In observational survival studies, delayed treatment initiation can induce immortal time bias in effect estimation when treatment groups are defined by future uptake. Despite originating from distinct predictive or causal inference paradigms, time-dependent approaches (e.g. the time-dependent Cox model, landmark supermodel, multi-state model, and g-formula) are often treated as interchangeable in applied research when addressing immortal time bias. These models effectively reclassify person-time according to time-varying exposure, yet the interpretation of their target estimands depends on assumptions about the underlying disease process and clinically relevant time scales. We study effect estimation for allogeneic hematopoietic stem cell transplantation under baseline intention-to-transplant strategies in acute myeloid leukemia (i.e. transplantation is planned for a prespecified time, subject to the patient's eligibility), within a multi-state framework allowing time-inhomogeneous Markov, semi-Markov, and state arrival extended semi-Markov dynamics. Using target trial emulation, we benchmark, on the probability scale, estimates derived from Cox-type time-dependent models and the g-formula against the corresponding theoretical values implied by the stochastic data-generating process. Decomposing the partial likelihood score, we show that single-time-scale models can be systematically biased when death intensities from different originating states are not proportional on a common time scale, as can occur when the clock is reset after intermediate events. We quantify these findings in a phase III simulation study and illustrate their implications in an application to data from three acute myeloid leukemia trials.

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