Validation of the Smooth Test of Goodness-of-Fit for Proportional Hazards in Cancer Survival Studies

Collins Odhiambo; John Odhiambo; Bernard Omolo

doi:10.6000/1929-6029.2017.06.02.1

Authors

Collins Odhiambo Strathmore Institute of Mathematical Sciences, Strathmore University, Ole Sangale Road, Nairobi, Kenya
John Odhiambo Strathmore Institute of Mathematical Sciences, Strathmore University, Ole Sangale Road, Nairobi, Kenya
Bernard Omolo Division of Mathematics & Computer Science, University of South Carolina-Upstate, 800 University Way, Spartanburg, South Carolina, USA

DOI:

https://doi.org/10.6000/1929-6029.2017.06.02.1

Keywords:

Cancer, Cox proportional hazards model, Global test, Neyman’s smooth test, Two-sample problem

Abstract

In this study, we validate the smooth test of goodness-of-fit for the proportionality of the hazard function in the two-sample problem in cancer survival studies. The smooth test considered here is an extension of Neyman’s smooth test for proportional hazard functions. Simulations are conducted to compare the performance of the smooth test, the data-driven smooth test, the Kolmogorov-Smirnov proportional hazards test and the global test, in terms of power. Eight real cancer datasets from different settings are assessed for the proportional hazard assumption in the Cox proportional hazard models, for validation. The smooth test performed best and is independent of the number of covariates in the Cox proportional hazard models.

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