A semiparametric approach, typified by the Cox proportional
hazards regression model, makes no assumptions about the baseline hazard function. A nonlinear relationship between the hazard
function and predictors is assumed. However, the proportional
hazards assumption needs to be checked. It states that the hazard
ratio comparing any two observations is constant over time where
the predictors do not vary with time. Using Kaplan-Meier curves, a
graph of the log(-log(survival)) vs log of survival time should show
parallel curves. An example of a Cox proportional hazards fit of
drug data is shown in Figure 4.
The whole model shows a Chi-square test of the hypothesis
that there is no difference in survival time among the effects. For a
categorical parameter estimates, a confidence interval that does not
include zero indicates that the difference between the level and the
average of all levels is significant.
Survival analysis is an important technique used in medical,
engineering, social and economic sciences and is related to reliability. Evaluation of data distribution with consideration of censoring and a suitable approach to the type of model selected are key
components to an evaluation of the process.
Note: All graphs were generated using JMP v. 11. 2.0 software.
Mark Anawis is a Principal Scientist and ASQ Six Sigma Black
Belt at Abbott. He may be reached at firstname.lastname@example.org
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