13_AS_3_lec_a

# Central question how can we model separately dierent

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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 non-smokers) 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: Semi-parametric 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 non-smoking) 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: Semi-parametric methods: Cox Regression Model Introduction Notation For the i th life we will denote the covariates (ris...
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