Estimating the Median Lethal Dose of Breast Cancer with Modified Weibull Statistical Model

Nadia H. Al-Noor; Iden Hasan  Hussein; Shaima Abbas  Jasim

doi:10.30526/37.3.3442

Authors

Nadia H. Al-Noor 2Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq https://orcid.org/0000-0002-4433-9044
Iden Hasan Hussein Department of Mathematics, College of Science for Women, Baghdad University, Baghdad, Iraq https://orcid.org/0000-0002-6492-8196
Shaima Abbas Jasim Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq https://orcid.org/0000-0002-7879-7668

DOI:

https://doi.org/10.30526/37.3.3442

Keywords:

Biological experiment, Median lethal dose, Modified Weibull, Traditional estimation methods

Abstract

In this paper, based on a linear relationship between the natural logarithms of the scale parameter and dose, nineteen models are constructed using the modified Weibull statistical model to describe the relationship of dose-response and time for multivariate dual-response life experiments with two-replicate. The real biological data set is considered to evaluate the response rates of breast cancer cells treated with the therapeutic zinc selenide prepared in two different ways (physically and environmentally/organically). The unknown parameters are estimated using two estimation methods. The mean square error is used to select the best model. The median lethal dose is then determined on the basis of a new formula at successive times. The best models for each estimation method show that the experiment's replications are unimportant and that the median lethal dose estimates exhibit a decreasing dose-time relationship over the days.

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