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Efficient and Adaptive Estimation for Semiparametric Models

Efficient and Adaptive Estimation for Semiparametric Models
Author: Peter J. Bickel
Publisher: Springer
Total Pages: 588
Release: 1998-06-01
Genre: Mathematics
ISBN: 0387984739

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This book deals with estimation in situations in which there is believed to be enough information to model parametrically some, but not all of the features of a data set. Such models have arisen in a wide context in recent years, and involve new nonlinear estimation procedures. Statistical models of this type are directly applicable to fields such as economics, epidemiology, and astronomy.


Small Clinical Trials

Small Clinical Trials
Author: Institute of Medicine
Publisher: National Academies Press
Total Pages: 221
Release: 2001-01-01
Genre: Medical
ISBN: 0309171148

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Clinical trials are used to elucidate the most appropriate preventive, diagnostic, or treatment options for individuals with a given medical condition. Perhaps the most essential feature of a clinical trial is that it aims to use results based on a limited sample of research participants to see if the intervention is safe and effective or if it is comparable to a comparison treatment. Sample size is a crucial component of any clinical trial. A trial with a small number of research participants is more prone to variability and carries a considerable risk of failing to demonstrate the effectiveness of a given intervention when one really is present. This may occur in phase I (safety and pharmacologic profiles), II (pilot efficacy evaluation), and III (extensive assessment of safety and efficacy) trials. Although phase I and II studies may have smaller sample sizes, they usually have adequate statistical power, which is the committee's definition of a "large" trial. Sometimes a trial with eight participants may have adequate statistical power, statistical power being the probability of rejecting the null hypothesis when the hypothesis is false. Small Clinical Trials assesses the current methodologies and the appropriate situations for the conduct of clinical trials with small sample sizes. This report assesses the published literature on various strategies such as (1) meta-analysis to combine disparate information from several studies including Bayesian techniques as in the confidence profile method and (2) other alternatives such as assessing therapeutic results in a single treated population (e.g., astronauts) by sequentially measuring whether the intervention is falling above or below a preestablished probability outcome range and meeting predesigned specifications as opposed to incremental improvement.


Estimation in Semiparametric Models

Estimation in Semiparametric Models
Author: Johann Pfanzagl
Publisher: Springer
Total Pages: 124
Release: 1990
Genre: Mathematics
ISBN:

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Assume one has to estimate the mean J x P( dx) (or the median of P, or any other functional t;;(P)) on the basis ofi.i.d. observations from P. Ifnothing is known about P, then the sample mean is certainly the best estimator one can think of. If P is known to be the member of a certain parametric family, say {Po: {) E e}, one can usually do better by estimating {) first, say by {)(n)(.̃.), and using J XPo(n)(;r.) (dx) as an estimate for J xPo(dx). There is an "intermediate" range, where we know something about the unknown probability measure P, but less than parametric theory takes for granted. Practical problems have always led statisticians to invent estimators for such intermediate models, but it usually remained open whether these estimators are nearly optimal or not. There was one exception: The case of "adaptivity", where a "nonparametric" estimate exists which is asymptotically optimal for any parametric submodel. The standard (and for a long time only) example of such a fortunate situation was the estimation of the center of symmetry for a distribution of unknown shape.


Population-based Cancer Survival Analysis

Population-based Cancer Survival Analysis
Author: Paul W. Dickman
Publisher: Wiley
Total Pages: 0
Release: 2022-12-27
Genre: Mathematics
ISBN: 9780470028599

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There has been increased interest in studying cancer patient survival in recent years, which has prompted advances in methods for estimating and modeling cancer patient survival. This book is the first focused on this topic, and uses real data and software to illustrate the methods involved. The supporting website provides code to enable readers to reproduce the analysis top illustrate the examples included in the book. The book presents methods for population-based cancer survival analysis, that is, the analysis of patient survival using data collected by population-based cancer registries. The primary focus will be on the statistical methods but non-statistical issues that arise in population-based studies of cancer patient survival, such as registration, coding and classification, and follow up procedures are also discussed.