7. Why did they adjust for sex, which is very similar in the early and late retirement groups? What would we expect the effect of this to be?
Sex is a strong predictor of the risk of death, males having a greater risk of death than females at all ages and particularly so at ages greater than 65. As sex is not related to age at retirement, we might expect intuitively that adjusting for it should not alter the estimated hazard ratio. In multiple regression, it would improve the prediction and make the unexplained variance smaller. The standard errors would then be smaller and the estimate would be better. This would in turn narrow the confidence interval for the estimated coefficient of retirement age. In Cox regression improving the prediction may alter the hazard ratio rather than narrow the confidence interval. Because sex is a strong predictor of the risk of death after age 65, adjusting for it should improve the prediction and make the estimate of the hazard ratio more accurate. It may do this by removing some bias rather than by making the estimate more precise.
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