Modeling the Agreement of Discrete Bivariate Survival Times using Kappa Coefficient

Using local kappa coefficients, we develop a method to assess the agreement between two discrete survival times that are measured on the same subject by different raters or methods. We model the marginal distributions for the two event times and local kappa coefficients in terms of covariates. An estimating equation is used for modeling the marginal distributions and a pseudo-likelihood procedure is used to estimate the parameters in the kappa model. The performance of the estimation procedure is examined through simulations. The proposed method can be extended to multivariate discrete survival distributions.     

Estimation methods for time‐dependent AUC models with survival data

The performance of clinical tests for disease screening is often evaluated using the area under the receiver‐operating characteristic (ROC) curve (AUC). Recent developments have extended the traditional setting to the AUC with binary time‐varying failure status. Without considering covariates, our first theme is to propose a simple and easily computed nonparametric estimator for the time‐dependent AUC. Moreover, we use generalized linear models with time‐varying coefficients to characterize the time‐dependent AUC as a function of covariate values. The corresponding estimation procedures are proposed to estimate the parameter functions of interest. The derived limiting Gaussian processes and the estimated asymptotic variances enable us to construct the approximated confidence regions for the AUCs. The finite sample properties of our proposed estimators and inference procedures are examined through extensive simulations. An analysis of the AIDS Clinical Trials Group (ACTG) 175 data is further presented to show the applicability of the proposed methods. The Canadian Journal of Statistics 38:8–26; 2010 © 2009 Statistical Society of Canada     

Data driven smooth test for paired populations

In this paper we propose a smooth test of comparison of two distribution functions. This test adapts to the classical two-sample problem as well as that of paired populations, including discrete distributions. A simulation study and an application to real data show its good performances.     

On the behaviour of tests based on sample spacings for moderatesamples

We revisit the question about optimal performance of goodness-of-fit tests based on sample spacings. We reveal the importance of centering of the test-statistic and of the sample size when choosing a suitable test-statistic from a family of statistics based on power transformations of sample spacings. In particular, we find that a test-statistic based on empirical estimation of the Hellinger distance between hypothetical and data-supported distribution does possess some optimality properties for moderate sample sizes. These findings confirm earlier statements about the robust behaviour of the test-statistic based on the Hellinger distance and are in contrast to findings about the asymptotic (when sample size approaches infinity) of statistics such as Moran's and/or Greenwood's statistic. We include simulation results that support our findings.     

Buckley–James Type Estimator for Censored Data with Covariates Missing by Design

Abstract. The Buckley–James estimator (BJE) is a well‐known estimator for linear regression models with censored data. Ritov has generalized the BJE to a semiparametric setting and demonstrated that his class of Buckley–James type estimators is asymptotically equivalent to the class of rank‐based estimators proposed by Tsiatis. In this article, we revisit such relationship in censored data with covariates missing by design. By exploring a similar relationship between our proposed class of Buckley–James type estimating functions to the class of rank‐based estimating functions recently generalized by Nan, Kalbfleisch and Yu, we establish asymptotic properties of our proposed estimators. We also conduct numerical studies to compare asymptotic efficiencies from various estimators.     

Simple correspondence analysis using adjusted residuals

Correspondence analysis is a versatile statistical technique that allows the user to graphically identify the association that may exist between variables of a contingency table. For two categorical variables, the classical approach involves applying singular value decomposition to the Pearson residuals of the table. These residuals allow for one to use a simple test to determine those cells that deviate from what is expected under independence. However, the assumptions concerning these residuals are not always satisfied and so such results can lead to questionable conclusions.One may consider instead, an adjustment of the Pearson residual, which is known to have properties associated with the standard normal distribution. This paper explores the application of these adjusted residuals to correspondence analysis and determines how they impact upon the configuration of points in the graphical display.     

Conditional estimation of average on the basis of weighting data

LetF(x,y) be a distribution function of a two dimensional random variable (X,Y). We assume that a distribution functionF _x(x) of the random variableX is known. The variableX will be called an auxiliary variable. Our purpose is estimation of the expected valuem=E(Y) on the basis of two-dimensional simple sample denoted by:U=[(X ₁, Y₁)…(X_n, Y_n)]=[X Y]. LetX=[X ₁…X _n]andY=[Y ₁…Y _n].This sample is drawn from a distribution determined by the functionF(x,y). LetX _(k)be the k-th (k=1, …,n) order statistic determined on the basis of the sampleX. The sampleU is truncated by means of this order statistic into two sub-samples: % MathType!End!2!1! and % MathType!End!2!1!.Let % MathType!End!2!1! and % MathType!End!2!1! be the sample means from the sub-samplesU _k,1 andU _k,2, respectively. The linear combination % MathType!End!2!1! of these means is the conditional estimator of the expected valuem. The coefficients of this linear combination depend on the distribution function of auxiliary variable in the pointx _(k).We can show that this statistic is conditionally as well as unconditionally unbiased estimator of the averagem. The variance of this estimator is derived. The variance of the statistic % MathType!End!2!1! is compared with the variance of the order sample mean. The generalization of the conditional estimation of the mean is considered, too.     

Multivariate outlier tests with structured co variance matrices

Outlier tests are developed for multivariate data where there is a structure to the covariance or correlation matrix. Particular structures considered are the block diagonal structure where there are reasons to assume that one set of variables is independent of another, and the equicorrelation structure where it may be assumed that all pairs of variables have the same correlation. Likelihood ratio tests for an outlier are derived for these situations and critical values, under the null hypothesis of no outliers present, are determined for selected sample sizes and dimensions, using Bonferroni bounds or simulation. The powers of the tests are compared with those of the Wilks′ statistic for a variety of situations. It is shown that the test procedures which incorporate knowledge of the correlation structure have considerably greater power than the usual tests particularly in relatively small samples with several dimensions.     

An extension of the Anderson–Darling k-sample test to arbitrary sample space partition sizes

In this paper we first show that the k-sample Anderson–Darling test is basically an average of Pearson statistics in 2?×?k contingency tables that are induced by observation-based partitions of the sample space. As an extension, we construct a family of rank test statistics, indexed by c?∈??, which is based on similarly constructed c?×?k partitions. An extensive simulation study, in which we compare the new test with others, suggests that generally very high powers are obtained with the new tests. Finally we propose a decomposition of the test statistic in interpretable components.     

A modified Cp statistic in a system-of-equations model

A new statistic, SΓ(p), is developed for variable selection in a system-of-equations model. The standardized total mean square error in the SΓ(p)statistic is weighted by the covariance matrix of dependent variables instead of the error covariance matrix of the true model as in the original definition. The new statistic can be also used for model selection in the non-nested models. The estimate of SΓ(p), SC(p), is derived and shown to become SC_ε(p) in the similar form of C_p in a single-equation model when the covariance matrix of sampled dependent variables is replaced by the error covariance matrix under the full model.