Variable selection for nonparametric additive Cox model with interval-censored data

The standard Cox model is perhaps the most commonly used model for regression analysis of failure time data but it has some limitations such as the assumption on linear covariate effects. To relax this, the nonparametric additive Cox model, which allows for nonlinear covariate effects, is often employed, and this paper will discuss variable selection and structure estimation for this general model. For the problem, we propose a penalized sieve maximum likelihood approach with the use of Bernstein polynomials approximation and group penalization. To implement the proposed method, an efficient group coordinate descent algorithm is developed and can be easily carried out for both low- and high-dimensional scenarios. Furthermore, a simulation study is performed to assess the performance of the presented approach and suggests that it works well in practice. The proposed method is applied to an Alzheimer's disease study for identifying important and relevant genetic factors.     

Nonparametric estimation of a Markov 'illness-death' process from interval-censored observations, with application to diabetes survival data

The nonparametric estimation of the cumulative transition intensityfunctions in a threestate time-nonhomogeneous Markov processwith irreversible transitions, an ‘illness-death’model, is considered when times of the intermediate transition,e.g. onset of a disease, are interval-censored. The times of‘death’ are assumed to be known exactly or to beright-censored. In addition the observed process may be left-truncated.Data of this type arise when the process is sampled periodically.For example, when the patients are monitored through periodicexaminations the observations on times of change in their diseasestatus will be interval-censored. Under the sampling schemeconsidered here the Nelson–Aalen estimator (Aalen, 1978)for a cumulative transition intensity is not applicable. Inthe proposed method the maximum likelihood estimators of someof the transition intensities are derived from the estimatorsof the corresponding subdistribution functions. The maximumlikelihood estimators are shown to have a self-consistency property.The self-consistency algorithm is developed for the computationof the estimators. This approach generalises the results fromTurnbull (1976) and Frydman (1992). The methods are illustratedwith diabetes survival data.     

Efficient computation of subset selection probabilities with application to Cox regression

An efficient method is presented to compute the probabilityof selection of a specified subset from the set of all subsetsof a fixed size where the subsets are taken from a populationwhose units have varying individual probabilities of selection.The problem is motivated by the computation of the exact marginallikelihood for the Cox proportional hazards model.     

Weighted Likelihood Method for Grouped Survival Data in Case–Cohort Studies with Application to HIV Vaccine Trials

Summary Grouped failure time data arise often in HIV studies. In a recent preventive HIV vaccine efficacy trial, immune responses generated by the vaccine were measured from a case–cohort sample of vaccine recipients, who were subsequently evaluated for the study endpoint of HIV infection at prespecified follow‐up visits. Gilbert et al. (2005, Journal of Infectious Diseases 191 , 666–677) and Forthal et al. (2007, Journal of Immunology 178, 6596–6603) analyzed the association between the immune responses and HIV incidence with a Cox proportional hazards model, treating the HIV infection diagnosis time as a right‐censored random variable. The data, however, are of the form of grouped failure time data with case–cohort covariate sampling, and we propose an inverse selection probability‐weighted likelihood method for fitting the Cox model to these data. The method allows covariates to be time dependent, and uses multiple imputation to accommodate covariate data that are missing at random. We establish asymptotic properties of the proposed estimators, and present simulation results showing their good finite sample performance. We apply the method to the HIV vaccine trial data, showing that higher antibody levels are associated with a lower hazard of HIV infection.     

A general clustering approach with application to the Miyazawa-Jernigan potentials for amino acids

In this article, we address the problem of classification of amino acids. Starting from the Miyazawa-Jernigan matrix obtained from the relative positions of amino acids in the crystal structure of globular proteins, we develop a fully unsupervised method of classification for the amino acids. The method is based in the subdominant ultrametric associated to the distance induced by the Miyazawa-Jernigan matrix and the maximum likelihood principle to determine the cluster structure. We obtain a classification consistent with the five groups used in the literature, although with some peculiarities. We also show the stability of our results against changes of the method used to classify the amino acids. Proteins 2004.     

A penalized likelihood approach for an illness-death model with interval-censored data: application to age-specific incidence of dementia

We consider the problem of estimating the intensity functions for a continuous time 'illness-death' model with intermittently observed data. In such a case, it may happen that a subject becomes diseased between two visits and dies without being observed. Consequently, there is an uncertainty about the precise number of transitions. Estimating the intensity of transition from health to illness by survival analysis (treating death as censoring) is biased downwards. Furthermore, the dates of transitions between states are not known exactly. We propose to estimate the intensity functions by maximizing a penalized likelihood. The method yields smooth estimates without parametric assumptions. This is illustrated using data from a large cohort study on cerebral ageing. The age-specific incidence of dementia is estimated using an illness-death approach and a survival approach.     

Hypothesis tests for stratified mark‐specific proportional hazards models with missing covariates,with application to HIV vaccine efficacy trials

This article develops hypothesis testing procedures for the stratified mark‐specific proportional hazards model with missing covariates where the baseline functions may vary with strata. The mark‐specific proportional hazards model has been studied to evaluate mark‐specific relative risks where the mark is the genetic distance of an infecting HIV sequence to an HIV sequence represented inside the vaccine. This research is motivated by analyzing the RV144 phase 3 HIV vaccine efficacy trial, to understand associations of immune response biomarkers on the mark‐specific hazard of HIV infection, where the biomarkers are sampled via a two‐phase sampling nested case‐control design. We test whether the mark‐specific relative risks are unity and how they change with the mark. The developed procedures enable assessment of whether risk of HIV infection with HIV variants close or far from the vaccine sequence are modified by immune responses induced by the HIV vaccine; this question is interesting because vaccine protection occurs through immune responses directed at specific HIV sequences. The test statistics are constructed based on augmented inverse probability weighted complete‐case estimators. The asymptotic properties and finite‐sample performances of the testing procedures are investigated, demonstrating double‐robustness and effectiveness of the predictive auxiliaries to recover efficiency. The finite‐sample performance of the proposed tests are examined through a comprehensive simulation study. The methods are applied to the RV144 trial.     

A penalized likelihood approach for a progressive three-state model with censored and truncated data: application to AIDS

We consider the estimation of the intensity and survival functions for a continuous time progressive three-state semi-Markov model with intermittently observed data. The estimator of the intensity function is defined nonparametrically as the maximum of a penalized likelihood. We thus obtain smooth estimates of the intensity and survival functions. This approach can accommodate complex observation schemes such as truncation and interval censoring. The method is illustrated with a study of hemophiliacs infected by HIV. The intensity functions and the cumulative distribution functions for the time to infection and for the time to AIDS are estimated. Covariates can easily be incorporated into the model.     

Model selection and parameter estimation for ion channel recordings with an application to the K + outward-rectifier in barley leaf

We present a statistical method, and its accompanying algorithms, for the selection of a mathematical model of the gating mechanism of an ion channel and for the estimation of the parameters of this model. The method assumes a hidden Markov model that incorporates filtering, colored noise and state-dependent white excess noise for the recorded data. The model selection and parameter estimation are performed via a Bayesian approach using Markov chain Monte Carlo. The method is illustrated by its application to single-channel recordings of the K⁺ outward-rectifier in barley leaf.Acknowledgement The authors thank Sake Vogelzang, Bert van Duijn and Bert de Boer for their helpful advice and useful comments and suggestions.     

A new meta-ANOVA approach for synthesizing information under signal-heterogeneity setting with application to nuclear magnetic resonance spectroscopic data

A new synthesizing statistical methodology is proposed to resolve issues of signal-heterogeneity in data sets collected through high-resolution ¹H nuclear magnetic resonance (NMR) spectroscopy. This signal-heterogeneity is typically caused by subjective operations for processing spectral profiles and measuring peak areas, non-homogeneous biological phases of experimental subjects, and variations of systems in multi-center. All these causes are likely to simultaneously impact signals of metabolic changes and their precision in a nonlinear fashion. As a combined effect, signal-heterogeneity chiefly manifests through non-homomorphic patterns of standardized treatment mean deviations spanning all experiments, and makes most remedial statistical models with linearity structure invalid. By avoiding a huge and very complex model, we develop a simple meta-ANOVA approach to synthesize many one-way-layout ANOVA analyses from individual experiments. A scale-invariant F-ratio statistic is taken as the summarizing sufficient statistic of a non-centrality parameter that supposedly captures the information about metabolic change from each experiment. Then a joint-likelihood function of a common non-centrality is constructed as the basis for maximum likelihood estimation and Chi-square likelihood ratio testing for statistical inference. We apply the meta-ANOVA to detect metabolic changes of three metabolites identified through pattern recognition on NMR spectral profiles obtained from muscle and liver tissues. We also detect effect differences among different treatments via meta-ANOVA multiple comparison.