TY - GEN
T1 - B-Spline in the Cox Regression with Application to Cervical Cancer
AU - Purnomo, Jerry Dwi Trijoyo
AU - Purnami, Santi Wulan
AU - Mulyani, Sri
N1 - Publisher Copyright:
© 2019, Springer Nature Singapore Pte Ltd.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - B-spline
KW - Locally weighted scatterplot smoothing
KW - Martingale residual
UR - http://www.scopus.com/inward/record.url?scp=85076097423&partnerID=8YFLogxK
U2 - 10.1007/978-981-15-0399-3_13
DO - 10.1007/978-981-15-0399-3_13
M3 - Conference contribution
AN - SCOPUS:85076097423
SN - 9789811503986
T3 - Communications in Computer and Information Science
SP - 159
EP - 168
BT - Soft Computing in Data Science - 5th International Conference, SCDS 2019, Proceedings
A2 - Berry, Michael W.
A2 - Yap, Bee Wah
A2 - Mohamed, Azlinah
A2 - Köppen, Mario
PB - Springer
T2 - 5th International Conference on Soft Computing in Data Science, SCDS 2019
Y2 - 28 August 2019 through 29 August 2019
ER -