Measures of influence and weighted partial likelihood estimation for cox proportional hazards regression
In this study, we consider the development of influential diagnostics to assess case influence for the Cox proportional hazards model and stratified Cox proportional hazards regression model. We examine various residuals previously proposed for these models and develop a diagnostics method using...
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| Main Author: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
2016
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/69191/1/FS%202016%2053%20-%20IR.pdf |
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| Summary: | In this study, we consider the development of influential diagnostics to assess case
influence for the Cox proportional hazards model and stratified Cox proportional
hazards regression model. We examine various residuals previously proposed for these
models and develop a diagnostics method using the case-deletion technique. However,
existing diagnostics methods are affected by masking effect. This effect may cause
diagnostics methods to fail to correctly detect influential cases. Therefore, we propose
an influential diagnostics method that has lower masking effect as compared to other
methods. The proposed influential diagnostics method is approximately Chi-square
distribution with p degress of freedom.
The simulation study is implemented to evaluate the performance of the proposed
influential diagnostics method via comparison with existing diagnostics method. Then,
the diagnostics methods are applied into the real data such as kidney catheter data,
Worcester Heart Attack study and also Stanford Heart Transplant study. The
performance of the proposed influential detection method is better than that of the
existing influential detection method. The partial likelihood estimation for the Cox
regression model is biased when there are measurement errors in the covariate.
Therefore, a weighted partial likelihood estimation for Cox regression model is
proposed when there is violation of underlying assumptions due to measurement error
in the covariates. In the simulation study, the proposed weighted partial likelihood
estimations for parameter coefficients have smaller bias, root mean square errors, and
ratio of bias over standard error than the existing parameter estimators, both with and
without contamination of the covariates. The demonstrated performance of the
proposed influential methods and weighted partial likelihood estimators are superior to
existing influential detection methods and parameter estimators. |
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