(Aalen, 1989) Write the additive model (4.54) in the following way where the Xj are random variables. a) Assume that one of the covariates, say Xp, is dropped from the model, for example, because...

(Aalen, 1989) Write the additive model (4.54) in the following way

where the X_j
are random variables.

a) Assume that one of the covariates, say X_p, is dropped from the model, for example, because it is unmeasured. Show that, if the X_j
are independent, you still have an additive model where only the baseline regression function β₀(t) is changed.

b) Assume that the X_j
are dependent and multivariate normally distributed. How would the model change in this case when the covariate X_p
is dropped?