Fernando Plo

Minimal quasi-stationary distributions under nullR-recurrence

The existence of quasi-stationary distributions (QSD) in an absorbing Markov chain entails a stationary behaviour before absorption. In general, depending on the initial distribution, several QSDs may exist. Under some conditions upon the transition matrix between non-absorbing states, we prove that the QSD associated with any Dirac initial distribution, when it exists, is unique, and is the minimal QSD. In other words, if we take this QSD as an initial distribution, the process has the smallest probability of not being absorbed in the first jump.

On Testing Hypotheses in Response-Adaptive Designs Targeting the Best Treatment

We considerer a sequential, response-adaptive design for clinical trials which is characterized by the fact that it assigns patients to the best treatment with a probability converging to one. This property is optimal from an ethical point of view; in this paper we analyze some inferential problems related to the design. In particular, we want to establish, by means of a test of hypothesis, which treatment is superior, in the sense that it has greater mean response. Together with the natural generalization of the classical t-statistic, we introduce a statistic based on the probability of assigning patients to a treatment conditional on past observations. Theoretical properties of the tests are studied, together with numerical evaluations of the power for dichotomous responses.

Randomization Based Inference for the Drop-The-Loser Rule

In the framework of clinical trials, legal and ethical restrictions make a population model unrealistic for sampling. Randomization tests are a viable alternative to classical inference. Their theoretical properties depend heavily on the random rule used to allocate patients to treatments, so that Ad-Hoc theoretical studies are necessary for each allocation design. In this paper, we obtain theoretical results for randomization tests when the drop-the-loser rule is used.

Asymptotic Behavior of a Randomization Test for a Response-Adaptive Design

Abstract Response-adaptive designs allow the incorporation of ethical goals in the performance of a clinical trial, and they have been thoroughly studied assuming that treatment responses follow a population model. However, in some clinical trials, population models are not appropriate and randomization tests appear as a plausible alternative to make inference. Randomization-based tests can be devised but the calculation of their exact p-values when a response-adaptive design is used to allocate patients is either time consuming or not feasible for moderate to large sample sizes and so asymptotic results become helpful. Nevertheless, these asymptotic results are not available for response-adaptive designs with good properties. The Klein allocation rule is a response-adaptive design, with good ethical and inferential properties, that generalizes the classical Ehrenfest urn design by making the replacement policy dependent on the response of the last patient. The goal of this article is to study the asymptotic distribution of a test statistic under a randomization-based approach when patients are allocated by using the Klein allocation rule.

Saturation Conditions For Stochastic Petri Nets

We give a necessary condition and a sufficient one for the saturation of a Markovian Stochastic Petri Net. These conditions can be explicitly checked in practical situations. As a particular case, we show that our conditions are equivalent to the classical condition of saturation for Jackson Queuing Networks. The applicability of the method is demonstrated also on examples of OSQN and OMS networks.