Testing the Avrami-Dobrzyński model of cancer transformation using mutation-count clinical data across multiple tumour types

BACKGROUND: The Avrami-Dobrzyński (A-D) model interprets malignant transformation as a phase-transition-like process, mathematically equivalent to the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation from condensed-matter physics.In this framework, the cumulative probability of neoplastic transformation follows a Weibull-type sigmoidal function of the somatic mutation burden, parametrised by a shape constant a and a critical scaling exponent k. Purpose: To test the generalisability of the A-D model by fitting its cumulative distribution function to clinical mutation-count data spanning 24 cancer types, and to analyse meaning of its parameters across a heterogeneous patient population. Methods: Mutation-count data for 70 studies (24 tumour types, n ≥ 100 per study) were retrieved from cBioPortal. For each cohort, an empirical cumulative distribution P(m) was constructed from total non-synonymous mutation counts per sample. One-, two-, and three-component A-D mixture models (equivalent to Weibull mixture distributions) were fitted. Results: Single-component A-D fits adequately described a minority of cohorts; the majority exhibited a characteristic "knee" or wave-like inflection in the linearised representation, requiring two-or three-component mixture models. The scaling exponent k varied widely across and fell below unity in 37 of 136 fitted components, indicating a decreasing-hazard regime. The k-a parameter space showed systematic co-variation with mean mutation burden. Superposition of decreasing-and increasing-hazard components within individual tumour categories generated composite hazard profiles, reflecting coexisting subpopulations with distinct transformation dynamics. Conclusions:The A-D model provides a physically grounded description of mutation-driven cancer transformation across diverse tumour types. Deviations from single-component behaviour are consistent with genuine biological heterogeneity within nominal tumour categories. These findings support the broader applicability of phase-transition concepts in computational oncology and provide a quantitative framework for integrating genomic data into cancer risk modelling.