Parametric Survival Analysis Using the Log-Lomax-Weibull Model: Application to Acute Myocardial Infarction Data

Abstract

This study proposes and applies the Log-Lomax-Weibull (LLW) parametric survival model to assess the survival experience of patients with Acute Myocardial Infarction (AMI). The LLW model integrates the flexibility of the Lomax and Weibull distributions to accommodate non-monotonic hazard functions and heavy-tailed behaviour often observed in medical survival data. The model's performance was evaluated using a real-world AMI dataset, where key covariates such as age, gender, and comorbidities were analyzed. Maximum Likelihood Estimation (MLE) was employed to estimate the model parameters. For the LLW result, significant covariates included γ₂ (Estimate = 0.9552, p = 0.0338) and γ₃ (Estimate = 0.9997, p = 0.0054), indicating that these predictors have a strong impact on survival time. Similarly, under the Cos-Snell residual for the LLW model, γ₂ and γ₃ remained statistically significant with estimates of 1.1059 (p = 0.0146) and 1.0491 (p = 0.0043), respectively, confirming their relevance in modelling AMI survival outcomes. The shape and scale parameters (β, α, σ) demonstrated statistical significance, with β = 2.0700 (p < 2.2e-16) indicating the accelerated failure time nature of the survival data. Model adequacy was further assessed using Cox-Snell residuals and graphical diagnostics, confirming the suitability of the LLW model for this dataset.