EGT is the primary indicator of engine health. The leakage caused by compressor blade and seal wear are the main causes of rising EGT as it relates to engine maintenance, which in turn reduces delivered air to the combustors. Typically, increased fuel flow will mirror the incremental reduction in EGT margins for a given thrust setting.
Dirt can cause problems in the turbine section, leading to wear either directly via abrasion, or indirectly due to clogged cooling passages causing higher local operating temps. For extreme cases, such as desert and dusty environments, the HP compressor is also prone to blade wear from the abrasive action of dirt and sand.
Other than volcanic ash events, dirt, FOD, and sand ingestion damage occurs on the ground during taxi, takeoff, and landing. From what I've been told, some operators observe a rigid cleaning schedule based on flight cycles, while others include EGT margin data in their scheduling. A logged event, such as sand ingestion or operation at certain known locations will also influence the intervals.