Continuous-time multi-type branching processes are fundamental models for expanding and migrating populations with cancer evolution being a prototypical example. Inferring model parameters, like mutation and growth rates, from time-series count data requires efficient computation of population size distributions. Existing methods are mainly based on large-time or large-number asymptotics, which rely on either restricted initial conditions or simplified interactions between cell types. Here, we introduce two numerical approximations of population size distributions for multi-type branching processes on directed graphs with arbitrary initialization. The first approach combines a saddle-point approximation with numerical integration of the probability generating function. We characterize admissibility and establish conditions for saddle-point existence and uniqueness. For directed acyclic graphs, the second approach provides a large-time small-mutation-rate alternative based on closed-form approximate Laplace transforms and efficient numerical inversion. We benchmark the accuracy and speed of both solutions in simulations, showing substantial improvement over the state-of-the-art large-number approximation and orders of magnitude speedup over Gillespie's stochastic simulation algorithm at matching accuracy. We apply our methods to analyze the relapse dynamics of an acute myeloid leukemia patient, where rapid parameter scans over a six-type patient-specific mutation tree quantify how unobserved remission burden and treatment-altered fitness can explain relapse. Our methods provide computational building blocks for future likelihood-based inference in cancer evolution and other expanding populations.
Xiang-Ge Luo, J. Kuipers, N. Beerenwinkel· 0 citations
Large language models (LLMs) are emerging as tools to support clinical decision making. HIV management is a compelling use case due to its complexity and dynamic nature, involving diverse treatment options, comorbidities, and adherence challenges. However, integrating LLMs into clinical practice raises concerns about accuracy, safety, and clinician acceptance. Despite growing interest, their performance in HIV care remains poorly studied, and benchmarking is lacking.
We developed HIVMedQA, a clinician-curated benchmark of HIV-related open-ended medical question-answer pairs spanning basic knowledge, clinical reasoning, complex patient vignettes, and bias-modified scenarios. We evaluated seven general-purpose and three medical LLMs. Performance was assessed using lexical similarity and an extended medical LLM-as-a-judge framework capturing key clinical dimensions, including question comprehension, reasoning, knowledge recall, bias, potential harm, and factual accuracy, to better capture nuances relevant to the medical domain, with additional evaluation by HIV-experienced physicians.
Performance varies substantially across models and task complexity. Gemini 2.5 Pro achieves the highest overall scores, followed by Claude 3.5 Sonnet and MedGemma-27B. Knowledge recall is generally stronger than question comprehension or clinical reasoning. Medical LLMs do not consistently outperform general-purpose models, and model size alone does not predict performance. Several models are sensitive to cognitive bias prompts. LLM-as-a-judge scoring aligns better with clinician assessment than lexical metrics.
HIVMedQA provides a structured benchmark for evaluating LLMs in HIV clinical decision support. Current LLMs show promise, but limitations in reasoning, bias robustness, and safety indicate that careful validation, domain-specific evaluation, and clinician oversight remain essential before clinical deployment.
Gonzalo Cardenal-Antolin, J. Fellay, Bashkim Jaha et al.· Communications Medicine· 0 citations
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