Tests designed to detect increasing hazard ratio against the proportional hazards hypothesis are generally consistent for other alternatives also. This article provides a test of the null hypothesis of increasing hazard ratio. The test is based on the separation between an empirical version of the relative trend function and its greatest convex minorant. The proportional hazards model, the leas...

The aim of this article is twofold. On one hand we give an overview, without any pretension of being exhaustive, of some theoretical tool of the modern theory of musical performance. On the other hand we present two mathematical models based on the ideas of Mazzola’s Mathematical Music Theory, that enable to concretely answer typical question on the way a player performs. For instance, now a cl...

Condition-Based Maintenance (CBM) optimization using Proportional Hazards Model (PHM) is a kind of maintenance optimization problem in which inspections of a system relevant to its failure rate depending on the age and value of covariates are performed in time intervals. The general approach for constructing a CBM based on PHM for a system is to minimize a long run average cost per unit of time...

Regression analysis of censored failure observations via the proportional hazards model permits time-varying covariates which are observed at death times. In practice, such longitudinal covariates are typically sparse and only measured at infrequent and irregularly spaced follow-up times. Full likelihood analyses of joint models for longitudinal and survival data impose stringent modelling assu...

This paper considers a panel duration model that has a proportional hazards specification with fixed effects. The paper shows how to estimate the baseline and integrated baseline hazard functions without assuming that they belong to known, finitedimensional families of functions. Existing estimators assume that the baseline hazard function belongs to a known parametric family. Therefore, the es...

This article presents a novel algorithm that efficiently computes L(1) penalized (lasso) estimates of parameters in high-dimensional models. The lasso has the property that it simultaneously performs variable selection and shrinkage, which makes it very useful for finding interpretable prediction rules in high-dimensional data. The new algorithm is based on a combination of gradient ascent opti...

We introduce a pathwise algorithm for the Cox proportional hazards model, regularized by convex combinations of ℓ1 and ℓ2 penalties (elastic net). Our algorithm fits via cyclical coordinate descent, and employs warm starts to find a solution along a regularization path. We demonstrate the efficacy of our algorithm on real and simulated data sets, and find considerable speedup between our algori...

The proportional hazards curemodel generalizes Cox’s proportional hazardsmodel which allows that a proportion of study subjects may never experience the event of interest. Here nonparametricmaximum likelihood approach is proposed to estimating the cumulative hazard and the regression parameters. The asymptotic properties of the resulting estimators are established using the modern empirical pro...

A measure of explained risk is developed for application with the proportional hazards model. The statistic, which is called the estimated explained relative risk, has a simple analytical form and is unaffected by censoring that is independent of survival time conditional on the covariates. An asymptotic confidence interval for the limiting value of the estimated explained relative risk is deri...