Personalized medicine requires the integration and processing of vast amounts of data. Here, we propose a solution to this challenge that is based on constructing Digital Twins. These are high-resolution models of individual patients that are computationally treated with thousands of drugs to find the drug that is optimal for the patient.

6It is sometimes the case that a theory proposes that the population means on two variables should have the same rank order across a set of experimental conditions. This paper presents a test of this hypothesis. The test statistic is based on the coupled monotonic regression algorithm developed by the authors. The significance of the test statistic is determined by comparison to an empirical distribution specific to each case, obtained via non-parametric or semi-parametric bootstrap. We present an analysis of the power and Type I error control of the test based on numerical simulation. Partial order constraints placed on the variables may sometimes be theoretically justified. These constraints are easily incorporated into the computation of the test statistic and are shown to have substantial effects on power. The test can be applied to any form of data, as long as an appropriate statistical model can be specified.

Monotonic regression is a standard method for extracting a monotone function from non-monotonic data, and it is used in many applications. However, a known drawback of this method is that its fitted response is a piecewise constant function, while practical response functions are often required to be continuous. The method proposed in this paper achieves monotonicity and smoothness of the regression by introducing an L2 regularization term. In order to achieve a low computational complexity and at the same time to provide a high predictive power of the method, we introduce a probabilistically motivated approach for selecting the regularization parameters. In addition, we present a technique for correcting inconsistencies on the boundary. We show that the complexity of the proposed method is O(n 2 ). Our simulations demonstrate that when the data are large and the expected response is a complicated function (which is typical in machine learning applications) or when there is a change point in the response, the proposed method has a higher predictive power than many of the existing methods.

IntroductionWHO has set a goal to reduce the prevalence of stunted child growth by 40% by the year 2025. To reach this goal, it is imperative to establish the relative importance of risk factors for stunting to deliver appropriate interventions. Currently, most interventions take place in late infancy and early childhood. This study aimed to identify the most critical prenatal and postnatal determinants of linear growth 0–24 months and the risk factors for stunting at 2 years, and to identify subgroups with different growth trajectories and levels of stunting at 2 years.MethodsConditional inference tree-based methods were applied to the extensive Maternal and Infant Nutrition Interventions in Matlab trial database with 309 variables of 2723 children, their parents and living conditions, including socioeconomic, nutritional and other biological characteristics of the parents; maternal exposure to violence; household food security; breast and complementary feeding; and measurements of morbidity of the mothers during pregnancy and repeatedly of their children up to 24 months of age. Child anthropometry was measured monthly from birth to 12 months, thereafter quarterly to 24 months.ResultsBirth length and weight were the most critical factors for linear growth 0–24 months and stunting at 2 years, followed by maternal anthropometry and parental education. Conditions after birth, such as feeding practices and morbidity, were less strongly associated with linear growth trajectories and stunting at 2 years.ConclusionThe results of this study emphasise the benefit of interventions before conception and during pregnancy to reach a substantial reduction in stunting.

Monotonic (isotonic) regression is a powerful tool used for solving a wide range of important applied problems. One of its features, which poses a limitation on its use in some areas, is that it produces a piecewise constant fitted response. For smoothing the fitted response, we introduce a regularization term in the monotonic regression, formulated as a least distance problem with monotonicity constraints. The resulting smoothed monotonic regression is a convex quadratic optimization problem. We focus on the case, where the set of observations is completely (linearly) ordered. Our smoothed pool-adjacent-violators algorithm is designed for solving the regularized problem. It belongs to the class of dual active-set algorithms. We prove that it converges to the optimal solution in a finite number of iterations that does not exceed the problem size. One of its advantages is that the active set is progressively enlarging by including one or, typically, more constraints per iteration. This resulted in solving large-scale test problems in a few iterations, whereas the size of that problems was prohibitively too large for the conventional quadratic optimization solvers. Although the complexity of our algorithm grows quadratically with the problem size, we found its running time to grow almost linearly in our computational experiments.