A method for treating pulmonary hypertension and other diseases involving a defect in collagen metabolism, by administration of an effective amount of a liposome encapsulated copolymer conjugate antifibrotic composition, is disclosed. The antifibrotic agent is preferably a proline analog, such as cis-4-hydroxy-L-proline (cHyp). Consistent, high loadings (>98%) of the antifibrotic agent are achieved by first forming a dipeptide with L-lysine, after which the dipeptide is copolymerized with the polymer component to form the copolymer conjugate. The polymer is preferably poly(ethylene glycol) having a weight average molecular weight of from about 500 to about 15,000. There is thus provided the efficient delivery and rateable release of the antifibrotic agent to inhibit collagen accumulation and thereby treat the diseases involved. Accordingly, there is a substantial reduction in the quantity of antifibrotic agent necessary, and thus a corresponding reduction in the potential for toxicity that would otherwise result from its prolonged administration.