Latent heterogeneity effects in modelling individual hazards: A non-proportional approach

• Modelling heterogeneity in innovation diffusion is separated in two directions.
• Bemmaor's methodology for latent propensities is included in the Cox model.
• Time scale parameter depends upon observed covariates at individual level.
• An illustrative and strictly reproducible example on ovarian pathology is given.

This paper proposes an extension of individual hazard modelling through diffusion of innovation methodologies with the introduction of latent neighbouring effects in individual hazards. The proposal combines the Bemmaor's methodology for latent heterogeneous factors in the Cox proportional hazards model. The new model, the Bass–Bemmaor–Cox model, defines a non-proportional approach driven by a mixture of shifted Gompertz individual distributions where the time scale parameter governing growth dynamics depends upon observed covariates at the individual level. Conversely, individual propensity to the change of state included in the Gompertz sub-model is heterogeneous and latent within observed population. Based on experimental data referred to an ovarian pathology under treatment, an illustrative example is given. Further applications may be relevant for quantitative forecasting in marketing and technological diffusion contexts.