Why no additive hazards models?

The intuitively attractive additive hazards model is compared with the proportional hazards and accelerated failure time models. The lack of identifiability limits the use of the model and prevents the application of regression versions using covariates. Fortunately, data analysis based on nonhomogeneous Poisson processes or on proportional hazards is likely to yield most of the information available in the data, even though they: 1) do not necessarily represent the underlying process, and 2) even seem unlikely in certain situations. In particular, proportional hazards modeling appears very robust and requires few assumptions

A Combined GEE/Buckley-James Method for Estimating an Accelerated Failure Time Model of Multivariate Failure Times

The present paper deals with the estimation of a frailty model of multivariate failure times. The failure times are modeled by an Accelerated Failure Time Model including observed covariates and an unobservable frailty component. The frailty is assumed random and differs across elementary units, but is constant across the spells of a unit or a group. We develop an estimator (of the regression parameters) that combines the GEE approach (Liang and Zeger, 1986) with the Buckley-James estimator for censored data. This estimator is robust against violations of the correlation structure and the distributional assumptions. Some simulation studies are conducted in order to study the empirical performance of the estimator. Finally, the methods are applied to data of repeated appearances of malign ventricular arrhythmias at patients with implanted defibrillator

A Quantile Regression Model for Failure-Time Data with Time-Dependent Covariates

Since survival data occur over time, often important covariates that we wish to consider also change over time. Such covariates are referred as time-dependent covariates. Quantile regression offers flexible modeling of survival data by allowing the covariates to vary with quantiles. This paper provides a novel quantile regression model accommodating time-dependent covariates, for analyzing survival data subject to right censoring. Our simple estimation technique assumes the existence of instrumental variables. In addition, we present a doubly-robust estimator in the sense of Robins and Rotnitzky (1992). The asymptotic properties of the estimators are rigorously studied. Finite-sample properties are demonstrated by a simulation study. The utility of the proposed methodology is demonstrated using the Stanford heart transplant dataset

Connections Between Adaptive Control and Optimization in Machine Learning

This paper demonstrates many immediate connections between adaptive control and optimization methods commonly employed in machine learning. Starting from common output error formulations, similarities in update law modifications are examined. Concepts in stability, performance, and learning, common to both fields are then discussed. Building on the similarities in update laws and common concepts, new intersections and opportunities for improved algorithm analysis are provided. In particular, a specific problem related to higher order learning is solved through insights obtained from these intersections.Comment: 18 page

The Association Between Rate and Severity of Exacerbations in Chronic Obstructive Pulmonary Disease: An Application of a Joint Frailty-Logistic Model.

Exacerbations are a hallmark of chronic obstructive pulmonary disease (COPD). Evidence suggests the presence of substantial between-individual variability (heterogeneity) in exacerbation rates. The question of whether individuals vary in their tendency towards experiencing severe (versus mild) exacerbations, or whether there is an association between exacerbation rate and severity, has not yet been studied. We used data from the MACRO Study, a 1-year randomized trial of the use of azithromycin for prevention of COPD exacerbations (United States and Canada, 2006-2010; n = 1,107, mean age = 65.2 years, 59.1% male). A parametric frailty model was combined with a logistic regression model, with bivariate random effects capturing heterogeneity in rate and severity. The average rate of exacerbation was 1.53 episodes/year, with 95% of subjects having a model-estimated rate of 0.47-4.22 episodes/year. The overall ratio of severe exacerbations to total exacerbations was 0.22, with 95% of subjects having a model-estimated ratio of 0.04-0.60. We did not confirm an association between exacerbation rate and severity (P = 0.099). A unified model, implemented in standard software, could estimate joint heterogeneity in COPD exacerbation rate and severity and can have applications in similar contexts where inference on event time and intensity is considered. We provide SAS code (SAS Institute, Inc., Cary, North Carolina) and a simulated data set to facilitate further uses of this method

Using Quantile Regression for Duration Analysis

Quantile regression methods are emerging as a popular technique in econometrics and biometrics for exploring the distribution of duration data. This paper discusses quantile regression for duration analysis allowing for a flexible specification of the functional relationship and of the error distribution. Censored quantile regression address the issue of right censoring of the response variable which is common in duration analysis. We compare quantile regression to standard duration models. Quantile regression do not impose a proportional effect of the covariates on the hazard over the duration time. However, the method can not take account of time{varying covariates and it has not been extended so far to allow for unobserved heterogeneity and competing risks. We also discuss how hazard rates can be estimated using quantile regression methods. A small application with German register data on unemployment duration for younger workers demonstrates the applicability and the usefulness of quantile regression for empirical duration analysis. --censored quantile regression,unemployment duration,unobserved heterogeneity,hazard rate