Nonparametric quantile inference with competing risks data

A conceptually simple quantile inference procedure is proposedfor cause-specific failure probabilities with competing risksdata. The quantiles are defined using the cumulative incidencefunction, which is intuitively meaningful in the competing–risksset–up. We establish the uniform consistency and weakconvergence of a nonparametric estimator of this quantile function.These results form the theoretical basis for extensions of standardone–sample and two–sample quantile inference forindependently censored data. This includes the constructionof confidence intervals and bands for the quantile function,and two–sample tests. Simulation studies and a real dataexample illustrate the practical utility of the methodology.     

Nonparametric inference for median costs with censored data

Summary Increasingly, estimations of health care costs are used to evaluate competing treatments or to assess the expected expenditures associated with certain diseases. In health policy and economics, the primary focus of these estimations has been on the mean cost, because the total cost can be derived directly from the mean cost, and because information about total resources utilized is highly relevant for policymakers. Yet, the median cost also could be important, both as an intuitive measure of central tendency in cost distribution and as a subject of interest to payers and consumers. In many prospective studies, cost data collection is sometimes incomplete for some subjects due to right censoring, which typically is caused by loss to follow-up or by limited study duration. Censoring poses a unique challenge for cost data analysis because of so-called induced informative censoring, in that traditional methods suited for survival data generally are invalid in censored cost estimation. In this article, we propose methods for estimating the median cost and its confidence interval (CI) when data are subject to right censoring. We also consider the estimation of the ratio and difference of two median costs and their CIs. These methods can be extended to the estimation of other quantiles and other informatively censored data. We conduct simulation and real data analysis in order to examine the performance of the proposed methods.     

Semiparametric inference for surrogate endpoints with bivariate censored data

Summary .   Considerable attention has been recently paid to the use of surrogate endpoints in clinical research. We deal with the situation where the two endpoints are both right censored. While proportional hazards analyses are typically used for this setting, their use leads to several complications. In this article, we propose the use of the accelerated failure time model for analysis of surrogate endpoints. Based on the model, we then describe estimation and inference procedures for several measures of surrogacy. A complication is that potentially both the independent and dependent variable are subject to censoring. We adapt the Theil–Sen estimator to this problem, develop the associated asymptotic results, and propose a novel resampling-based technique for calculating the variances of the proposed estimators. The finite-sample properties of the estimation methodology are assessed using simulation studies, and the proposed procedures are applied to data from an acute myelogenous leukemia clinical trial.     

On generalized latent factor modeling and inference for high-dimensional binomial data

We explore a hierarchical generalized latent factor model for discrete and bounded response variables and in particular, binomial responses. Specifically, we develop a novel two-step estimation procedure and the corresponding statistical inference that is computationally efficient and scalable for the high dimension in terms of both the number of subjects and the number of features per subject. We also establish the validity of the estimation procedure, particularly the asymptotic properties of the estimated effect size and the latent structure, as well as the estimated number of latent factors. The results are corroborated by a simulation study and for illustration, the proposed methodology is applied to analyze a dataset in a gene–environment association study.     

Nonparametric inference for local extrema with application to oligonucleotide microarray data in yeast genome

Identifying local extrema of expression profiles is one primary objective in some cDNA microarray experiments. To study the replication dynamics of the yeast genome, for example, local peaks of hybridization intensity profiles correspond to putative replication origins. We propose a nonparametric kernel smoothing (NKS) technique to detect local hybridization intensity extrema across chromosomes. The novelty of our approach is that we base our inference procedures on equilibrium points, namely those locations at which the first derivative of the intensity curve is zero. The proposed smoothing technique provides both point and interval estimation for the location of local extrema. Also, this technique can be used to test for the hypothesis of either one or multiple suspected locations being the true equilibrium points. We illustrate the proposed method on a microarray data set from an experiment designed to study the replication origins in the yeast genome, in that the locations of autonomous replication sequence (ARS) elements are identified through the equilibrium points of the smoothed intensity profile curve. Our method found a few ARS elements that were not detected by the current smoothing methods such as the Fourier convolution smoothing.     

BOSO: A novel feature selection algorithm for linear regression with high-dimensional data

With the frenetic growth of high-dimensional datasets in different biomedical domains, there is an urgent need to develop predictive methods able to deal with this complexity. Feature selection is a relevant strategy in machine learning to address this challenge. We introduce a novel feature selection algorithm for linear regression called BOSO (Bilevel Optimization Selector Operator). We conducted a benchmark of BOSO with key algorithms in the literature, finding a superior accuracy for feature selection in high-dimensional datasets. Proof-of-concept of BOSO for predicting drug sensitivity in cancer is presented. A detailed analysis is carried out for methotrexate, a well-studied drug targeting cancer metabolism.     

Structural inference in transition measurement error models for longitudinal data

We propose a new class of models, transition measurement error models, to study the effects of covariates and the past responses on the current response in longitudinal studies when one of the covariates is measured with error. We show that the response variable conditional on the error-prone covariate follows a complex transition mixed effects model. The naive model obtained by ignoring the measurement error correctly specifies the transition part of the model, but misspecifies the covariate effect structure and ignores the random effects. We next study the asymptotic bias in naive estimator obtained by ignoring the measurement error for both continuous and discrete outcomes. We show that the naive estimator of the regression coefficient of the error-prone covariate is attenuated, while the naive estimators of the regression coefficients of the past responses are generally inflated. We then develop a structural modeling approach for parameter estimation using the maximum likelihood estimation method. In view of the multidimensional integration required by full maximum likelihood estimation, an EM algorithm is developed to calculate maximum likelihood estimators, in which Monte Carlo simulations are used to evaluate the conditional expectations in the E-step. We evaluate the performance of the proposed method through a simulation study and apply it to a longitudinal social support study for elderly women with heart disease. An additional simulation study shows that the Bayesian information criterion (BIC) performs well in choosing the correct transition orders of the models.     

Bayesian predictive inference for time series count data

Correlated count data arise often in practice, especially in repeated measures situations or instances in which observations are collected over time. In this paper, we consider a parametric model for a time series of counts by constructing a likelihood-based version of a model similar to that of Zeger (1988, Biometrika 75, 621-629). The model has the advantage of incorporating both overdispersion and autocorrelation. We consider a Bayesian approach and propose a class of informative prior distributions for the model parameters that are useful for prediction. The prior specification is motivated from the notion of the existence of data from similar previous studies, called historical data, which is then quantified into a prior distribution for the current study. We derive the Bayesian predictive distribution and use a Bayesian criterion, called the predictive L measure, for assessing the predictions for a given time series model. The distribution of the predictive L measure is also derived, which will enable us to compare the predictive ability for each model under consideration. Our methodology is motivated by a real data set involving yearly pollen counts, which is examined in some detail.     

Extending conventional priors for testing general hypotheses in linear models

We consider that observations come from a general normal linearmodel and that it is desirable to test a simplifying null hypothesisabout the parameters. We approach this problem from an objectiveBayesian, model-selection perspective. Crucial ingredients forthis approach are ‘proper objective priors’ to beused for deriving the Bayes factors. Jeffreys-Zellner-Siow priorshave good properties for testing null hypotheses defined byspecific values of the parameters in full-rank linear models.We extend these priors to deal with general hypotheses in generallinear models, not necessarily of full rank. The resulting priors,which we call ‘conventional priors’, are expressedas a generalization of recently introduced ‘partiallyinformative distributions’. The corresponding Bayes factorsare fully automatic, easily computed and very reasonable. Themethodology is illustrated for the change-point problem andthe equality of treatments effects problem. We compare the conventionalpriors derived for these problems with other objective Bayesianproposals like the intrinsic priors. It is concluded that bothpriors behave similarly although interesting subtle differencesarise. We adapt the conventional priors to deal with nonnestedmodel selection as well as multiple-model comparison. Finally,we briefly address a generalization of conventional priors tononnormal scenarios.     

Score Tests for Exploring Complex Models: Application to HIV Dynamics Models

In biostatistics, more and more complex models are being developed. This is particularly the case in system biology. Fitting complex models can be very time‐consuming, since many models often have to be explored. Among the possibilities are the introduction of explanatory variables and the determination of random effects. The particularity of this use of the score test is that the null hypothesis is not itself very simple; typically, some random effects may be present under the null hypothesis. Moreover, the information matrix cannot be computed, but only an approximation based on the score. This article examines this situation with the specific example of HIV dynamics models. We examine the score test statistics for testing the effect of explanatory variables and the variance of random effect in this complex situation. We study type I errors and the statistical powers of this score test statistics and we apply the score test approach to a real data set of HIV‐infected patients.