Mathematical modeling of bedaquiline susceptibility transitions in Mycobacterium tuberculosis: From nonlinear curve fitting to interval-censored threshold models

Objective: To compare the structural adequacy and predictive performance of logarithmic and bounded nonlinear models for bedaquiline (BDQ) susceptibility and to develop an interval-censored threshold model using isolate-level response data. Methods: Using the original isolate-level dataset of 100 clinical Mycobacterium tuberculosis isolates tested at 11 bedaquiline concentrations (0.20-6.40 mg/L), we reproduced the previously used logarithmic, reciprocal-rational, and Gompertz-type models and extended the comparison to bounded lognormal-survival, log-logistic/Hill, and Weibull-survival functions. Model performance was evaluated with R 2 , mean absolute error (MAE), root mean squared error (RMSE), corrected Akaike information criterion (AICc), Bayesian information criterion (BIC), Akaike weights, and leave-one-concentration-out cross-validation. Results: The logarithmic and lognormal-survival models were numerically indistinguishable in-sample (R 2 =0.902 2; RMSE=5.719; AICc=43.864), while the log-logistic/Hill model yielded the smallest cross-validated RMSE (7.227). Unlike the logarithmic model, the bounded survival models remain within 0-100 and converge to zero resistant isolates as concentration increases. The isolate-level response sequences showed no reversals from a less resistant to a more resistant state as concentration increased, allowing a second analysis using interval-censored latent thresholds. Among lognormal, Weibull, gamma, and log-logistic threshold distributions, the lognormal model had the lowest AICc for both transitions. The estimated median resistance-loss threshold was 0.370 mg/L (bootstrap 95% CI 0.266-0.518), whereas the median susceptibility-onset threshold was 0.604 mg/L (95% CI 0.462-0.794); the median threshold ratio was 1.633 (95% CI 1.446-1.875). Conclusions: These results show that the apparent success of logarithmic regression is best interpreted as a local empirical approximation to a bounded threshold-survival process rather than evidence of temporal resistance dynamics. The interval-censored formulation uses the full isolate-level information and provides a mathematically admissible and reproducible framework for BDQ susceptibility transitions.