Properties of an MLE algorithm for the multivariate linear model with a separable covariance matrix structure

Summary In this paper we present properties of an algorithm to determine the maximum likelihood estimators of the covariance matrix when two processes jointly affect the observations. Additionally, one process is partially modeled by a compound symmetry structure. We perform a simulation study of the properties of an iteratively determined estimator of the covariance matrix.

Prediction model for best focus, power, and spherical aberration of the cornea: Raytracing on a large dataset of OCT data

Purpose To analyse corneal power based on a large optical coherence tomography dataset using raytracing, and to evaluate corneal power with respect to the corneal front apex plane for different definitions of best focus. Methods A large OCT dataset (10,218 eyes of 8,430 patients) from the Casia 2 (Tomey, Japan) was post-processed in MATLAB (MathWorks, USA). Using radius of curvature, corneal front and back surface asphericity, central corneal thickness, and pupil size (aperture) a bundle of rays was traced through the cornea. Various best focus definitions were tested: a) minimum wavefront error, b) root mean squared ray scatter, c) mean absolute ray scatter, and d) total spot diameter. All 4 target optimisation criteria were tested with each best focus plane. With the best-fit keratometer index the difference of corneal power and keratometric power was evaluated using a multivariate linear model. Results The mean corneal powers for a/b/c/d were 43.02±1.61/42.92±1.58/42.91±1.58/42.94±1.59 dpt respectively. The root mean squared deviations of corneal power from keratometric power (nK = 1.3317/1.3309/1.3308/1.3311 for a/b/c/d) were 0.308/0.185/0.171/0.209 dpt. With the multivariate linear model the respective RMS error was reduced to 0.110/0.052/0.043/0.065 dpt (R² = 0.872/0.921/0.935/0.904). Conclusions Raytracing improves on linear Gaussian optics by considering the asphericity of both refracting surfaces and using Snell’s law of refraction in preference to paraxial simplifications. However, there is no unique definition of best focus, and therefore the calculated corneal power varies depending on the definition of best focus. The multivariate linear model enabled more precise estimation of corneal power compared to the simple keratometer equation.

Effect of Altitude on Covid-19 Mortality in Ecuador: an Ecological Study

BackgroundThe SARS-CoV-2/COVID-19 pandemic has claimed nearly 900,000 lives worldwide and infected more than 27 million people. Researchers worldwide are studying ways to decrease SARS-CoV-2 transmission and COVID-19 related deaths. Several studies found altitude having a negative association with both COVID-19 incidence and deaths. Ecuadorian data was used to explore the relationship between altitude and COVID-19. MethodsThis is an ecological study examining province-level data. To explore a relationship between altitude and COVID-19, this study utilized publicly available COVID-19 data and population statistics. ANOVA, correlation statistics, and a multivariate linear model explored the relationship between different Ecuadorian altitudes against incidence, mortality, and case-fatality rates. Populations statistics attributed to COVID-19 were included in the linear model to control for confounding factors. ResultsRegional differences were observed for incidence, mortality, and case fatality rate suggesting an association between altitude and SARS-CoV-2 transmission and COVID-19 disease severity. In both the correlation analysis and linear model altitude showed a statistically significant negative correlation between altitude and COVID-19 mortality. ConclusionAltitude may have an effect on COVID-19 mortality rates. More research is needed to understand why altitude may have a protective effect against COVID-19 mortality and how this may be applicable in a clinical setting.

Generalized Vertical Components of built-up areas from global Digital Elevation Models by multi-scale linear regression modelling

The estimation of the vertical components of built-up areas from free Digital Elevation Model (DEM) global data filtered by multi-scale convolutional, morphological and textural transforms are generalized at the spatial resolution of 250 meters using linear least-squares regression techniques. Six test cases were selected: Hong Kong, London, New York, San Francisco, Sao Paulo, and Toronto. Five global DEM and two DEM composites are evaluated in terms of 60 combinations of linear, morphological and textural filtering and different generalization techniques. Four generalized vertical components estimates of built-up areas are introduced: the Average Gross Building Height (AGBH), the Average Net Building Height (ANBH), the Standard Deviation of Gross Building Height (SGBH), and the Standard Deviation of Net Building Height (SNBH). The study shows that the best estimation of the net GVC of built-up areas given by the ANBH and SNBH, always contains a greater error than their corresponding gross GVC estimation given by the AGBH and SGBH, both in terms of mean and standard deviation. Among the sources evaluated in this study, the best DEM source for estimating the GVC of built-up areas with univariate linear regression techniques is a composite of the 1-arcsec Shuttle Radar Topography Mission (SRTM30) and the Advanced Land Observing Satellite (ALOS) World 3D–30 m (AW3D30) using the union operator (CMP_SRTM30-AW3D30_U). A multivariate linear model was developed using 16 satellite features extracted from the CMP_SRTM30-AW3D30_U enriched by other land cover sources, to estimate the gross GVC. A RMSE of 2.40 m and 3.25 m was obtained for the AGBH and the SGBH, respectively. A similar multivariate linear model was developed to estimate the net GVC. A RMSE of 6.63 m and 4.38 m was obtained for the ANBH and the SNBH, respectively. The main limiting factors on the use of the available global DEMs for estimating the GVC of built-up areas are two. First, the horizontal resolution of these sources (circa 30 and 90 meters) corresponds to a sampling size that is larger than the expected average horizontal size of built-up structures as detected from nadir-angle Earth Observation (EO) data, producing more reliable estimates for gross vertical components than for net vertical component of built-up areas. Second, post-production processing targeting Digital Terrain Model specifications may purposely filter out the information on the vertical component of built-up areas that are contained in the global DEMs. Under the limitations of the study presented here, these results show a potential for using global DEM sources in order to derive statistically generalized parameters describing the vertical characteristics of built-up areas, at the scale of 250x250 meters. However, estimates need to be evaluated in terms of the specific requirements of target applications such as spatial population modelling, urban morphology, climate studies and so on.

Executive Function in Infants and Toddlers Born Low Birth Weight and Preterm

Infants born low birth weight (LBW) and preterm were evaluated in a high-risk follow-up clinic and compared with infants born full term. A multivariate linear model was used to examine the overall differences on Bayley Scales of Infant Toddler Development (BSID-III) among three groups: full term, heavy LBW (<2,500 g ≥2,000 g), light LBW (<2,000 g). Results indicated no significant differences in BSID-III scores between the groups. The BSID-III was used to extrapolate indicators of executive function (EF) components. Dimensions of Mastery Motivation (DMQ 18) was correlated with the EF components. Findings showed that both LBW groups scored significantly lower than the full-term group on the EF components which include attention, plan/organize, working memory, and inhibit. Implications for research is discussed.

A concise, machine learning-based questionnaire that screens for insomnia and apnoea in the general population

Poor sleep is a major public health problem with implications for a wide range of critical health outcomes, including cardiovascular disease, obesity, mental health, and neurodegenerative disease.1,2 The most prevalent sleep disorders are insomnia and sleep apnoea. While questionnaires aimed at detecting and quantifying sleep problems have been used for years and proven to be reliable,3-6 they are often very extensive and scientifically worded. Here, we propose that the general population can use the SleepHubs Check-up (SHC), a concise questionnaire as a screening tool for sleep apnoea and insomnia. We validated the SHC against widely-used sleep questionnaires. These include the Insomnia Sleep Index (ISI)5 for detection of insomnia risk, as well as STOP-Bang3 and Multivariable Apnoea Prediction Index (MAPI)7,8 for the detection of sleep apnoea risk. We built a multivariate linear model to predict the ISI score based on the SHC questions and obtained an R2 of 0.60. For the detection of sleep apnoea, we constructed a convoluted neural network to predict the risk of apnoea from the SHC questions, and obtained an accuracy of 0.91. The SHC is therefore a reliable and accessible tool for the detection of latent sleep problems in the general public. Future work will aim at increasing the input data to improve the accuracy.

Impact of Climate Factors in Modeling and Predicting the Transmission of Meningitis in Africa: The Case of Burkina Faso

Background: Meningitis is a major cause of morbidity in the world. Previous studies showed that climate factors influence the occurrence of meningitis. A multiple linear regression model was developed to forecast meningitis cases in Burkina Faso using climate factors. However, the multivariate linear regression model based on times series data may produce fallacious results given the autocorrelation of errors. Aims: The aim of the study is to develop a model to quantify the effect of climate factors on meningitis cases, and then predict the expected weekly incidences of meningitis for each district. Data and methods: The weekly cases of meningitis come from the Ministry of Health and covers the period 2005-2017. Climate data were collected daily in 10 meteorological stations from 2005 to 2017 and were provided by the national meteorological Agency of Burkina Faso. An ARIMAX and a multivariate linear regression model were estimated separately for each district. Results: The multivariate linear model is inappropriate to model the number of meningitis cases due to autocorrelation of errors. With the ARIMAX Model, Temperature is significantly associated with an increase of meningitis cases in 3 of 10 districts, while relative humidity is significantly associated with a decrease of meningitis cases in 3 of the 10 districts. The effect of wind speed and precipitation is not significant at the 5% level in all 10 districts. The prediction of meningitis cases with 8 test observations provides an average absolute error ranging from 0.99 in Boromo and Bogandé to 7.22 in the district of Ouagadougou. Conclusion: The ARIMAX model is more appropriate than the multivariate linear model to analyze the dynamics of meningitis cases. Climatic factors such as temperature and relative humidity have a significant influence on the occurrence of meningitis in Burkina Faso; the temperature influences it positively and the relative humidity influences it negatively.