Evaluating the Identifiability of Temporal Delay and Response Attenuation in Endometrial Decidualization

Endometriosis is associated with impaired endometrial decidualization, yet conventional differential expres-sion analyses cannot readily distinguish delayed transcriptional activation from reduced response amplitude.These mechanisms may produce similar expression differences at individual time points while implying distinct biological interpretations. Establishing when they can be distinguished is therefore a computational identifiability problem.We implement an identifiability-aware analysis of temporal displacement and amplitude attenuation in longitudinal transcriptomic responses. The approach combines reference trajectories, constrained amplitude-only and amplitude-plus-delay models, analytical examples of observational equivalence, and simulation-based assessments of mechanism distinguishability. Held-out time-point evaluation and culture-level sensitivity analyses examine the stability of model-dependent conclusions.In GSE246591, a candidate-delay-dependent dynamic-range filter excluded 30.9 - 38.3% of initially dynamic features under a hypothetical 24-hour shift across four endometrial stromal cultures. A two-component diagnostic separating retained dynamic range from affine shape similarity revealed that small projection residuals can arise from either loss of observable dynamics or similarity of response shapes. These findings demonstrate why a single separation statistic may be insufficient for interpreting temporal identifiability.Complementary independent in vivo analyses provided biological context. In GSE51981, an endometrial progesterone-response-associated transcriptional score was reduced in endometriosis samples (phase-model estimate 0.155, 95% CI 0.222 to 0.088). GSE6364 showed a directionally consistent but statistically inconclusive difference (0.033, 95% CI 0.068 to 0.002). Neither observation independently establishes a temporal delay.Together, these results support selection-aware evaluation of temporal transcriptomic responses, distin-guishing structural ambiguity and loss of dynamic signal from evidence of a biological timing change.