The Accelerated Failure Time Regresssion Model Under the Generalised Gull Alpha Power Log Logistic Distribution for Handling Survival Data in Presence of Covariates

This study develops a Generalised Gull Alpha Power Log-Logistic Accelerated Failure Time (GGAPLL-AFT) regression model for analysing censored survival data in the presence of covariates. The model was developed by integrating the Generalised Gull Alpha Power Log-Logistic (GGAPLL) distribution into the Accelerated Failure Time framework, thereby combining the flexibility of the GGAPLL distribution with the interpretability of AFT regression. The proposed model is intended to provide a flexible approach for survival data characterised by different hazard rate structures, including increasing, decreasing, and unimodal hazards. The mathematical formulation of the proposed model was established by deriving its cumulative distribution function, probability density function, survival function, hazard function, and conditional survival function. The AFT formulation relates the logarithm of survival time to a linear function of covariates and a GGAPLL-distributed error term, allowing covariate effects to be interpreted in terms of acceleration or deceleration of survival time. The unknown model parameters were estimated using the Maximum Likelihood Estimation (MLE) method. Since the resulting likelihood equations are nonlinear and do not have closed-form solutions, numerical optimisation was performed using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. The performance of the proposed estimators was evaluated through a Monte Carlo simulation study under increasing, decreasing, and unimodal hazard scenarios. Simulations were conducted for different sample sizes and censoring levels, with estimator performance assessed using Absolute Bias (AB), Root Mean Square Error (RMSE), coverage probability, and Akaike Information Criterion (AIC). The simulation results showed that estimator performance improved as sample size increased, with reductions in bias and RMSE and coverage probabilities approaching the nominal 95% level. These findings demonstrate that the proposed GGAPLL-AFT model provides a flexible and reliable framework for parameter estimation and survival regression under diverse hazard structures.