4. What is the Cox proportional hazards model, what are its assumptions,
The Cox proportional hazards model provides a regression method for survival data. It uses data from all subjects, including those who are still surviving. The assumptions required include independence, that those who are censored are not different from those followed up to death, and that the ratio of the risks of events for different values of the predicting variables is not related to time of follow-up, even though the risks themselves may change (the proportional hazards assumption).
It was used here because there are several variables which may be related to survival. These may be related to the predictor variable of interest (age at retirement), in which case Cox regression will remove any spurious relationship between age at retirement and survival which might be produced by the factor, or may be related only to survival, in which case they will improve the fit of the regression model.
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