normal model we propose: 1) an optimality analysis, to compare the solutions yielded by the alternative classes of losses; 2) a regret analysis, to evaluate the additional loss of standard non-optimal intervals of fixed credibility. The article uses an application to a clinical trial as an illustrative example
Monitoring of sequential trials using a robust Bayesian stopping rule
No full textIn this paper we consider a method for monitoring a clinical trial whose patients are sequentially evaluated for response. We focus on a parameter representing treatment effect. Adopting a Bayesian approach we suggest to update progressively prior information on this unknown quantity: in particular, we monitor the trend of the posterior probability that the parameter is larger than a minimally clinical relevant value, as responses are collected. The trial is terminated with success as soon as this probability exceeds a prefixed threshold; if this does not happen before a preplanned maximum sample size is reached, the treatment is declared ineffective. Hence, the sample size is a random variable associated to the chosen stopping rule. With a simulation study we show that the expected sample size is always smaller than the preplanned optimal sample size and we illustrate an application to compare the sequential and the non sequential procedure. Finally, a robust version of the sequential criterion is proposed in which a single prior distribution is replaced by a suitable class of prior distributions
A BAYESIAN METHOD FOR THE CHOICE OF THE SAMPLE SIZE IN EQUIVALENCE TRIALS
No full textIn this paper we consider a Bayesian predictive approach to sample size determination in equivalence trials. Equivalence experiments are conducted to show that the unknown difference between two parameters is small. For instance, in clinical practice this kind of experiment aims to determine whether the effects of two medical interventions are therapeutically similar. We declare an experiment successful if an interval estimate of the effects-difference is included in a set of values of the parameter of interest indicating a negligible difference between treatment effects (equivalence interval). We derive two alternative criteria for the selection of the optimal sample size, one based on the predictive expectation of the interval limits and the other based on the predictive probability that these limits fall in the equivalence interval. Moreover, for both criteria we derive a robust version with respect to the choice of the prior distribution. Numerical results are provided and an application is illustrated when the normal model with conjugate prior distributions is assumed
- …
