The depth of any test effort depends on the amount of time and resources management is willing to spend on it. This decision is largely based on the application under test ranging from applications that have significantly high ramifications if defects occur (ie. code for an ATM where money is dispersed) to applications that have no tangible impact at all (ie.
code that structures how something will behave on an application that has little
value to the company).
Of course if the application under test can have potentially significant
impact on revenue or on customer perception then management will be more
willing to devote more testing resources to it. In these conditions it would be
worthwhile to conduct more than just a sanity test.
Nevertheless in any situation one begins with sanity testing paying
particular attention to functionality that is influenced by the modified code.
Beyond that it is best to identify any dependencies that other modules may have
on this module and sanity test them as well. If time permits you would then
sanity check other major functionalities even though they may not be directly
dependent on the modified module.