Using joint models to adjust for informative drop-out when modelling a longitudinal biomarker: an application to type 2 diabetes disease progression

Linear mixed effects models are frequently used in biomedical statistics to model the trajectory of a repeatedly measured longitudinal variable, such as a biomarker, over time. However, population-level estimates may be biased by censoring bias resulting from exit criteria that depend on the variable in question. A joint longitudinal-survival model, in which the exit criteria and longitudinal variable are modelled simultaneously, may address this bias. Using blood glucose progression (change in HbA1c) in type 2 diabetes patients on metformin monotherapy as an example, we study the potential benefit of using joint models to model trajectory of a biomarker in observational data. 7,712 patients with type 2 diabetes initiating metformin monotherapy were identified in UK Biobank's general practice (GP) linked records. Genetic information was extracted from UK Biobank, and prescription records, baseline clinical features and biomarkers, and longitudinal HbA1c measures were extracted from GP records. Exit criteria for follow-up for a patient was defined as progression to an additional glucose-lowering drug (which is more likely in patient with higher HbA1c). Estimates of HbA1c trajectory over time were compared using linear mixed effect model approaches (which do not account for censoring bias) and joint models. In the primary analysis, a 0.19 mmol/mol per year higher (p = 0.01) HbA1c gradient was estimated using the joint model compared to the linear mixed effects model. This difference between models was attenuated (0.13 mmol/mol per year higher, p=0.43) when baseline clinical features and biomarkers were included as additional covariates. Censoring bias should be carefully considered when modelling trajectories of repeatedly measured longitudinal variables in observational data. Joint longitudinal-survival models are a useful approach to identify and potentially correct for censoring bias when estimating population-level trajectories.

APPROXIMATE ANALYTICAL SOLUTION OF THE PROBLEM OF CONJUGATE HEAT TRANSFER BETWEEN THE BOUNDARY LAYER AND THE ANISOTROPIC STRIP

Optimization of technological processes in metallurgy related to transfer and use of heat energy makes more complicated demands for calculation of heat exchange. Therefore, the work, the approximate analytical method for solving the conjugate problems of viscous gas-dynamic boundary layer and thermal conductivity in the anisotropic strip, has been developed. The paper uses modern numerical methods for solving differential equations in partial derivative and analytic methods on the basis of an integral transform of Fourier and Laplace. Boundary equations have been solved analytically with certain simplifications, and the problem of anisotropic heat conduction has been solved analytically. The heat flows are determined analytically by the longitudinal variable at the interface boundary. It has been established that temperature increase of the external surface contributes to that all factors directly impacting on the magnitude of heat flows act towards their reduction. The analytical solution for the problem of thermal conductivity in the anisotropic strip with a general type of anisotropy when the heat flows from the boundary layer are determined at the boundaries is obtained. The conducted research for the temperature of external boundary and heat flow from gas to it demonstrates that with increasing the degree of longitudinal anisotropy the surface temperature of the strip downstream increases from increasing longitudinal heat conduction An original conjugation method using the continuous heat flows, and temperatures at the interface boundary is found. The numerical results for the heat flows and temperatures at the interface boundary have been obtained and analyzed.

Linear vibrations of triple-walled carbon nanotubes

In this paper, the linear vibrations of triple-walled carbon nanotubes (TWNTs) are investigated. A multiple elastic thin shell model is applied. The TWNT dynamics is studied in the framework of the Sanders–Koiter shell theory. The van der Waals interaction between any two layers of the TWNT is modelled by a radius-dependent function. The shell deformation is described in terms of longitudinal, tangential and radial displacements. Simply supported, clamped and free boundary conditions are applied. The three displacement fields are expanded by means of a double mixed series based on Chebyshev polynomials for the longitudinal variable and harmonic functions for the tangential variable. The Rayleigh–Ritz method is applied to obtain approximate natural frequencies and mode shapes. The present model is validated in the linear field by means of comparisons with data from the literature. This study is focused on determining the effect of geometry and boundary conditions on the natural frequencies of TWNTs.

The influence of variation of electroconductivity on ionized gas flow in the boundary layer along a porous wall

This paper investigates ionized gas flow in the boundary layer when its electroconductivity is varied. The flow is planar and the contour is porous. At first, it is assumed that the ionized gas electroconductivity ? depends only on the longitudinal variable. Then we adopt that it is a function of the ratio of the longitudinal velocity and the velocity at the outer edge of the boundary layer. For both electroconductivity variation laws, by application of the general similarity method, the governing boundary layer equations are brought to a generalized form and numerically solved in a four-parametric three times localized approximation. Based on many tabular solutions, we have shown diagrams of the most important nondimensional values and characteristic boundary layer functions for both of the assumed laws. Finally, some conclusions about influence of certain physical values on ionized gas flow in the boundary layer have been drawn. .