29,960 research outputs found
Regularization for Cox's proportional hazards model with NP-dimensionality
High throughput genetic sequencing arrays with thousands of measurements per
sample and a great amount of related censored clinical data have increased
demanding need for better measurement specific model selection. In this paper
we establish strong oracle properties of nonconcave penalized methods for
nonpolynomial (NP) dimensional data with censoring in the framework of Cox's
proportional hazards model. A class of folded-concave penalties are employed
and both LASSO and SCAD are discussed specifically. We unveil the question
under which dimensionality and correlation restrictions can an oracle estimator
be constructed and grasped. It is demonstrated that nonconcave penalties lead
to significant reduction of the "irrepresentable condition" needed for LASSO
model selection consistency. The large deviation result for martingales,
bearing interests of its own, is developed for characterizing the strong oracle
property. Moreover, the nonconcave regularized estimator, is shown to achieve
asymptotically the information bound of the oracle estimator. A coordinate-wise
algorithm is developed for finding the grid of solution paths for penalized
hazard regression problems, and its performance is evaluated on simulated and
gene association study examples.Comment: Published in at http://dx.doi.org/10.1214/11-AOS911 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
An Interval-Censored Proportional Hazards Model
We fit a Cox proportional hazards (PH) model to interval-censored survival data by first subdividing each individual\u27s failure interval into non-overlapping sub-intervals. Using the set of all interval endpoints in the data set, those that fall into the individual\u27s interval are then used as the cut points for the sub-intervals. Each sub-interval has an accompanying weight calculated from a parametric Weibull model based on the current parameter estimates. A weighted PH model is then fit with multiple lines of observations corresponding to the sub-intervals for each individual, where the lower end of each sub-interval is used as the observed failure time with the accompanying weights incorporated. Right-censored observations are handled in the usual manner. We iterate between estimating the baseline Weibull distribution and fitting the weighted PH model until the regression parameters of interest converge. The regression parameter estimates are fixed as an offset when we update the estimates of the Weibull distribution and recalculate the weights. Our approach is similar to Satten et al.\u27s (1998) method for interval-censored survival analysis that used imputed failure times generated from a parametric model in a PH model. Simulation results demonstrate apparently unbiased parameter estimation for the correctly specified Weibull model and little to no bias for a mis-specified log-logistic model. Breast cosmetic deterioration data and ICU hyperlactemia data are analyzed
joineR: Joint modelling of repeated measurements and time-to-event data
The joineR package implements methods for analysing data from longitudinal studies in which the response
from each subject consists of a time-sequence of repeated measurements and a possibly censored time-toevent
outcome. The modelling framework for the repeated measurements is the linear model with random
effects and/or correlated error structure. The model for the time-to-event outcome is a Cox proportional
hazards model with log-Gaussian frailty. Stochastic dependence is captured by allowing the Gaussian
random effects of the linear model to be correlated with the frailty term of the Cox proportional hazards
model
Statistical estimation in the proportional hazards model with risk set sampling
Thomas' partial likelihood estimator of regression parameters is widely used
in the analysis of nested case-control data with Cox's model. This paper
proposes a new estimator of the regression parameters, which is consistent and
asymptotically normal. Its asymptotic variance is smaller than that of Thomas'
estimator away from the null. Unlike some other existing estimators, the
proposed estimator does not rely on any more data than strictly necessary for
Thomas' estimator and is easily computable from a closed form estimating
equation with a unique solution. The variance estimation is obtained as minus
the inverse of the derivative of the estimating function and therefore the
inference is easily available. A numerical example is provided in support of
the theory.Comment: Published by the Institute of Mathematical Statistics
(http://www.imstat.org) in the Annals of Statistics
(http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000051
Proportional hazards models with continuous marks
For time-to-event data with finitely many competing risks, the proportional
hazards model has been a popular tool for relating the cause-specific outcomes
to covariates [Prentice et al. Biometrics 34 (1978) 541--554]. This article
studies an extension of this approach to allow a continuum of competing risks,
in which the cause of failure is replaced by a continuous mark only observed at
the failure time. We develop inference for the proportional hazards model in
which the regression parameters depend nonparametrically on the mark and the
baseline hazard depends nonparametrically on both time and mark. This work is
motivated by the need to assess HIV vaccine efficacy, while taking into account
the genetic divergence of infecting HIV viruses in trial participants from the
HIV strain that is contained in the vaccine, and adjusting for covariate
effects. Mark-specific vaccine efficacy is expressed in terms of one of the
regression functions in the mark-specific proportional hazards model. The new
approach is evaluated in simulations and applied to the first HIV vaccine
efficacy trial.Comment: Published in at http://dx.doi.org/10.1214/07-AOS554 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Regularization Paths for Cox's Proportional Hazards Model via Coordinate Descent
We introduce a pathwise algorithm for the Cox proportional hazards model, regularized by convex combinations of l_1 and l_2 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 algorithm and competing methods.
Semiparametric estimation of a panel data proportional hazards model with fixed effects
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 estimators presented here
are more general than existing ones. This paper also presents a method for estimating
the parametric part of the proportional hazards model with dependent right censoring,
under which the partial likelihood estimator is inconsistent. The paper presents some
Monte Carlo evidence on the small sample performance of the new estimators
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