A note on testing the regression functions via nonparametric smoothing

The authors present a consistent lack‐of‐fit test in nonlinear regression models. The proposed procedure possesses some nice properties of Zheng's test such as the consistency, the ability to detect any local alternatives approaching the null at rates slower than the parametric rate. What's more, for a predetermined kernel function, the proposed test is more powerful than Zheng's test and the validity of these findings is confirmed by the simulation studies and a real data example. In addition, the authors find out a close connection between the choices of normal kernel functions and the bandwidths. The Canadian Journal of Statistics 39: 108–125; 2011 © 2011 Statistical Society of Canada     

Two‐sample empirical likelihood ratio tests for medians in application to biomarker evaluations

The median is a commonly used parameter to characterize biomarker data. In particular, with two vastly different underlying distributions, comparing medians provides different information than comparing means; however, very few tests for medians are available. We propose a series of two‐sample median‐specific tests using empirical likelihood methodology and investigate their properties. We present the technical details of incorporating the relevant constraints into the empirical likelihood function for in‐depth median testing. An extensive Monte Carlo study shows that the proposed tests have excellent operating characteristics even under unfavourable occasions such as non‐exchangeability under the null hypothesis. We apply the proposed methods to analyze biomarker data from Western blot analysis to compare normal cells with bronchial epithelial cells from a case–control study. The Canadian Journal of Statistics 39: 671–689; 2011. © 2011 Statistical Society of Canada     

A note on Läuter-type robust design for polynomial regression models

In this paper, we consider the problem of model robust design for simultaneous parameter estimation among a class of polynomial regression models with degree up to k. A generalized D-optimality criterion, the Ψ_α‐optimality criterion, first introduced by Läuter (1974) is considered for this problem. By applying the theory of canonical moments and the technique of maximin principle, we derive a model robust optimal design in the sense of having highest minimum Ψ_α‐efficiency. Numerical comparison indicates that the proposed design has remarkable performance for parameter estimation in all of the considered rival models.     

Estimation of the bivariate cause-specific distribution function with doubly censored competing risks data

In this article, we consider estimating the bivariate cause-specific distribution function when both components are subject to double censoring. We propose two types of estimators as generalizations of the Dabrowska and Campbell and Földes estimators. The asymptotical properties of the proposed estimators are established. A simulation study is conducted to investigate the performance of the proposed estimators.     

ESTIMATION OF MULTIVARIATE SHANNON ENTROPY USING MOMENTS

Three new entropy estimators of multivariate distributions are introduced. The two cases considered here concern when the distribution is supported by a unit sphere and by a unit cube. In the former case, the consistency and the upper bound of the absolute error for the proposed entropy estimator are established. In the latter one, under the assumption that only the moments of the underlying distribution are available, a non‐traditional estimator of the entropy is suggested. We also study the practical performances of the constructed estimators through simulation studies and compare the estimators based on the moment‐recovered approaches with their counterparts derived by using the histogram and k th nearest neighbour constructions. In addition, one worked example is briefly discussed.     

A ratio-to-control Williams-type test for trend

Under certain conditions, many multiple contrast tests based on the difference of treatment means can also be conveniently expressed in terms of ratios. In this paper, a Williams test for trend is defined as ratios-to-control for ease of interpretation and to obtain directly comparable confidence intervals. Simultaneous confidence intervals for percentages are particularly helpful for interpretations in the case of multiple endpoints. Methods for constructing simultaneous confidence intervals are discussed under both homogeneous and heterogeneous error variances. This approach is available in the R extension package mratios. The proposed method is used to test for trend in an immunotoxicity study with several endpoints as an example.     

A course for clinical trial personnel in clinical study designs, randomization, allocation schedules, and interactive response systems

This continuing education course for professionals involved in all areas of clinical trials integrates concepts related to the role of randomization in the scientific process. The course includes two interactive lecture and discussion sections and a workshop practicum. The first interactive lecture introduces basic clinical trial issues and statistical principles such as bias, blinding, randomization, control groups, and the importance of formulating clear and discriminating clinical and statistical hypotheses. It then focuses on the most commonly used clinical study designs and the corresponding patient randomization schemes. The second interactive lecture focuses on the implementation of randomization of patients and drug supply through allocation and component ID schedules. The workshop practicum, conducted in small groups, enables students to apply the lecture concepts to real clinical studies. Flexibility was built into the workshop practicum materials to allow the course content to be customized to specific audiences, and the interactive lecture sessions can be stretched to cover more advanced topics according to class interest and time availability.     

Issues for stratified randomization based on a factor derived from a continuous baseline variable

Stratified randomization based on the baseline value of the primary analysis variable is common in clinical trial design. We illustrate from a theoretical viewpoint the advantage of such a stratified randomization to achieve balance of the baseline covariate. We also conclude that the estimator for the treatment effect is consistent when including both the continuous baseline covariate and the stratification factor derived from the baseline covariate. In addition, the analysis of covariance model including both the continuous covariate and the stratification factor is asymptotically no less efficient than including either only the continuous baseline value or only the stratification factor. We recommend that the continuous baseline covariate should generally be included in the analysis model. The corresponding stratification factor may also be included in the analysis model if one is not confident that the relationship between the baseline covariate and the response variable is linear. In spite of the above recommendation, one should always carefully examine relevant historical data to pre-specify the most appropriate analysis model for a perspective study.     

Unanticipated Educational Consequences of a Positive Parent‐Child Relationship

If today there exists a single transcendent idea about the family‐school connection, it is that a positive parent‐child relationship improves children's chances of succeeding in school. However, using data from the Texas Higher Education Opportunity Project (N = 5,836), we demonstrate that, although positive parent‐child relations are associated with better academic achievement in high school, they also are associated with an increased desire to live at home during college, which in turn decreases students' chances of enrolling in a 4‐year college. Furthermore, we replicated some of these associations using the National Longitudinal Study of Adolescent Health (N = 10,120), demonstrating that positive family dynamics can influence educational outcomes in potentially divergent and unanticipated directions.