Structural thresholds and nonlinear acceleration in clinical trial failure: a generalised additive model and change-point analysis of 134,724 registered trials (2016–2025)

Background Prior analyses of clinical trial termination have primarily modelled protocol complexity as a linear predictor of termination risk. However, linear models cannot detect structural inflection points, defined as values beyond which marginal increases in protocol complexity produce disproportionate acceleration in termination probability. Identifying these inflection points would transform protocol complexity from a continuous risk factor into a concrete planning threshold for protocol design. Methods Using a population-based cohort of 134,724 interventional trials from ClinicalTrials.gov (2016–2025), we modelled the relationship between protocol design features and trial termination using generalised additive models (GAMs) with penalised regression splines. Structural change-points were evaluated using the PELT algorithm with 1000 bootstrap resamples and temporal validation (training cohort: 2016–2021; validation cohort: 2022–2025). Reviewer-requested supplementary analyses included multivariable logistic regression adjusting for trial phase, sponsor class, intervention characteristics, geographical scope, allocation, masking, and outcome burden; formal interaction modelling; model diagnostic assessment; follow-up maturity sensitivity analyses; entropy robustness analyses; and counterfactual scenario modelling. Results GAM smoothing functions confirmed highly non-linear relationships for eligibility criteria (edf = 17.15, P < 0.001), total endpoints (edf = 16.96, P < 0.001), and the Protocol-Burden Index (edf = 17.14, P < 0.001). Bootstrap-supported change-point analysis identified an eligibility threshold at 16 criteria (95% CI 16–21), while temporal validation identified a corresponding threshold at 21 criteria. Multivariable logistic regression confirmed that protocol complexity remained independently associated with trial termination after adjustment for major trial characteristics. Formal interaction analyses demonstrated significant effect modification by both trial phase and sponsor class. Model diagnostics demonstrated acceptable discrimination (AUC = 0.716) and good numerical stability. Entropy sensitivity analyses consistently showed higher termination rates among protocols with increasingly concentrated structural burden. Under an equal-susceptibility counterfactual scenario, redesign of above-threshold protocols to below-threshold complexity corresponded to an estimated reduction of 5560 observed terminations (26.2% of terminated trials) under the specified counterfactual scenario. Conclusions Clinical trial termination risk exhibits robust nonlinear associations with protocol complexity across multiple complementary analytical approaches. The identified eligibility threshold should be interpreted as a population-level planning benchmark rather than a deterministic cutoff. These findings support prospective evaluation of complexity-aware trial design strategies and provide quantitative benchmarks for future protocol optimisation.