D-optimal design of the additive mixture model with multi-response

Response Surface Methodology (RSM) is a collection of statistical and mathematical techniques used to develop, improve, and optimize processes. It is particularly valuable when many input variables or factors potentially influence a response variable.
The process of RSM involves several key steps:

Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable due to more than one independent variable, also known as factors. Changes in worker productivity can be reasoned, for example, to be influenced by salary and other conditions, such as skill level. One way to test this hypothesis is by categorizing salary into three levels (low, moderate, and high) and skills sets into two levels (entry level...

Drugs exert their therapeutic effects by interacting with receptors, enzymes, or ion channels that are present throughout the human body. The strength and duration of the interaction between a drug and its target receptor are characterized by the selectivity and specificity of the drug. Selectivity refers to a drug's strong preference for its intended target over other targets. For instance, isoprenaline, a non-selective β-adrenergic agonist, interacts with both β1- and...

Agonists can bind with and activate receptors, resulting in the formation of drug-receptor complexes. Once formed, these complexes catalyze many biochemical processes at the cellular level and subsequently induce a pharmacologic response. The degree of response is directly proportional to the fraction of activated receptors, which in turn, depends on the concentration of the drug at the receptor site as well as the sensitivity of the receptor. An increase in the administered dose contributes to...

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...

Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...