Segmented regression to streamline semi-mechanistic pharmacodynamic modelling of antibiotic effects

Abstract

Purpose Semi-mechanistic pharmacodynamic (PD) models quantify bacterial dynamics from time-kill (TK) assays, often showing multi-phasic kill and regrowth dynamics. Regrowth is typically captured with two subpopulations with distinct concentration-effect relationships. Since only total bacterial counts are observed, subpopulation dynamics must be inferred, causing identifiability issues, sensitivity to initial estimates, and model-testing burden. We aimed to establish an efficient and robust approach for developing semi-mechanistic PD models, demonstrated with 24-hour TK data for colistin against Pseudomonas aeruginosa. Methods A three-step workflow was developed: (1) log-transformed TK data were segmented into kill and regrowth phases, with linear regression estimating phase-specific slopes per concentration and replicate; (2) empirical slopes were pooled to derive concentration-effect relationships; (3) selected relationships and parameter estimates were incorporated into a semi-mechanistic PD model. Results Segmented regression captured kill and regrowth slopes at all concentrations. Slope saturation with increasing colistin and consistently weaker drug effect during regrowth indicated a less susceptible subpopulation, motivating a two-subpopulation model. The semi-mechanistic model adequately described bacterial dynamics at all concentrations, with parameters comparable to Step 2. Conclusion This three-step workflow enables efficient and robust identification of concentration-effect relationships, reducing model testing and computational burden for streamlined semi-mechanistic antibiotic PD model development.