Cox Proportional Hazards Regression Models for Survival Data in Cancer Research
Survival analysis which studies the distribution of life times is one of the most commonly used statistical techniques in cancer research. Most frequently, the Kaplan-Merir (1958) estimator is used to estimate the survival probability and log-rank test is used to compare the survival probabilities between the treatment groups. However, in cancer research, some prognostic factors, such as patient characteristics and treatment-related risk factors, may be associated with outcomes. Patients and biomedical researchers may want to know “which prognostic factors are associated with the outcome?”, “how does the prognostic factors affect the outcome?”, “does the risk factor have the same effect for different treatments?”, “what is the predicted survival probability at a certain time after the treatment for a particular patient?”, or “which treatment has better survival probabilities when adjusted for prognostic factors?”. We can use regression analysis to answer these questions. Cox (1972) proposed a proportional hazards regression model in analyzing the survival data. It has gained enormous popularity. We will discuss the techniques used in fitting a Cox regression model. Most of these techniques have been introduced and discussed in various books. Klein and Moeschberger (1997) gives an introduction and a number of examples to the Cox model. Fleming and Harrington (1991) and Andersen et al (1993) give a detailed theoretical discussions for these techniques.
KeywordsWhite Blood Cell Count Conditioning Regimen Cell Dose Karnofsky Score Proportionality Assumption
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