The balanced allocation of experimental units with regard to various known covariates among several treatment groups, before the physical experiment takes place, is often considered to be the most reasonable allocation scheme in all intervention studies and clinical trials. It is well-known that covariate mean balance over various treatment groups ensures widely used D- and A-optimality. However, it is not well-understood if the reverse proposition holds or not. For continuous covariates, it has been observed previously by the same authors, through a computationally intensive method, that covariate mean balance is nearly achieved for an optimal design. In the present paper, it has been analytically established that, with categorical covariates, the covariate mean balance can be ensured through D- and A-optimality.

The determination and ordering of the influencers of customer satisfaction are of paramount interest in various service industries. The theory of logistic regression may be exploited to relate customer satisfaction usually measured in an ordinal scale with possible covariates, measured in metrical, ordinal or binary scales. However, some of the confounders are themselves determined by other covariates under study. This necessitates the use of a simultaneous equation with ordinal endogenous variables. We propose one such approach and demonstrate its efficacy with a real life example.

Cardiovascular diseases are severe global health issues with side effects. Current treatments are unclear and can cause side effects. Marine carotenoids, found in plants, are a promising source for drug discovery due to their biological activities and chemical variety. Their physiological actions may prevent degenerative diseases and have antioxidant effects. The biological activities and chemical variety of marine natural products have made them an attractive source for drug discovery. This review focuses on the specific functions and mechanisms of these active constituents in coronary artery disease, highlighting their abilities such as reducing lipid levels, acting as antioxidants, inhibiting platelet aggregation, and possessing anticoagulant properties. This presents a challenge for the food industry, as consumers now seek foods that are not only nutritious but also convenient and pleasurable to eat.