1,003 research outputs found
Gibbs-Markov structures and limit laws for partially hyperbolic attractors with mostly expanding central direction
We consider a partially hyperbolic set on a Riemannian manifold whose
tangent space splits as , for which the
centre-unstable direction expands non-uniformly on some local unstable
disk. We show that under these assumptions induces a Gibbs-Markov
structure. Moreover, the decay of the return time function can be controlled in
terms of the time typical points need to achieve some uniform expanding
behavior in the centre-unstable direction. As an application of the main result
we obtain certain rates for decay of correlations, large deviations, an almost
sure invariance principle and the validity of the Central Limit Theorem.Comment: 23 page
Explosion of smoothness for conjugacies between multimodal maps
Let and be smooth multimodal maps with no periodic attractors and no
neutral points. If a topological conjugacy between and is
at a point in the nearby expanding set of , then is a smooth
diffeomorphism in the basin of attraction of a renormalization interval of .
In particular, if and are unimodal maps and
is at a boundary of then is in .Comment: 22 page
Response-adaptive dose-finding under model uncertainty
Dose-finding studies are frequently conducted to evaluate the effect of
different doses or concentration levels of a compound on a response of
interest. Applications include the investigation of a new medicinal drug, a
herbicide or fertilizer, a molecular entity, an environmental toxin, or an
industrial chemical. In pharmaceutical drug development, dose-finding studies
are of critical importance because of regulatory requirements that marketed
doses are safe and provide clinically relevant efficacy. Motivated by a
dose-finding study in moderate persistent asthma, we propose response-adaptive
designs addressing two major challenges in dose-finding studies: uncertainty
about the dose-response models and large variability in parameter estimates. To
allocate new cohorts of patients in an ongoing study, we use optimal designs
that are robust under model uncertainty. In addition, we use a Bayesian
shrinkage approach to stabilize the parameter estimates over the successive
interim analyses used in the adaptations. This approach allows us to calculate
updated parameter estimates and model probabilities that can then be used to
calculate the optimal design for subsequent cohorts. The resulting designs are
hence robust with respect to model misspecification and additionally can
efficiently adapt to the information accrued in an ongoing study. We focus on
adaptive designs for estimating the minimum effective dose, although
alternative optimality criteria or mixtures thereof could be used, enabling the
design to address multiple objectives.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS445 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Practical considerations for optimal designs in clinical dose finding studies
Determining an adequate dose level for a drug and, more broadly, characterizing its dose response relationship, are key objectives in the clinical development of any medicinal drug. If the dose is set
too high, safety and tolerability problems are likely to result, while selecting too low a dose makes it difficult to establish adequate efficacy in the confirmatory phase, possibly leading to a failed program.
Hence, dose finding studies are of critical importance in drug development and need to be planned carefully. In this paper we focus on practical considerations for establishing efficient study designs to estimate target doses of interest. We consider optimal designs for both the estimation of the minimum effective dose (MED) and the dose achieving 100p% of the maximum treatment effect (EDp). These designs are compared with D-optimal designs for a given dose response model. Extensions to robust
designs accounting for model uncertainty are also discussed. A case study is used to motivate and illustrate the methods from this paper
LINEAR AND NONLINEAR MIXED-EFFECTS MODELS
Recent developments in computational methods for maximum likelihood (ML) or restricted maximum likelihood (REML) estimation of parameters in general linear mixed-effects models have made the analysis of data in typical agricultural settings much easier. With software such as SAS PROC MIXED we are able to handle data from random-effects one-way classifications, from blocked designs including incomplete blocked designs, from hierarchical designs such as splitplot designs, and other types of data that may be described as repeated measures or longitudinal data or growth-curve data. It is especially helpful that the new computational methods do not depend on balance in the data so we are able to deal more easily with observational studies or with randomly missing data in a designed experiment .
We describe some of the new computational approaches and how they are implemented in the nlme3.0 library for the S-PLUS language. One of the most powerful features of this language is the graphics capabilities, especially the trellis graphics facilities developed by Bill Cleveland and his coworkers at Bell Labs. Although most participants in this conference may be more familiar with SAS, and most of the models described here can be fit with PROC MIXED or the NLiNMIX macro or new PROC NLM IXED in SAS version 7, some exposure to the combination of graphical display and model-fitting approaches from S-PLUS may be informative .
We show how data exploration with trellis graphics, followed by fitting and comparing mixedeffects models, followed by graphical assessment of the fitted model can be used in a variety of situations. On some occasions, such as modeling growth curves, a linear trend or polynomial trend or other types of linear statistical models for the within-subject time dependence are just not going to do an adequate job of representing the data. In those cases, a nonlinear model is more appropriate. We show how the concept of a random coefficient model can be extended to nonlinear models so as to fit nonlinear mixed-effects models
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