Journal of Statistical Planning and Inference

In this article we investigate the optimal design problem for some wavelet regression models. Wavelets are very flexible in modeling complex relations, and optimal designs are appealing as a means of increasing the experimental precision. In contrast to the designs for the Haar wavelet regression model (Herzberg and Traves 1994; Oyet and Wiens 2000), the I -optimal designs we construct are different from the D -optimal designs. We also obtain c -optimal designs. Optimal ( D - and I -) quadratic spline wavelet designs are constructed, both analytically and numerically...

Modern clinical trials are often complex, with multiple competing objectives and multiple endpoints. Such trials should be both ethical and efficient. In this paper, we overcome the obstacles introduced by the large number of unknown parameters and the possible correlations between the multiple endpoints. We obtain the optimal allocation proportions for the following two optimization problems: (1) maximizing the power of the test of homogeneity with a fixed sample size, and (2) minimizing the expected weighted number of failures with a fixed power...

We use optimal design theory and construct locally optimal designs based on the maximum quasi-likelihood estimator (MqLE), which is derived under less stringent conditions than those required for the MLE method. We show that the proposed locally optimal designs are asymptotically as efficient as those based on the MLE when the error distribution is from an exponential family, and they perform just as well or better than optimal designs based on any other asymptotically linear unbiased estimators such as the least square estimator (LSE)...

We propose a cost-effective outcome-dependent sampling design for the failure time data and develop an efficient inference procedure for data collected with this design. To account for the biased sampling scheme, we derive estimators from a weighted partial likelihood estimating equation. The proposed estimators for regression parameters are shown to be consistent and asymptotically normally distributed. A criteria that can be used to optimally implement the ODS design in practice is proposed and studied. The small sample performance of the proposed method is evaluated by simulation studies...

Current status data arise frequently in demography, epidemiology, and econometrics where the exact failure time cannot be determined but is only known to have occurred before or after a known observation time. We propose a quantile regression model to analyze current status data, because it does not require distributional assumptions and the coefficients can be interpreted as direct regression effects on the distribution of failure time in the original time scale. Our model assumes that the conditional quantile of failure time is a linear function of covariates...

Missing values present challenges in the analysis of data across many areas of research. Handling incomplete data incorrectly can lead to bias, over-confident intervals, and inaccurate inferences. One principled method of handling incomplete data is multiple imputation. This article considers incomplete data in which values are missing for three or more qualitatively different reasons and applies a modified multiple imputation framework in the analysis of that data. Included are a proof of the methodology used for three-stage multiple imputation with its limiting distribution, an extension to more than three types of missing values, an extension to the ignorability assumption with proof, and simulations demonstrating that the estimator is unbiased and efficient under the ignorability assumption...

Varying coefficient models are useful for modeling longitudinal data and have been extensively studied in the past decade. Motivated by commonly encountered dichotomous outcomes in medical and health cohort studies, we propose a two-step method to estimate the regression coefficient functions in a logistic varying coefficient model for a longitudinal binary outcome. The model depicts time-varying covariate effects without imposing stringent parametric assumptions. The proposed estimation is simple and can be conveniently implemented using existing statistical packages such as SAS and R...

This manuscript is concerned with relating two approaches that can be used to explore complex dependence structures between categorical variables, namely Bayesian partitioning of the covariate space incorporating a variable selection procedure that highlights the covariates that drive the clustering, and log-linear modelling with interaction terms. We derive theoretical results on this relation and discuss if they can be employed to assist log-linear model determination, demonstrating advantages and limitations with simulated and real data sets...

In practice, disease outcomes are often measured in a continuous scale, and classification of subjects into meaningful disease categories is of substantive interest. To address this problem, we propose a general analytic framework for determining cut-points of the continuous scale. We develop a unified approach to assessing optimal cut-points based on various criteria, including common agreement and association measures. We study the nonparametric estimation of optimal cut-points. Our investigation reveals that the proposed estimator, though it has been ad-hocly used in practice, pertains to nonstandard asymptotic theory and warrants modifications to traditional inferential procedures...

The Schwarz criterion or Bayes Information Criterion (BIC) is often used to select a model dimension, and some variations of the BIC have been proposed in the context of change-point problems. In this paper, we consider a segmented line regression model with an unknown number of change-points and study asymptotic properties of Schwarz type criteria in selecting the number of change-points. Noticing the overestimating tendency of the traditional BIC observed in some empirical studies and being motivated by asymptotic behavior of the modified BIC proposed by Zhang and Siegmund (2007), we consider a variation of the Schwarz type criterion that applies a harsher penalty equivalent to the model with one additional unknown parameter per segment...

We develop a modeling framework for joint factor and cluster analysis of datasets where multiple categorical response items are collected on a heterogeneous population of individuals. We introduce a latent factor multinomial probit model and employ prior constructions that allow inference on the number of factors as well as clustering of the subjects into homogenous groups according to their relevant factors. Clustering, in particular, allows us to borrow strength across subjects, therefore helping in the estimation of the model parameters, particularly when the number of observations is small...

In this article, we propose rigorous sample size methods for estimating the means of random variables, which require no information of the underlying distributions except that the random variables are known to be bounded in a certain interval. Our sample size methods can be applied without assuming that the samples are identical and independent. Moreover, our sample size methods involve no approximation. We demonstrate that the sample complexity can be significantly reduced by using a mixed error criterion...

We discuss fully Bayesian inference in a class of species sampling models that are induced by residual allocation (sometimes called stick-breaking) priors on almost surely discrete random measures. This class provides a generalization of the well-known Ewens sampling formula that allows for additional flexibility while retaining computational tractability. In particular, the procedure is used to derive the exchangeable predictive probability functions associated with the generalized Dirichlet process of Hjort (2000) and the probit stick-breaking prior of Chung and Dunson (2009) and Rodriguez and Dunson (2011)...

We propose an L (2)-norm based global testing procedure for the null hypothesis that multiple group mean functions are equal, for functional data with complex dependence structure. Specifically, we consider the setting of functional data with a multilevel structure of the form groups-clusters or subjects-units, where the unit-level profiles are spatially correlated within the cluster, and the cluster-level data are independent. Orthogonal series expansions are used to approximate the group mean functions and the test statistic is estimated using the basis coefficients...

We take the perspective of a researcher planning a randomized trial of a new treatment, where it is suspected that certain subpopulations may benefit more than others. These subpopulations could be defined by a risk factor or biomarker measured at baseline. We focus on situations where the overall population is partitioned into two, predefined subpopulations. When the true average treatment effect for the overall population is positive, it logically follows that it must be positive for at least one subpopulation...

This paper addresses the following general scenario: A scientist wishes to perform a battery of experiments, each generating a sequential stream of data, to investigate some phenomenon. The scientist would like to control the overall error rate in order to draw statistically-valid conclusions from each experiment, while being as efficient as possible. The between-stream data may differ in distribution and dimension but also may be highly correlated, even duplicated exactly in some cases. Treating each experiment as a hypothesis test and adopting the familywise error rate (FWER) metric, we give a procedure that sequentially tests each hypothesis while controlling both the type I and II FWERs regardless of the between-stream correlation, and only requires arbitrary sequential test statistics that control the error rates for a given stream in isolation...

This paper is concerned with model selection and model averaging procedures for partially linear single-index models. The profile least squares procedure is employed to estimate regression coefficients for the full model and submodels. We show that the estimators for submodels are asymptotically normal. Based on the asymptotic distribution of the estimators, we derive the focused information criterion (FIC), formulate the frequentist model average (FMA) estimators and construct proper confidence intervals for FMA estimators and FIC estimator, a special case of FMA estimators...

This paper considers 2×2 tables arising from case-control studies in which the binary exposure may be misclassified. We found circumstances under which the inverse matrix method provides a more efficient odds ratio estimator than the naive estimator. We provide some intuition for the findings, and also provide a formula for obtaining the minimum size of a validation study such that the variance of the odds ratio estimator from the inverse matrix method is smaller than that of the naive estimator, thereby ensuring an advantage for the misclassification corrected result...

This paper discusses characteristics of standard conjugate priors and their induced posteriors in Bayesian inference for von Mises-Fisher distributions, using either the canonical natural exponential family or the more commonly employed polar coordinate parameterizations. We analyze when standard conjugate priors as well as posteriors are proper, and investigate the Jeffreys prior for the von Mises-Fisher family. Finally, we characterize the proper distributions in the standard conjugate family of the (matrix-valued) von Mises-Fisher distributions on Stiefel manifolds...

Most statistical methods for microarray data analysis consider one gene at a time, and they may miss subtle changes at the single gene level. This limitation may be overcome by considering a set of genes simultaneously where the gene sets are derived from prior biological knowledge. We call a pathway as a predefined set of genes that serve a particular cellular or physiological function. Limited work has been done in the regression settings to study the effects of clinical covariates and expression levels of genes in a pathway on a continuous clinical outcome...