Binary isotonic regression procedures, with application to cancer biomarkers

There is a lot of interest in the development and characterization of new biomarkers for screening large populations for disease. In much of the literature on diagnostic testing, increased levels of a biomarker correlate with increased disease risk. However, parametric forms are typically used to associate these quantities. In this article, we specify a monotonic relationship between biomarker levels with disease risk. This leads to consideration of a nonparametric regression model for a single biomarker. Estimation results using isotonic regression-type estimators and asymptotic results are given. We also discuss confidence set estimation in this setting and propose three procedures for computing confidence intervals. Methods for estimating the receiver operating characteristic (ROC) curve are also described. The finite-sample properties of the proposed methods are assessed using simulation studies and applied to data from a pancreatic cancer biomarker study

Anharmonic quantum contribution to vibrational dephasing

Based on a quantum Langevin equation and its corresponding Hamiltonian within a c-number formalism we calculate the vibrational dephasing rate of a cubic oscillator. It is shown that leading order quantum correction due to anharmonicity of the potential makes a significant contribution to the rate and the frequency shift. We compare our theoretical estimates with those obtained from experiments for small diatomics $N_2$, $O_2$ and $CO$.Comment: 21 pages, 1 figure and 1 tabl

Semiparametric binary regression under monotonicity constraints

Summary: We study a binary regression model where the response variable $\Delta$ is the indicator of an event of interest (for example, the incidence of cancer) and the set of covariates can be partitioned as $(X,Z)$ where $Z$ (real valued) is the covariate of primary interest and $X$ (vector valued) denotes a set of control variables. For any fixed $X$, the conditional probability of the event of interest is assumed to be a monotonic function of $Z$. The effect of the control variables is captured by a regression parameter $\beta$. We show that the baseline conditional probability function (corresponding to $X=0$) can be estimated by isotonic regression procedures and develop a likelihood ratio based method for constructing confidence intervals for this function that obviates the need to estimate nuisance parameters from the data. We also show how confidence intervals for the regression parameter can be constructed using asymptotically $\chi^2$ likelihood ratio statistics. The confidence sets for the regression parameter and those for the conditional probability function are combined using Bonferroni\u27s inequality to construct conservative confidence intervals for the conditional probability of the event of interest at different fixed values of $X$ and $Z$. We present simulation results to illustrate the theory and apply our results to a prostate cancer data set

Addressing nutritional gaps and suggesting a practical framework to reduce the risk of malnutrition and improve nutrition security in santhal tribal communities in India

Background The double burden of malnutrition is a growing problem, which is disproportionately represented across the Indian population, with undernutrition dominating rural areas. This study aimed to identify nutritional gaps in traditional recipes of Santhal tribes, create a recipe book to address deficiencies and support diet diversity. Methods Food Frequency Questionnaires (FFQ) were conducted to analyse dietary patterns of Santhal communities. Recipes were collected from five villages and shortlisted into 37 dishes based on availability, acceptability and popularity. Commonly consumed templates were based on FFQ findings and individual dishes. Nutritics software was used to identify nutritional gaps. In total, 24 recommended templates, were created to satisfy adequate intake of nutrients. Mann-Whitney and unpaired t-test were performed and findings were presented as mean (standard deviation(SD)) and median (25th–75th percentile). Results Less than one-fifth of consumed templates met energy requirements, 27% met protein recommendations, and 4% met requirements for fibre, total fat, monounsaturated and polyunsaturated fat. Other nutrients of concern included vitamins B12, B9, iodine, calcium and iron. Recommended templates significantly increased energy (Consumed (C): 996.0kcal(930-1090); Recommended (R): 1183.0kcal(1094-1341); p<0.0001), protein (C: 25.0g(8.4); R: 40.5g(33.2-52.3); p<0.0001), total fat (C: 7.4g(6.1-8.8); R: 17.2g(14.1-22.9); p<0.0001) and fibre (C: 5.0g(4.0-6.5); R: 8.2g(5.8-11.7); p=0.0013) compared to consumed templates. Additionally, calcium (C: 108.5mg(36.0-302.5); R: 245.5mg(152.3-528.3); p=0.0121), iron (C: 5.3mg(2.1-8.2); R: 10.7mg(8.2-13.2); p=0.0002), vitamin B6 (C: 0.4mg(0.3-0.7); R: 1.1mg(0.6-1.6); p=0.0001), B9 (C: 54.5ug(36.3-172.8); R: 252ug(179.4); p=0.0026) and B12 (C: 0ug(0-0); R: 1.0ug(0-2.1); p=0.0001) were also significantly increased. Conclusion This study provides a novel insight on the nutritional adequacy of indigenous Santhal recipes and highlights the need to enhance the nutrition status of these communities. Concerted efforts should be made to increase communication for nutritional advocacy, both nationally and internationally. Future research should evaluate the acceptability, practicality, and uptake of this recipe book in addressing malnutrition in rural communities

Inhomogeneous quantum diffusion and decay of a meta-stable state

We consider the quantum stochastic dynamics of a system whose interaction with the reservoir is considered to be linear in bath co-ordinates but nonlinear in system co-ordinates. The role of the space-dependent friction and diffusion has been examined in the decay rate of a particle from a meta-stable well. We show how the decay rate can be hindered by inhomogeneous dissipation due nonlinear system-bath coupling strength.Comment: To be published in Phys. Lett.