B-Spline in the Cox Regression with Application to Cervical Cancer

Jerry Dwi Trijoyo Purnomo*, Santi Wulan Purnami, Sri Mulyani

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Recently, Cox proportional hazard (PH) models have played an important role and become increasingly famous in survival analysis. A crucial assumption of the Cox model is the proportional hazards assumption, that is the covariates do not vary over time. One way to check this assumption is to utilize martingale residuals. Martingale residual is an estimate of the overage of events seen in the data but not covered by the model. These residuals are used to examine the best functional form for a given covariate using an assumed Cox model for the remaining covariates. However, one problem that could be occurred when applying martingale residuals is that they tend to be asymmetric and the line does not fall around zero. Hence, in this paper, the main discussion will focus on the use of smoothing martingale residuals, another type of martingale residuals that give a higher rate of flexibility, by using B-spline and the relation to another smoothing technique, locally weighted scatterplot smoothing (LOWESS). An analysis of variables that probably affect the survival rate of patients with cervical cancer is used for illustration.

Original languageEnglish
Title of host publicationSoft Computing in Data Science - 5th International Conference, SCDS 2019, Proceedings
EditorsMichael W. Berry, Bee Wah Yap, Azlinah Mohamed, Mario Köppen
PublisherSpringer
Pages159-168
Number of pages10
ISBN (Print)9789811503986
DOIs
Publication statusPublished - 2019
Event5th International Conference on Soft Computing in Data Science, SCDS 2019 - Iizuka, Japan
Duration: 28 Aug 201929 Aug 2019

Publication series

NameCommunications in Computer and Information Science
Volume1100
ISSN (Print)1865-0929
ISSN (Electronic)1865-0937

Conference

Conference5th International Conference on Soft Computing in Data Science, SCDS 2019
Country/TerritoryJapan
CityIizuka
Period28/08/1929/08/19

Keywords

  • B-spline
  • Locally weighted scatterplot smoothing
  • Martingale residual

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