# On the unification of zero-adjusted cure survival models

## TL;DR

This paper introduces a unified survival model that incorporates zero-adjustment and cure proportions, accommodating various cause distributions, and demonstrates its effectiveness through simulations and real obstetric data analysis.

## Contribution

It presents a novel, flexible survival model unifying zero-adjusted and cure models with multiple cause distributions, validated by simulations and real data.

## Key findings

- Model fits obstetric data well with geometric causes.
- Simulation shows improved estimator accuracy with larger samples.
- Flexible framework applicable to diverse survival data.

## Abstract

This paper proposes a unified version of survival models that accounts for both zero-adjustment and cure proportions in various latent competing causes, useful in data where survival times may be zero or cure proportions are present. These models are particularly relevant in scenarios like childbirth duration in sub-Saharan Africa. Different competing cause distributions were considered, including Binomial, Geometric, Poisson, and Negative Binomial. The model's maximum likelihood point estimators and asymptotic confidence intervals were evaluated through simulation, demonstrating improved accuracy with larger sample sizes. The model best fits real obstetric data when assuming geometrically distributed causes. This flexible model, capable of considering different distributions for the lifetime of susceptible individuals and competing causes, is an effective tool for adjusting survival data, indicating broad application potential.