摘要:

A problem that arises frequently in the analysis of clinical trials is accounting for covariates observed postrandomization. Two examples are patient compliance measured through pill counts and the dose of a concomitant medication. Typically these are measured concurrently with the primary endpoint at the regularly scheduled follow-ups during the course of the study. To account for these effects, the confounders are sometimes introduced as time-dependent covariates into the statistical model. But there are conceptual and statistical difficulties with this approach. In this article we adopt the view that because the confounder is observed postrandomization, it must be considered as an endpoint in its own right. A seemingly unrelated regression (SUR) model is proposed to relate the two sets of repeated measures to important explanatory variables, and a vector autoregressive moving average (ARMA) time series model is used to characterize the disturbance terms within and across the two series. This accommodates the evolving relationship between the two variables and results in a parsimonious structure in the joint covariance matrix. Maximum likelihood estimation is applied using a Fisher scoring algorithm. Inference in this model is then performed by considering hypotheses on the primary endpoint conditionally on some behavior for the confounder. For example, if the two treatment groups had received an equivalent amount of concomitant medication, is there a significant difference in the primary endpoint? The methodology is illustrated with an example.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476512

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We consider the problem of filtering and smoothing in state-space models, which include nonlinear and non-Gaussian models. We do not make any distributional assumptions about the processes involved. Our approach to these problems is based on the theory of estimating functions. Filter and smoother are obtained as solutions of estimating equations that are optimal in appropriate classes. We illustrate our procedures by simulation studies of a model where the observational variance depends on the state and a binomial logit model with a covariate. In non-Gaussian cases, procedures based on estimating equations often perform considerably better than the existing semiparametric procedures.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476513

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476514

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Strong theoretical arguments imply that for directly representing and interpreting statistical data as evidence, the proper vehicle is the likelihood function. These arguments have had limited impact on statistical practice. One reason for this is that likelihood functions are explicitly model dependent and thus appear to be inherently nonrobust. In this article we examine the concept of robustness as it relates to likelihood functions. We note five ways that likelihood functions can be used to represent and interpret statistical data as evidence. These various uses suggest corresponding senses in which one likelihood function can approximate another, and these in turn suggest different senses in which a likelihood function can be “robust.” We establish some general relationships among these senses of robustness, and examine two general techniques for producing robust likelihoods.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476515

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Restricted parameter spaces for covariance matrices, such as∑= σ2Ior∑= αI+ βJ, are often used to simplify estimation. In addition, fixed upper and/or lower bounds may be needed to ensure that estimates satisfy a priori hypotheses. With multivariate variance components models, several covariance matrices need to be simultaneously estimated and, even with a reduced parameter space, estimation can be difficult. In earlier work we have discussed estimation for a widely-used class of models where the variance components matrices need only be nonnegative definite. In this article we extend these results to handle a wide class of restricted parameter spaces. We state the conditions required for a parameterization to be a member of the class, discuss the implementation of the results for several different members of the class, and discuss estimation with both balanced and unbalanced data. We give several examples to demonstrate the results.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476516

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

The Stahel-Donoho estimators (t, V) of multivariate location and scatter are defined as a weighted mean and a weighted covariance matrix with weights of the formw(r), wherewis a weight function andris a measure of “outlyingness,” obtained by considering all univariate projections of the data. It has a high breakdown point for all dimensions and order √nconsistency. The asymptotic bias ofVfor point mass contamination for suitable weight functions is compared with that of Rousseeuw's minimum volume ellipsoid (MVE) estimator. A simulation shows that for a suitablew,tandVexhibit high efficiency for both normal and Cauchy distributions and are better than their competitors for normal data with point-mass contamination. The performances of the estimators for detecting outliers are compared for both a real and a synthetic data set.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476517

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

A score-type statistic,Ts, is introduced for testingH: ψ = 0 againstK: ψ ≥ 0 and more general one-sided hypotheses when nuisance parameters may be present; ψ is a vector parameter. The main advantages ofTs, are that it requires estimation of the model only under the null hypothesis and that, it is asymptotically equivalent to the likelihood ratio statistic; these are precisely the reasons for the popularity of the score tests for testing against two-sided alternatives. In this sense,Tspreserves the main attractive features of the classical two-sided score test. The theoretical results are presented in a general framework where the likelihood-based score function is replaced by an estimating function so that the test is applicable even if the exact population distribution is unknown. Computation ofTs, is simplified by the fact that it can be computed easily once the corresponding two-sided statistic has been computed. The relevance and simplicity ofTsare illustrated by discussing a data example in detail. This example involves an autoregressive conditional heteroscedasticity (ARCH) model, and the objective is to test for the presence of ARCH effect. The null and alternative hypotheses turn out to be of the formH: ψ = 0 andK: ψ ≥ 0 respectively where ψ is the vector of ARCH parameters. In contrast to the likelihood ratio and other equivalent forms that are currently available for testing against such one-sided hypotheses, we note the following:Tsis convenient to apply, because the full ARCH model need not be estimated subject to the inequality constraint ψ ≥ 0 and we do not need to know the exact likelihood becauseTsis based on estimating equations rather than likelihoods.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476518

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

This article concerns itself with exploratory data analysis in hyperspace, and discusses a method of data reduction intended to allow insight into the geometry of ap-dimensional data set wherep> 2. The essential idea is to examine various “views” through the data set using a suitably chosen line, the baseline, for defining a viewing direction. For a given data point, its distance from a suitable point on the baseline, called the vertex, and the angular separation between the baseline and the line connecting the vertex to the data point are taken as coordinates of an ordinary polar coordinate plot in two dimensions. The bulk of the article discusses empirical evidence for the utility of such a plot, which can be referred to as a coneplot, because points are essentially identified with the intersection inpdimensions of a hypersphere and a ray of a hypercone.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476519

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

This article examines the use of the probability-probability plot (p-p plot) as a method for comparing treatment effects. To begin in the context of three examples the p-p plot is contrasted with the quantile-quantile plot (q-q plot), which is an alternative means of describing treatment effects. In these examples it is shown that p-p plots representing different experimental conditions or patient populations allow scale-invariant comparisons of treatment effects but q-q plots do not; that the presentation of the treatment effect by the p-p plot is not obscured by outliers, whereas it may be in the q-q plot; and that the p-p plot encompasses information in the control distributions that is important for the assessment of treatment effects but that is not incorporated in the q-q plot. Theoretical considerations are presented that show that under appropriate assumptions, the p-p plot is a maximal invariant and contains all the information necessary to make scale-invariant comparisons of treatment effects. Further, statistical methods for assessing patterns observed in the p-p plots are presented and illustrated in two examples.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476520

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Simultaneous confidence interval procedures for multinomial proportions are used in many areas of science. In this article two new simultaneous confidence interval procedures are introduced. Numerical results are presented to evaluate these procedures and compare their performance with established methods that have been used in statistical literature. From the results presented in this article, it is evident that the new procedures are more accurate than the established ones, where the accuracy of the procedure is measured by the volume of the confidence region corresponding to the nominal coverage probability and the probability of coverage it achieves. In the sample size determination problem, the new procedures provide a sizable amount of savings as compared to the procedures that have been used in many applications. Because both procedures performed equally well, the procedure that requires the least amount of computing time is recommended.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476521

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor