B767 CREW TOOK OFF AFTER RECEIVING CLRNC FOR ANOTHER ACFT.

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WE FOLLOWED 5 ACFT ON TXWY A TO RWY 1R SFO. FO WAS MAKING TKOF AND I WAS HANDLING RADIOS. WE WERE CLRED INTO POS AND DID SO. AS WE CAME TO A STOP; I HEARD WHAT I THOUGHT WAS TKOF CLRNC. I ACKNOWLEDGED THIS WITH OUR CALL SIGN. WE CALLED OUT FINAL ITEMS ON TKOF CHKLIST AND BEGAN PWR UP AND TKOF ROLL WITH ME CALLING OUT PWR UP; ACKNOWLEDGEMENT OF THROTTLE CTL XFER; ENG AND AIRSPD CHKS; ETC. CONTINUING TO GEAR UP AND RESPONDING TO FO'S CALLOUTS FOR CONFIGN CHANGES; ETC. AFTER 1000 FT I NOTICED AN ACFT AHEAD AND TO MY L. ABOUT THAT TIME TWR GAVE US A TURN TO 030 DEG RADIAL AWAY FROM THE TFC AND GAVE US A LEVELOFF AT 4000 FT; A CHANGE FROM OUR PDC ALT OF 15000 FT. I CONSIDERED THIS TO BE FOR SEPARATION FROM THE OBSERVED TFC ON MY L. TWR THEN GAVE US DEP CTL FREQ. I ACKNOWLEDGED THE HDOF AND RPTED I HAD OBSERVED THE TFC. TWR THEN ASKED ME TO CALL ON REACHING ATL. WE WERE VECTORED BY DEP CTL ONTO THE DEP SID AND CONTINUED TO ATL. I WAS LATER INFORMED THAT I HAD ACTED ON ANOTHER ACFT TKOF CLRNC WHICH HAD DEPARTED RWY 1L. (I HAVE NOT YET HEARD THE TWR TAPES.) FACTORS INFLUENCING ACTIONS: 1) NO ACFT AHEAD OF US HAD USED RWY 1L. 2) I WAS FAMILIAR WITH THE CRISS-CROSS PATTERN; IE; AN ACFT LANDS RWY 28 THEN ONE DEPARTS RWY 1. THIS MAY HAVE CAUSED A MIND SET THAT WHILE HOLDING IN POS AND OBSERVING AN ACFT LNDG RWY 28; I WAS PRECONDITIONED TO HEARING A TKOF CLRNC FOR MY ACFT. 3) THE LIGHT RAIN HAD OBSCURED VISION THROUGH THE L SIDE WINDOW (NO WIPERS) AND I FAILED TO OBSERVE THE OTHER ACFT ON RWY 1L. 4) ONCE PWR UP BEGAN; THOUGHT PROCESS REVERTED TO INSIDE COCKPIT; GAUGES; CALLOUTS; ETC; WHICH DIVERTED MY ATTN SO THAT NEITHER MYSELF NOR THE FO HEARD ANY CORRECTION TO THE ACKNOWLEDGEMENT OF THE TKOF CLRNC WHICH I HAD XMITTED.