Comparative Analysis of Parameter Estimation Methods in Logistic Regression for LD50 and Survival Function Estimation

The study aims to evaluate the efficiency of the Logistic regression model in analyzing dose-response data to estimate the effects of different doses on the survival rates of organisms. Four statistical methods were employed to estimate the model parameters: the Maximum Likelihood Estimation using the Newton-Raphson algorithm (MLE N-R) and the Downhill algorithm (MLE D-H), in addition to the Chi-Square Minimization method and the Bayesian method. The results showed that the MLE N-R and MLE D-H methods were the most accurate and stable, providing identical estimates for the median lethal dose (LD50) with consistent and reliable performance across various sample sizes. While the Chi-Square method demonstrated acceptable performance, it was less accurate, particularly when dealing with data that did not conform to the assumed distribution. Conversely, the Bayesian method exhibited variable and unstable performance when estimating median doses for certain variables, making it less reliable. When comparing the survival function, the MLE N-R method produced the highest estimates for survival probabilities, indicating a slower and more gradual decline in survival rates compared to the other methods. On the other hand, the Bayesian method showed the least accuracy, with survival estimates demonstrating a sharp and unexpected decrease. These findings highlight the superiority of MLE N-R as a robust analytical tool for dose-response data analysis.