Treat-and-Extend as a Threshold Search Problem—A Deterministic Model of Injection Interval Strategies

Background and Objective: Treat-and-extend(TREX) dosing is widely used for anti-VEGF therapy in macular disease but no principled basis exists for choosing interval-change rules. We frame TREX as a threshold-search problem and compare rules in terms of search efficiency and overshoot.Patients and Methods: A deterministic model represented TREX as a threshold search for the true maximum dry interval(T_max) on a 1-week grid(4–16 weeks). Four rules were evaluated:+2/−2,+4/−2,+4/−4 with midpoint refinement, and a midpoint binary-like rule. Visits to maintenance interval and overshoot metrics were calculated for each rule and T_max.Results: No single rule was optimal. The +2/−2 rule minimised overshoot (maximum 2 weeks) but required most visits. The +4/−2 rule was fastest. In long-durability eyes, midpoint search matched +4/−2 in speed with overshoot comparable to +2/−2.Conclusion: Framing TREX as a threshold search makes the speed-overshoot trade-off explicit and provides a principled basis for choosing and justifying interval-change rules.