Local Linear Estimation for Time-Dependent Coefficients in Cox's Regression Models
By Zongwu Cai, Yanqing Sun. 2003
173 citations recorded by the source corpus.
This article develops a local partial likelihood technique to estimate the time-dependent coefficients in Cox's regression model. The basic idea is a simple extension of the local linear fitting technique used in the scatterplot smoothing. The coefficients are estimated locally based on the partial likelihood in a window around each time point. Multiple time-dependent covariates are incorporated in the local partial likelihood procedure. The procedure is useful as a diagnostic tool and can be used in uncovering time-dependencies or departure from the proportional hazards model. The programming involved in the local partial likelihood estimation is relatively simple and it can be modified with few efforts from the existing programs for the proportional hazards model. The asymptotic properties of the resulting estimator are established and compared with those from the local constant fitting. A consistent estimator of the asymptotic variance is also proposed. The approach is illustrated by a real data set from the study of gastric cancer patients and a simulation study is also presented.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/35a65338aec3cecceb46e07b42695f82b25295d0
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In Statistics and Probability
- Ruwanthi Kolamunnage-Dona
- Lu Tian
- David M. Zucker
- Lee-Jen Wei
- T. Cox
- A. Kamarudin
- Danyu Lin
- Ying Zhang
Citations in the corpus
- Survival Model Predictive Accuracy and ROC Curves (2005, unknown): “Cai and Sun (2003) prove the pointwise consistency and asymptotic normality of the resulting function estimator, ˆ γ(t).”
- On the Cox Model With Time-Varying Regression Coefficients (2005, methodology): “Cai and Sun (2003) showed the pointwise consistency of β̂(t) for each fixed time t.”
- Time-dependent ROC curve analysis in medical research: current methods and applications (2017, methodology): “Heagerty and Zheng [12] suggested using flexible semiparametric methods such as locally weighted maximum partial likelihood (MPL) by Cai and Sun [25] as the regression-smoothing method in (i), and simple local”