Handling Tied Events in Cox Proportional Hazard Regression Modeling Open Access

Dong, Huaying (Spring 2019)

Permanent URL: https://etd.library.emory.edu/concern/etds/m326m273w?locale=en


Handling Tied Events in Cox Proportional Hazard Regression Modeling

By Huaying Dong

Background: Tied survival times are quite common in real-life survival analysis as survival time is usually measured discretely. One of the assumptions of the Cox proportional hazard model is that there are no tied survival times. However, the violation of the assumption does not mean the Cox proportional hazard model should be discarded.

Application: There are four methods that have been developed to handle ties. The exact and discrete methods provide the gold standard, but they are computationally intensive especially when the percentage of ties is high. Early recognition of these computational difficulties led to the development of Breslow’s and Efron’s procedures. Breslow’s approximation performs well when the percentage of tied observations is not too high; Efron’s approximation, on the other hand, almost always gives results very close to the exact method, and it performs well even when the percentage of tied observations is high.

Discussion: In general, Breslow’s approximation is recommended when the number of ties is not extensive. When the percentage of ties is high, Efron’s approximation could be used as a good substitute of the exact method or discrete method. When computation time is not a concern and accuracy is required, the exact method or the discrete method is appropriate.

Key words: Cox proportional model, partial likelihood function, tied survival times

Table of Contents

Table of Contents

Chapter 1 Background. 1

1.1 Partial Likelihood. 1

1.2 Tied Event Times. 2

1.3 Approaches dealing with tied event times. 3

1.4 Software Options. 3

1.4.1 SAS. 3

1.4.2 R.. 3

1.4.3 STATA.. 4

1.5 Objectives of This Thesis & Significance of This Problem.. 4

Chapter 2 Exact & Discrete Method. 6

Chapter 3 Approximation. 7

3.1 Breslow’s Approach. 7

3.2 Efron’s Approach. 7

Chapter 4 Applications & Discussion. 9

4.1 Divorce Dataset 9

4.2 Readmission Dataset 15

Chapter 5 Conclusion & Recommendation. 18

Bibliography. 19

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