The phrase "according to the statement" is a commonly used expression to indicate that the information being presented is based on a particular statement or source. However, there are a variety of synonyms that could be used instead to convey similar meaning. Some of these alternatives include "as indicated by," "per the declaration of," "in accordance with the report," "according to the assertion," "in keeping with the account," and "in line with the testimony." It's always helpful to have a breadth of language options available when crafting a written or verbal piece.