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Recently the shape-restricted inference has gained popularity in statistical and econometric literature to relax the linear or quadratic covariate effect in regression analyses. The typical shape-restricted covariate effect includes monotone increasing, decreasing, convexity or concavity. In this paper, we introduce the shape-restricted inference to the celebrated Cox regression model (SR-Cox), in which the covariate response is modelled as shape-restricted additive functions. The SR-Cox regression approximates the shape-restricted functions using a spline basis expansion with data-driven choice of knots. The underlying minimization of negative log-likelihood function is formulated as a convex optimization problem, which is solved with an active-set optimization algorithm. The highlight of this algorithm is that it eliminates the superfluous knots automatically. When covariate effects include combinations of convex or concave terms with unknown forms and linear terms, the most interesting finding is that SR-Cox produces accurate linear covariate effect estimates which are comparable to the maximum partial likelihood estimates if indeed the forms are known. We conclude that concave or convex SR-Cox models could significantly improve nonlinear covariate response recovery and model goodness of fit. [ABSTRACT FROM AUTHOR]

The New Journal of Chemistry, published by The Royal Society of Chemistry and the Centre National de la Recherche Scientifique, is a scientific journal that aims to connect the world with the chemical sciences. The contents list for the September 21, 2024 issue includes a variety of articles and papers on topics such as the synthesis of nanomaterials, nonlinear optical crystals, and the detection of formaldehyde. The journal provides recognition and professional development opportunities for scientists. Some specific papers in this issue cover the preparation of superhydrophobic/superhydrophilic sodium alginate aerogels for oil absorption, improved efficiency of quantum dot-sensitized solar cells, and the electrocatalytic activity of nickel-doped manganese oxide nanorods. Other topics include the synthesis of nanocomposites for supercapacitor performance, the selective adsorption and photodegradation of residual norfloxacin in water, and the targeted delivery of ifosfamide for cancer treatment. [Extracted from the article]