A New Statistical Formula for Estimating the Breast Cancer's Median Lethal Dose based on Inverse Weibull Model

Abstract

This paper estimates the median lethal dose of a two-replicate multivariate biological experiment through a new statistical formula related to the best model among eleven models constructed to describe the relationship of dose-response and time based on the inverse Weibull. The real biological experiment focused on using actual data to biologically cure breast cancer using therapeutic zinc selenide, produced either by a plasma-physically approach or by employing an environmental plant extract (Calgan plant). The unknown parameters associated with the eleven models are estimated using two traditional estimation methods: ordinary least squares and maximum likelihood. Because these estimates could not be determined directly, the Newton-Raphson iterative technique is used. The mean squared error is used to choose the best model. Then, at successive time points, the breast cancer's median lethal dose is calculated. The results clearly show that the mean square error values of maximum likelihood are always lower than those of the ordinary least squares, and the median lethal dose exhibits a decreasing relationship over time. Further, the new procedure for measuring the median lethal dose allows for several estimates with subsequent periods, which allows for several effective concentrations of 50% in the experimental units.