Pilot of small aircraft reported a NMAC while departing the traffic pattern. After the event the other aircraft radioed they did not see the other aircraft.

Narrative

Earlier today I departed VFR from Runway XX at ZZZ. On the down-wind leg I made my last radio call on ZZZ CTAF announcing a departure to the southeast. After confirming there was no traffic on final; I turned toward a heading of 133 degrees and started a climb from pattern altitude to my chosen enroute altitude of 2500 ft. After announcing my departure I continued to listen to the radio and watch targets on my ADS-B traffic advisory screen. One target caught my eye as it was on a collision course with me approaching from the northeast heading southwest at nearly the same altitude - they appeared to be cruising at 2500 ft.; the altitude I was climbing to. After watching the target on my screen and quickly realizing they were not changing their course per FAR 91.113; I quickly arrested my climb. Shortly after I arrested my climb I watched their N number pass by approximately 200 ft. above us; off my nose; I could not see them on the left due to my high wing. After writing down their N number; I called the CTAF and asked if they were on channel. They stated they were and I asked if they saw me 200 ft. below as they passed. They stated they did not. I said; 'OK' in reply. End of event.