The phrase "assuming substantial" is correct and usable in written English.
It can be used in contexts where you are making a hypothesis or condition based on a significant amount of something, such as evidence or resources.
Example: "Assuming substantial evidence is presented, the case could lead to a different verdict."
Alternatives: "presuming significant" or "considering considerable".
What's more, spending cuts by the Government, assuming substantial reductions are made in line with the budget-balancing law, make it likely that this sector will prove something of a drag on the economy.
In some states, funding basically operates in the same way for pre-K as it does for K-12 with state and local governments both assuming substantial shares.
Alternative values, assuming substantial underreporting, are also reported.
Last week, an airstrike appears to have killed Abu Alaa al-Afari, who had assumed substantial control of ISIS following the wounding of Abu Bakr al-Baghdadi, ISIS's founder.
Considering this addiction to chop and change, and to the mustering of sound and vision into a restless collage, it may be inevitable that, when Bowie did assume substantial roles, in other people's films, he seemed less light on his feet.
In its response, the company argued that it assumed substantial risk for the development and manufacturing of the vaccine and that the price "was based on independent negotiations with two agencies of the US government", both of which "determined the price to be fair and justified".
In targeted advertisements, the advertisers assume substantial knowledge in the audience.
"PPP involves a contract between a public sector authority and a private party, in which the private party provides a public service or project and assumes substantial financial, technical and operational risk in the project". .
Particularly the United States and Australia stipulated that, based on their current share in global emissions and future growth trends, emerging economies should assume substantial commitments for cutting emissions beyond 2012.
If one assumes substantial differences in pathogenicity, the allocation of MAC isolates to defined species may facilitate diagnosis of mycobacterial lung disease.
In many practical situations, one should assume substantial residual bias due to unobserved determinants of the exposure X, which, in turn, affect Y.
