These days most companies are operating purely from the manufacturers guidelines. (Presumably with the odd change here and there).
This is verbatim from the Boeing 767 QRH. (And would guess that due to boeing standardisation the 777, 737 and 747 are the same)
Rejected Takeoff
The Captain has the sole responsibility for the decision to reject the takeoff. The decision must be made in time to start the rejected takeoff manoeuvre by V1.