Gaussian and Lerch Models for Unimodal Time Series Forcasting.

We consider unimodal time series forecasting. We propose Gaussian and Lerch models for this forecasting problem. The Gaussian model depends on three parameters and the Lerch model depends on four parameters. We estimate the unknown parameters by minimizing the sum of the absolute values of the residuals. We solve these minimizations with and without a weighted median and we compare both approaches. As a numerical application, we consider the daily infections of COVID-19 in China using the Gaussian and Lerch models. We derive a confident interval for the daily infections from each local minima.

Mixture of longitudinal factor analyzers and their application to the assessment of chronic pain.

Multivariate longitudinal data are used in a variety of research areas not only because they allow to analyze time trajectories of multiple indicators, but also to determine how these trajectories are influenced by other covariates. In this article, we propose a mixture of longitudinal factor analyzers. This model could be used to extract latent factors representing multiple longitudinal noisy indicators in heterogeneous longitudinal data and to study the impact of one or several covariates on these latent factors. One of the advantages of this model is that it allows for measurement non-invariance, which arises in practice when the factor structure varies between groups of individuals due to cultural or physiological differences. This is achieved by estimating different factor models for different latent classes. The proposed model could also be used to extract latent classes with different latent factor trajectories over time. Other advantages of the model include its ability to take into account heteroscedasticity of errors in the factor analysis model by estimating different error variances for different latent classes. We first define the mixture of longitudinal factor analyzers and its parameters. Then, we propose an EM algorithm to estimate these parameters. We propose a Bayesian information criterion to identify both the number of components in the mixture and the number of latent factors. We then discuss the comparability of the latent factors obtained between subjects in different latent groups. Finally, we apply the model to simulated and real data of patients with chronic postoperative pain.

Stochastic Expectation Maximization Algorithm for Linear Mixed-Effects Model with Interactions in the Presence of Incomplete Data.

The purpose of this paper is to propose a new algorithm based on stochastic expectation maximization (SEM) to deal with the problem of unobserved values when multiple interactions in a linear mixed-effects model (LMEM) are present. We test the effectiveness of the proposed algorithm with the stochastic approximation expectation maximization (SAEM) and Monte Carlo Markov chain (MCMC) algorithms. This comparison is implemented to highlight the importance of including the maximum effects that can affect the model. The applications are made on both simulated psychological and real data. The findings demonstrate that our proposed SEM algorithm is highly preferable to the other competitor algorithms.

Semi-Parametric Estimation Using Bernstein Polynomial and a Finite Gaussian Mixture Model.

The central focus of this paper is upon the alleviation of the boundary problem when the probability density function has a bounded support. Mixtures of beta densities have led to different methods of density estimation for data assumed to have compact support. Among these methods, we mention Bernstein polynomials which leads to an improvement of edge properties for the density function estimator. In this paper, we set forward a shrinkage method using the Bernstein polynomial and a finite Gaussian mixture model to construct a semi-parametric density estimator, which improves the approximation at the edges. Some asymptotic properties of the proposed approach are investigated, such as its probability convergence and its asymptotic normality. In order to evaluate the performance of the proposed estimator, a simulation study and some real data sets were carried out.

A Novel Multi-Dimensional Clinical Response Index Dedicated to Improving Global Assessment of Pain in Patients with Persistent Spinal Pain Syndrome after Spinal Surgery, Based on a Real-Life Prospective Multicentric Study (PREDIBACK) and Machine Learning Techniques.

The multidimensionality of chronic pain forces us to look beyond isolated assessment such as pain intensity, which does not consider multiple key parameters, particularly in post-operative Persistent Spinal Pain Syndrome (PSPS-T2) patients. Our ambition was to produce a novel Multi-dimensional Clinical Response Index (MCRI), including not only pain intensity but also functional capacity, anxiety-depression, quality of life and quantitative pain mapping, the objective being to achieve instantaneous assessment using machine learning techniques. Two hundred PSPS-T2 patients were enrolled in the real-life observational prospective PREDIBACK study with 12-month follow-up and received various treatments. From a multitude of questionnaires/scores, specific items were combined, as exploratory factor analyses helped to create a single composite MCRI; using pairwise correlations between measurements, it appeared to more accurately represent all pain dimensions than any previous classical score. It represented the best compromise among all existing indexes, showing the highest sensitivity/specificity related to Patient Global Impression of Change (PGIC). Novel composite indexes could help to refine pain assessment by informing the physician's perception of patient condition on the basis of objective and holistic metrics, and also by providing new insights regarding therapy efficacy/patient outcome assessments, before ultimately being adapted to other pathologies.

Finite Mixture Models Based on Pain Intensity, Functional Disability and Psychological Distress Composite Assessment Allow Identification of Two Distinct Classes of Persistent Spinal Pain Syndrome after Surgery Patients Related to Their Quality of Life.

Persistent Spinal Pain Syndrome Type 2 (PSPS-T2), (Failed Back Surgery Syndrome), dramatically impacts on patient quality of life, as evidenced by Health-Related Quality of Life (HRQoL) assessment tools. However, the importance of functioning, pain perception and psychological status in HRQoL can substantially vary between subjects. Our goal was to extract patient profiles based on HRQoL dimensions in a sample of PSPS-T2 patients and to identify factors associated with these profiles. Two classes were clearly identified using a mixture of mixed effect models from a clinical data set of 200 patients enrolled in "PREDIBACK", a multicenter observational prospective study including PSPS-T2 patients with one-year follow-up. We observed that HRQoL was more impacted by functional disability for first class patients (n = 136), and by pain perception for second class patients (n = 62). Males that perceive their work as physical were more impacted by disability than pain intensity. Lower education level, lack of adaptive coping strategies and higher pain intensity were significantly associated with HRQoL being more impacted by pain perception. The identification of such classes allows for a better understanding of HRQoL dimensions and opens the gate towards optimized health-related quality of life evaluation and personalized pain management.

Machine Learning Algorithms Provide Greater Prediction of Response to SCS Than Lead Screening Trial: A Predictive AI-Based Multicenter Study.

Persistent pain after spinal surgery can be successfully addressed by spinal cord stimulation (SCS). International guidelines strongly recommend that a lead trial be performed before any permanent implantation. Recent clinical data highlight some major limitations of this approach. First, it appears that patient outco mes, with or without lead trial, are similar. In contrast, during trialing, infection rate drops drastically within time and can compromise the therapy. Using composite pain assessment experience and previous research, we hypothesized that machine learning models could be robust screening tools and reliable predictors of long-term SCS efficacy. We developed several algorithms including logistic regression, regularized logistic regression (RLR), naive Bayes classifier, artificial neural networks, random forest and gradient-boosted trees to test this hypothesis and to perform internal and external validations, the objective being to confront model predictions with lead trial results using a 1-year composite outcome from 103 patients. While almost all models have demonstrated superiority on lead trialing, the RLR model appears to represent the best compromise between complexity and interpretability in the prediction of SCS efficacy. These results underscore the need to use AI-based predictive medicine, as a synergistic mathematical approach, aimed at helping implanters to optimize their clinical choices on daily practice.

Two new nonparametric kernel distribution estimators based on a transformation of the data.

In this paper, we propose two kernel distribution estimators based on a data transformation. We study the properties of these estimators and we compare them with two conventional estimators. It appears that with an appropriate choice of the parameters of the two proposed estimators, the convergence rate of two estimators will be faster than that of the two conventional estimators and the Mean Integrated Square Error will be smaller than the two conventional estimators. We corroborate these theoretical results through simulations as well as a real data set.

Mechanisms of FH Protection Against Neovascular AMD.

A common allele (402H) of the complement factor H (FH) gene is the major risk factor for age-related macular degeneration (AMD), the leading cause of blindness in the elderly population. Development and progression of AMD involves vascular and inflammatory components partly by deregulation of the alternative pathway of the complement system (AP). The loss of central vision results from atrophy and/or from abnormal neovascularization arising from the choroid. The functional link between FH, the main inhibitor of AP, and choroidal neovascularization (CNV) in AMD remains unclear. In a murine model of CNV used as a model for neovascular AMD (nAMD), intraocular human recombinant FH (recFH) reduced CNV as efficiently as currently used anti-VEGF (vascular endothelial growth factor) antibody, decreasing deposition of C3 cleavage fragments, membrane attack complex (MAC), and microglia/macrophage recruitment markers in the CNV lesion site. In sharp contrast, recFH carrying the H402 risk variant had no effect on CNV indicating a causal link to disease etiology. Only the recFH NTal region (recFH1-7), containing the CCPs1-4 C3-convertase inhibition domains and the CCP7 binding domain, exerted all differential biological effects. The CTal region (recFH7-20) containing the CCP7 and CCPs19-20 binding domains was antiangiogenic but did not reduce the microglia/macrophage recruitment. The antiangiogenic effect of both recFH1-20 and recFH-CCP7-20 resulted from thrombospondin-1 (TSP-1) upregulation independently of the C3 cleavage fragments generation. This study provides insight on the mechanistic role of FH in nAMD and invites to reconsider its therapeutic potential.

Dynamic Changes in Renal Function Are Associated With Major Cardiovascular Events in Patients With Type 2 Diabetes.

OBJECTIVE: The pattern of renal function decline prior to cardiovascular (CV) events in type 2 diabetes is not well known. Our aim was to describe the association between renal function trajectories and the occurrence of a CV event. RESEARCH DESIGN AND METHODS: We considered patients with type 2 diabetes from the SURDIAGENE (Survie, Diabete de type 2 et Genetique) study (discovery cohort) and the DIABHYCAR (Non-Insulin-Dependent Diabetes, Hypertension, Microalbuminuria or Proteinuria, Cardiovascular Events, and Ramipril) study (replication cohort). Global patterns of estimated glomerular filtration rate (eGFR) (Chronic Kidney Disease Epidemiology Collaboration [CKD-EPI]) and serum creatinine (SCr) prior to a major CV event (MACE) or last update were determined using a linear mixed-effects model and annual individual slopes computed by simple linear regression. RESULTS: In the 1,040 participants of the discovery cohort, establishment of global patterns including 22,227 SCr over 6.3 years of follow-up showed an annual eGFR decline and an annual SCr increase that were significantly greater in patients with MACE compared with patients without (-3.0 and -1.7 mL/min/1.73 m(2)/year and +10.7 and +4.0 µmol/L/year, respectively; P < 0.0001 for both). Median annual individual slopes were also significantly steeper in patients with MACE, and adjusted risk of MACE was 4.11 times higher (3.09-5.45) in patients with rapid decline in eGFR (change less than -5 mL/min/1.73 m(2)/year). Consideration of renal function trajectories provided significant additive information helping to explain the occurrence of MACE for both SCr and eGFR (PIDI < 0.0001 and P = 0.0005, respectively). These results were confirmed in the replication cohort. CONCLUSIONS: Renal function decline was associated with a higher risk of MACE. The pattern of renal function decline, beyond baseline kidney function, is an independent factor of CV risk.

Genome wide linkage study, using a 250K SNP map, of Plasmodium falciparum infection and mild malaria attack in a Senegalese population.

Multiple factors are involved in the variability of host's response to P. falciparum infection, like the intensity and seasonality of malaria transmission, the virulence of parasite and host characteristics like age or genetic make-up. Although admitted nowadays, the involvement of host genetic factors remains unclear. Discordant results exist, even concerning the best-known malaria resistance genes that determine the structure or function of red blood cells. Here we report on a genome-wide linkage and association study for P. falciparum infection intensity and mild malaria attack among a Senegalese population of children and young adults from 2 to 18 years old. A high density single nucleotide polymorphisms (SNP) genome scan (Affimetrix GeneChip Human Mapping 250K-nsp) was performed for 626 individuals: i.e. 249 parents and 377 children out of the 504 ones included in the follow-up. The population belongs to a unique ethnic group and was closely followed-up during 3 years. Genome-wide linkage analyses were performed on four clinical and parasitological phenotypes and association analyses using the family based association tests (FBAT) method were carried out in regions previously linked to malaria phenotypes in literature and in the regions for which we identified a linkage peak. Analyses revealed three strongly suggestive evidences for linkage: between mild malaria attack and both the 6p25.1 and the 12q22 regions (empirical p-value=5x10(-5) and 9x10(-5) respectively), and between the 20p11q11 region and the prevalence of parasite density in asymptomatic children (empirical p-value=1.5x10(-4)). Family based association analysis pointed out one significant association between the intensity of plasmodial infection and a polymorphism located in ARHGAP26 gene in the 5q31-q33 region (p-value=3.7x10(-5)). This study identified three candidate regions, two of them containing genes that could point out new pathways implicated in the response to malaria infection. Furthermore, we detected one gene associated with malaria infection in the 5q31-q33 region.