The semiparametric proportional means model specifies that the mean functio
n for the cumulative medical cost over time conditional on a set of covaria
tes is equal to an arbitrary baseline mean function multiplied by an expone
ntial regression function. We demonstrate how to estimate the vector-valued
regression parameter using possibly censored lifetime costs. The. estimato
r is consistent and asymptotically normal with an easily estimable covarian
ce matrix. Simulation studies show that the proposed methodology is appropr
iate for practical use. An application to AIDS is provided.