# Proportional Hazards Model Question

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Consider a situation with two covariates X and Z. Suppose the data generating mechanism is generated by the Cox model when conditioning on both X and Z:

$$\lambda(t|X,Z) = \lambda_0(t)e^{\beta_xX +\beta_zZ}$$

a) How would I go about deriving the Hazard function when only conditioning on $$X$$ ?

b) Furthermore, what would happen if $$X$$ and $$Y$$ are independent?

c) Suppose we observe $$n$$ iid replicates from the above model and allow for (independent) right-censoring. Suppose also that we now ﬁt a Cox-model to the data using only the ﬁrst covariate $$X$$. Show that the Cox-score function, $$U(β)$$, in this case does not have mean zero and give an expression for the bias term.