On fitting Cox's regression model with time-dependent coefficients

Marzec, Leszek; Marzec, Paweł

doi:10.1093/biomet/84.4.901

Cited by 35 publications

(18 citation statements)

References 15 publications

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“…Time-varying coefficients, which are left out in this article, make a major source of nonproportionality and are often the alternatives to test against when assessing the proportional hazards assumption. More flexible models that incorporate this effect have been studied by Murphy and Sen (1991), Hastie and Tibshirani (1993), Verweij and van Houwelingen (1995), Sargent (1997), Marzec and Marzec (1997b), Cai and Sun (2003), Tian et al (2005), Fan et al (2006), and more recently by Chen et al (2012). In practice, the graphical tools in the survival package enable us to check if there are any time-varying coefficients .…”

Section: Discussionmentioning

confidence: 99%

Diagnostics for the Cox model

Xue

Schifano

2017

CSAM

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The most popular regression model for the analysis of time-to-event data is the Cox proportional hazards model. While the model specifies a parametric relationship between the hazard function and the predictor variables, there is no specification regarding the form of the baseline hazard function. A critical assumption of the Cox model, however, is the proportional hazards assumption: when the predictor variables do not vary over time, the hazard ratio comparing any two observations is constant with respect to time. Therefore, to perform credible estimation and inference, one must first assess whether the proportional hazards assumption is reasonable. As with other regression techniques, it is also essential to examine whether appropriate functional forms of the predictor variables have been used, and whether there are any outlying or influential observations. This article reviews diagnostic methods for assessing goodness-of-fit for the Cox proportional hazards model. We illustrate these methods with a case-study using available R functions, and provide complete R code for a simulated example as a supplement.

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Section: Discussionmentioning

confidence: 99%

Diagnostics for the Cox model

Xue

Schifano

2017

CSAM

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“…See, for instance, Gray (1990), Lin and Wei (1991), Burke and Yuen (1995), McKeague and Sun (1996), Marzec and Marzec (1997), Verweij, Van Houwelingen and Stijnen (1998) and Peña (1998). Several methods are presented in these papers based on different approaches: cumulative hazard function estimation (smoothed or not), information matrix score tests and extensions of smooth specification tests.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Goodness-of-fit tests for conditional models under censoring and truncation

Cao¹,

González–Manteiga²

2008

Journal of Econometrics

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To cite this version:Ricardo Cao, Wenceslao González-Manteiga. Goodness-of-fit tests for conditional models under censoring and truncation.Journal of Econometrics, Elsevier, 2008, 143 (1) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A c c e p t e d m a n u s c r i p t ABSTRACTThe problem of specification tests for conditional models is studied when the data are subject to left truncation and right censoring. A general method is applied to derive tests for the polynomial regression, the proportional hazards, the additive risks and the proportional odds models. Bootstrap versions to approximate the critical values of the test are introduced and proved to work both from a theoretical viewpoint as well as in a small simulation study.JEL Classification: C12, C15, C24

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“…Although model resembles the time‐dependent coefficient (TDC), Cox model proposed by a number of authors, including Zucker & Karr ), Murphy & Sen (), Gamerman (), Murphy (), Marzec & Marzec (), Martinussen et al (), Cai & Sun (), Tian et al () and Fan et al (), it differs in that β (·) in our model is a vector of functions of the gap time t − t i , as opposed to the current ‘calendar’ time t . The estimation of model ( is more difficult than that for the traditional TDC Cox model, because the existing nonparametric technique (e.g., kernel smoothing) is not directly applicable to the model .…”

Section: Introductionmentioning

confidence: 99%

A Semiparametrically Efficient Estimator of the Time‐Varying Effects for Survival Data with Time‐Dependent Treatment

Lin

Fei

2015

Scandinavian J Statistics

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The timing of a time-dependent treatment—e.g., when to perform a kidney transplantation—is an important factor for evaluating treatment efficacy. A naïve comparison between the treated and untreated groups, while ignoring the timing of treatment, typically yields biased results that might favor the treated group because only patients who survive long enough will get treated. On the other hand, studying the effect of a time-dependent treatment is often complex, as it involves modeling treatment history and accounting for the possible time-varying nature of the treatment effect. We propose a varying-coefficient Cox model that investigates the efficacy of a time-dependent treatment by utilizing a global partial likelihood, which renders appealing statistical properties, including consistency, asymptotic normality and semiparametric efficiency. Extensive simulations verify the finite sample performance, and we apply the proposed method to study the efficacy of kidney transplantation for end-stage renal disease patients in the U.S. Scientific Registry of Transplant Recipients (SRTR).

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On fitting Cox's regression model with time-dependent coefficients

Cited by 35 publications

References 15 publications

Diagnostics for the Cox model

Diagnostics for the Cox model

Goodness-of-fit tests for conditional models under censoring and truncation

A Semiparametrically Efficient Estimator of the Time‐Varying Effects for Survival Data with Time‐Dependent Treatment

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