Generalized martingale-residual processes for goodness-of-fit inference in Cox's type regression models

Marzec, Leszek; Marzec, Paweł

doi:10.1214/aos/1031833669

Cited by 17 publications

(10 citation statements)

References 45 publications

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“…Marzec and Marzec (1997a) established the asymptotic behavior of processes based on sums of weighted martingale-transformed residuals. They developed Kolmogorov-Smirnov and Cramér-von Mises types of omnibus tests using the fact that, in special cases, they appear to be transformed Brownian motions or Brownian bridges.…”

Section: Diagnostics Based On Martingale Residualsmentioning

confidence: 99%

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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: Diagnostics Based On Martingale Residualsmentioning

confidence: 99%

“…They developed Kolmogorov-Smirnov and Cramér-von Mises types of omnibus tests using the fact that, in special cases, they appear to be transformed Brownian motions or Brownian bridges. As the derivation is complicated, please see Marzec and Marzec (1997a) for further details.…”

Section: Diagnostics Based On Martingale Residualsmentioning

confidence: 99%

Diagnostics for the Cox model

Xue

Schifano

2017

CSAM

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“…Among others, we mention the tests on parameters or those on the functional form of a covariate (a survey of these tests can be found in Therneau and Grambsch, 2000). Besides these tests focused on specific departures from the Cox model, there are also global tests; some of them are based on the doubly cumulative hazard function (McKeague and Utikal, 1991) and others are based on the martingale residual process (Marzec and Marzec, 1997).…”

Section: Cox-aalen Survival Modelmentioning

confidence: 99%

An Application of the Cox-Aalen Model for Breast Cancer Survival

Baldi

Ciccone

Ponti

et al. 2016

AJS

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Semiparametric hazard function regression models are among the well studied risk models in survival analysis. The Cox proportional hazards model has been a popular choice in modelling data from epidemiological settings. The Cox-Aalen model is one of the tools for handling the problem of non-proportional effects in the Cox model. We show an application on Piedmont cancer registry data. We initially fit standard Cox model and with the help of the score process we detect the violation of the proportionality assumption. Covariates and risk factors that, on the basis of clinical reasoning, best model baseline hazard are then moved into the additive part of the Cox-Aalen model. Multiplicative effects results are consistent with those of the Cox model whereas only the Cox-Aalen model fully represents the timevarying effect of tumour size.

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“…Diagnostic measures including martingale residuals and Cook's distance have been widely used to identify influential observations and to test model misspecification in survival models (Storer & Crowley, 1985; Pettitt & Daud, 1989; Therneau, Grambsch, & Fleming, 1990; Escobar & Meeker, 1992; Henderson & Oman, 1993; Lin, Wei & Ying, 1993; Barlow, 1997; Marzec & Marzec, 1997; Klein and Moeschberger, 2003; Martinussen and Scheike, 2006). For instance, Pettitt & Daud (1989) applied Cook's (1986) local influence method to the proportional hazards model and derived several useful diagnostics.…”

Section: Introductionmentioning

confidence: 99%

Diagnostic measures for the Cox regression model with missing covariates

Zhu¹,

Ibrahim²,

Chen³

2015

Biometrika

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Summary This paper investigates diagnostic measures for assessing the influence of observations and model misspecification in the presence of missing covariate data for the Cox regression model. Our diagnostics include case-deletion measures, conditional martingale residuals, and score residuals. The Q-distance is proposed to examine the effects of deleting individual observations on the estimates of finite-dimensional and infinite-dimensional parameters. Conditional martingale residuals are used to construct goodness of fit statistics for testing possible misspecification of the model assumptions. A resampling method is developed to approximate the p-values of the goodness of fit statistics. Simulation studies are conducted to evaluate our methods, and a real data set is analyzed to illustrate their use.

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Generalized martingale-residual processes for goodness-of-fit inference in Cox's type regression models

Cited by 17 publications

References 45 publications

Diagnostics for the Cox model

Diagnostics for the Cox model

An Application of the Cox-Aalen Model for Breast Cancer Survival

Diagnostic measures for the Cox regression model with missing covariates

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