Strictly speaking, the word "contract" can be pronounced with the accent both on the first and on the last syllable. This is recorded in contemporary dictionaries of the Russian language and not an error. But unlike such words as "cheese – curd" or "barge-barge" when both accents are considered to be common and literary in equal measure, in the case of "contractmedicine" still has its own quirks.
To say "contract" (with the accent on the first syllable) is acceptable in informal oral speech, and this version is sometimes found in dictionaries are marked as "colloquial". But "contract" is simply a literary norm, using that word in any situation – and nobody can accuse you of poor knowledge of the Russian language.
Many believe that the pronunciation of the word "contract" with the accent on the first syllable – the result of "total ignorance" of the last years. But it is not. That is the accent in spoken language is acceptable, indicated pronouncing dictionaries published in the mid-twentieth century. And Korney Chukovsky in his book on the Russian language "Live as life" (published in 1962) talked about the fact that the pronunciation of can in the foreseeable future become a literary norm.