1,721,182 research outputs found
Convergence rate for Ehrenfest-type urn designs
No full textIn questo lavoro si analizza il problema della velocità di
convergenza per esperimenti markoviani generati attraverso processi
di tipo Ehrenfest, ossia opportune estensioni del classico modello
ad urne introdotto dai coniugi Ehrenfest nell'ambito della meccanica
statistica. Si definiscono markoviani quegli esperimenti sequenziali
in cui il ricercatore decide ad ogni passo come effettuare
l'osservazione successiva sulla base della sola osservazione più
recente. Tali procedure possono essere adeguatamente studiate per
mezzo di una catena di Markov, la cui distribuzione stazionaria
descrive completamente il comportamento asintotico dell'esperimento.
Sulla base di risultati per passeggiate aleatorie ergodiche è
possibile fornire alcune condizioni che permettono di caratterizzare
in modo esatto la velocità di convergenza della catena alla
distribuzione stazionaria
Generalized Pòlya Urn designs with null balance
No full textIn this paper we propose a class of sequential urn designs based on Generalized Pòlya Urn (GPU) models for balancing the allocations of two treatments in sequential clinical trials. In particular, we consider a GPU model characterized by a 2 x 2 random addition matrix with null balance (i.e. null row sums) and replacement rule depending upon the urn composition. Under this scheme, the urn process has a Markovian structure and can be regarded as a random extension of the classical Ehrenfest model. We establish almost sure convergence and asymptotic normality for the frequency of treatment allocations and show that in some peculiar cases the asymptotic variance of the design admits a natural representation based on the set of orthogonal polynomials associated to the corresponding Markov process
A new 'biased coin design' for the sequential allocation of two treatments
No full textEfron's (1971) Biased Coin Design is a well-known randomization technique that helps neutralize selection bias in sequential clinical trials for comparing treatments, while keeping the experiment fairly balanced. Extensions of the BCD have been proposed by several authors, who have focused mainly on the large sample properties of their designs. We modify Efron's procedure by introducing an Adjustable Biased Coin Design (ABCD), more flexible than his. We compare it to other existing coin designs; in terms of balance and lack of predictability, its performance for small samples appears in many cases to be an improvement with respect to the other sequential randomized allocation procedure
Is the classical Wald test always suitable under response-adaptive randomization?
Full text linkThe 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 theWald 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
A new inferential approach for response-adaptive clinical trials: the variance-stabilized bootstrap
Full text linkThis paper discusses disadvantages and limitations of the available inferential
approaches in sequential clinical trials for treatment comparisons managed via
response-adaptive randomization. Then, we propose an inferential methodology for
response-adaptive designs which, by exploiting a variance stabilizing transformation
into a bootstrap framework, is able to overcome the above-mentioned drawbacks,
regardless of the chosen allocation procedure aswell as the desired target.We derive the
theoretical properties of the suggested proposal, showing its superiority with respect
to likelihood, randomization and design-based inferential approaches. Several illustrative
examples and simulation studies are provided in order to confirm the relevance
of our results
A simple solution to the inadequacy of asymptotic likelihood-based inference for response-adaptive clinical trials
Full text linkThe present paper discusses drawbacks and limitations of likelihood-based inference
in sequential clinical trials for treatment comparisons managed viaResponse-Adaptive
Randomization. Taking into account the most common statistical models for the primary
outcome—namely binary, Poisson, exponential and normal data—we derive the
conditions under which (i) the classical confidence intervals degenerate and (ii) the
Wald test becomes inconsistent and strongly affected by the nuisance parameters, also
displaying a non monotonic power. To overcome these drawbacks, we provide a very
simple solution that could preserve the fundamental properties of likelihood-based
inference. Several illustrative examples and simulation studies are presented in order
to confirm the relevance of our results and provide some practical recommendations
Estimation accuracy under covariate-adaptive randomization procedures
Full text linkIn this paper we provide some general asymptotic properties of covariate-adaptive (CA) randomized designs aimed at balancing the allocations of two treatments across a set of chosen covariates. In particular, we establish the central limit theorem for a vast class of covariate-adaptive procedures characterized by i) a different allocation function for each covariate profile and ii) sequences of allocation rules instead of a pre-fixed one. This result allows one to derive theoretically the asymptotic expressions of the loss of information induced by imbalance and the selection bias due to the lack of randomness, that are the fundamental properties for estimation of every CA rule, widely used in order to compare different CA procedures. Besides providing the proofs of unsolved conjectures about some CA designs suggested in the literature, explored up to now almost exclusively through simulations, our results provide substantial insight for future suggestions and represent an accurate tool for the large sample comparisons between CA designs. A numerical study is also performed to assess the validity of the suggested approach
Optimal designs for testing the efficacy of heterogeneous experimental groups
Full text linkThis paper develops a unified framework for deriving optimal
designs for hypothesis testing in the presence of several heteroscedastic
groups. In particular, the obtained optimal designs are generalized Neyman
allocations involving only two experimental groups. In order to account for
the ordering among the treatments, particularly relevant in the clinical
context for ethical reasons, we provide the optimal design for testing under
constraints reflecting their effectiveness. The advantages of the suggested
allocations are illustrated both theoretically and through several numerical
examples, also compared with other designs proposed in the literature,
showing a substantial gain in terms of both power and ethics
Simulated annealing for balancing covariates
Full text linkCovariate balance is one of the fundamental issues in designing experiments for
treatment comparisons, especially in randomized clinical trials. In this article,
we introduce a new class of covariate-adaptive procedures based on the Simulated
Annealing algorithm aimed at balancing the allocations of two competing
treatments across a set of pre-specified covariates. Due to the nature of the simulated
annealing, these designs are intrinsically randomized, thus completely
unpredictable, and very flexible: they can manage both quantitative and qualitative
factors and be implemented in a static version as well as sequentially.
The properties of the suggested proposal are described, showing a significant
improvement in terms of covariate balance and inferential accuracy with respect
to all the other procedures proposed in the literature. An illustrative example
based on real data is also discussed
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