Unformatted text preview: gression model?
Central question: How can we model separately diﬀerent factors
that are likely to impact the observed event, so that we can isolate
their individual eﬀects?
Heterogeneity: lives with very diﬀerent characteristics (eg
males and females, smokers and nonsmokers) have diﬀerent
level of mortality. In other words, diﬀerent factors (covariates)
may have diﬀerent eﬀects on the risk.
One method is to construct a model including the eﬀects of
the covariates on survival directly: a regression model.
The most widely used regression model is the proportional
hazards model (the Cox model)
3/45 Actuarial Statistics – Module 3: Semiparametric methods: Cox Regression Model
Introduction Covariates
In many survival analysis problems, covariates are of the
following types:
Demographic / Societal (eg age, gender, education)
Behavioral (eg smoking, physical activity level, alcohol)
Physiological (eg blood pressure, heart rate) Covariates can be
continuous measurements (weight)
discrete measurements (age last birthday)
indicators (1 for smoking, 0 for nonsmoking)
qualitative indicators (5 severe disease to 0 no symptoms) see K&M for a discussion of how to ‘code’ variables/factors
4/45 Actuarial Statistics – Module 3: Semiparametric methods: Cox Regression Model
Introduction Notation
For the i th life we will denote the covariates (ris...
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 Three '14
 Survival analysis, cox regression model

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