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Multi-stage models for cohort data are widely used in various fields, including disease progression, the biological development of plants and animals, and laboratory studies of life cycle development. However, the likelihood functions of these models are often intractable and complex. These complexities in the likelihood functions frequently result in significant biases and high computational costs when estimating parameters using current Bayesian methods. This paper aims to address these challenges by applying the enhanced Sequential Monte Carlo approximate Bayesian computation (ABC-SMC) method, which does not rely on explicit likelihood functions, to stage-structured development models with non-hazard rates and stage-wise constant hazard rates. Instead of using a likelihood function, the proposed method determines parameter estimates based on matching vector summary statistics. It incorporates stage-wise parameter estimations and retains accepted parameters across stages. This approach not only reduces model biases but also improves the computational efficiency of parameter estimations, despite the computational intractability of the likelihood functions. The proposed ABC-SMC method is validated through simulation studies on stage-structured development models and applied to a case study of breast development in New Zealand schoolgirls. The results demonstrate that the proposed methods effectively reduce biases in later-stage estimates for stage-structured models, enhance computational efficiency, and maintain accuracy and reliability in parameter estimations compared to the current methods.

An enhanced approximate Bayesian computation method for stage-structured development models