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The added value of new covariates to the brier score in cox survival models.

ABSTRACT: Calibration is an important measure of the predictive accuracy for a prognostic risk model. A widely used measure of calibration when the outcome is survival time is the expected Brier score. In this paper, methodology is developed to accurately estimate the difference in expected Brier scores derived from nested survival models and to compute an accompanying variance estimate of this difference. The methodology is applicable to time invariant and time-varying coefficient Cox survival models. The nested survival model approach is often applied to the scenario where the full model consists of conventional and new covariates and the subset model contains the conventional covariates alone. A complicating factor in the methodologic development is that the Cox model specification cannot, in general, be simultaneously satisfied for nested models. The problem has been resolved by projecting the properly specified full survival model onto the lower dimensional space of conventional markers alone. Simulations are performed to examine the method's finite sample properties and a prostate cancer data set is used to illustrate its application.

SUBMITTER: Heller G

PROVIDER: S-EPMC7855634 | biostudies-literature | 2021 Jan

REPOSITORIES: biostudies-literature

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The added value of new covariates to the brier score in cox survival models.

Heller Glenn G

Lifetime data analysis 20201022 1

Calibration is an important measure of the predictive accuracy for a prognostic risk model. A widely used measure of calibration when the outcome is survival time is the expected Brier score. In this paper, methodology is developed to accurately estimate the difference in expected Brier scores derived from nested survival models and to compute an accompanying variance estimate of this difference. The methodology is applicable to time invariant and time-varying coefficient Cox survival models. Th ...[more]

PMID: 33089436

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Project description:BackgroundIn cohort studies with time-to-event outcomes, covariates of interest often have values that change over time. The classical Cox regression model can handle time-dependent covariates but assumes linear effects on the log hazard function, which can be limiting in practice. Furthermore, when multiple correlated covariates are studied, it is of great interest to model their joint effects by allowing a flexible functional form and to delineate their relative contributions to survival risk.MethodsMotivated by the World Trade Center (WTC)-exposed Fire Department of New York cohort study, we proposed a partial-linear single-index Cox (PLSI-Cox) model to investigate the effects of repeatedly measured metabolic syndrome indicators on the risk of developing WTC lung injury associated with particulate matter exposure. The PLSI-Cox model reduces the dimensionality of covariates while providing interpretable estimates of their effects. The model's flexible link function accommodates nonlinear effects on the log hazard function. We developed an iterative estimation algorithm using spline techniques to model the nonparametric single-index component for potential nonlinear effects, followed by maximum partial likelihood estimation of the parameters.ResultsExtensive simulations showed that the proposed PLSI-Cox model outperformed the classical time-dependent Cox regression model when the true relationship was nonlinear. When the relationship was linear, both the PLSI-Cox model and classical time-dependent Cox regression model performed similarly. In the data application, we found a possible nonlinear joint effect of metabolic syndrome indicators on survival risk. Among the different indicators, BMI had the largest positive effect on the risk of developing lung injury, followed by triglycerides.ConclusionThe PLSI-Cox models allow for the evaluation of nonlinear effects of covariates and offer insights into their relative importance and direction. These methods provide a powerful set of tools for analyzing data with multiple time-dependent covariates and survival outcomes, potentially offering valuable insights for both current and future studies.

Dataset Information

The added value of new covariates to the brier score in cox survival models.

Publications

The added value of new covariates to the brier score in cox survival models.

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