Penalized wavelet estimation and robust denoising for irregular spaced data

Nonparametric univariate regression via wavelets is usually implemented under the assumptions of dyadic sample size, equally spaced fixed sample points, and i.i.d. normal errors. In this work, we propose, study and compare some wavelet based nonparametric estimation methods designed to recover a one-dimensional regression function for data that not necessary possess the above requirements. These methods use appropriate regularizations by penalizing the decomposition of the unknown regression function on a wavelet basis of functions evaluated on the sampling design. Exploiting the sparsity of wavelet decompositions for signals belonging to homogeneous Besov spaces, we use some efficient proximal gradient descent algorithms, available in recent literature, for computing the estimates with fast computation times. Our wavelet based procedures, in both the standard and the robust regression case have favorable theoretical properties, thanks in large part to the separability nature of the (non convex) regularization they are based on. We establish asymptotic global optimal rates of convergence under weak conditions. It is known that such rates are, in general, unattainable by smoothing splines or other linear nonparametric smoothers. Lastly, we present several experiments to examine the empirical performance of our procedures and their comparisons with other proposals available in the literature. An interesting regression analysis of some real data applications using these procedures unambiguously demonstrate their effectiveness.

Robust Identification of Temporal Biomarkers in Longitudinal Omics Studies

Longitudinal studies increasingly collect rich 'omics' data sampled frequently over time and across large cohorts to capture dynamic health fluctuations and disease transitions. However, the generation of longitudinal omics data has preceded the development of analysis tools that can efficiently extract insights from such data. In particular, there is a need for statistical frameworks that can identify not only which omics features are differentially regulated between groups but also over what time intervals. Additionally, longitudinal omics data may have inconsistencies, including nonuniform sampling intervals, missing data points, subject dropout, and differing numbers of samples per subject. In this work, we developed a statistical method that provides robust identification of time intervals of temporal omics biomarkers. The proposed method is based on a semi-parametric approach, in which we use smoothing splines to model longitudinal data and infer significant time intervals of omics features based on an empirical distribution constructed through a permutation procedure. We benchmarked the proposed method on five simulated datasets with diverse temporal patterns, and the method showed specificity greater than 0.99 and sensitivity greater than 0.72. Applying the proposed method to the Integrative Personal Omics Profiling (iPOP) cohort revealed temporal patterns of amino acids, lipids, and hormone metabolites that are differentially regulated in male versus female subjects following a respiratory infection. In addition, we applied the longitudinal multi-omics dataset of pregnant women with and without preeclampsia, and the method identified potential lipid markers that are temporally significantly different between the two groups. We provide an open-source R package, OmicsLonDA (Omics Longitudinal Differential Analysis): https://bioconductor.org/packages/OmicsLonDA to enable widespread use.

Fatigue in Incident Peritoneal Dialysis and Mortality: A Real-World Side-by-Side Study in Brazil and the United States

Background: We tested if fatigue in incident Peritoneal Dialysis associated with an increased risk for mortality, independently from main confounders. Methods: We conducted a side-by-side study from two of incident PD patients in Brazil and the United States. We used the same code to independently analyze data in both countries during 2004 to 2011. We included data from adults who completed KDQOL-SF vitality subscale within 90 days after starting PD. Vitality score was categorized in four groups: >50 (high vitality), >=40 to <=50 (moderate vitality), >35 to <40 (moderate fatigue), <=35 (high fatigue; reference group). In each country's cohort, we built four distinct models to estimate the associations between vitality (exposure) and all-cause mortality (outcome): (i) Cox regression model; (ii) competitive risk model accounting for technique failure events; (iii) multilevel survival model of clinic-level clusters; (iv) multivariate regression model with smoothing splines treating vitality as a continuous measure. Analyses were adjusted for age, comorbidities, PD modality, hemoglobin, and albumin. A mixed-effects meta-analysis was used to pool hazard ratios (HRs) from both cohorts to model mortality risk for each 10-unit increase in vitality. Results: We used data from 4,285 PD patients (Brazil n=1,388 and United States n=2,897). Model estimates showed lower vitality levels within 90 days of starting PD were associated with a higher risk of mortality, which was consistent in Brazil and the United States cohorts. In the multivariate survival model, each 10-unit increase in vitality score was associated with lower risk of all-cause mortality in both cohorts (Brazil HR=0.79 [95%CI 0.70 to 0.90] and United States HR=0.90 [95%CI 0.88 to 0.93], pooled HR=0.86 [95%CI 0.75 to 0.98]). Results for all models provided consistent effect estimates. Conclusions: Among patients in Brazil and the United States, lower vitality score in the initial months of PD was independently associated with all-cause mortality.

Pemodelan Kemiskinan di Sumatera Utara Menggunakan Regresi Nonparametrik Kernel dan Splines

Penanggulangan kemiskinan merupakan tujuan utama dari Sustainable Development Goals (SDGs). Masyarakat miskin disebabkan oleh rendahnya modal manusia. Salah satu indikator yang dapat mengukur modal manusia adalah Indeks Pembangunan Manusia (IPM). Sumatera Utara masih menemati posisi ke-lima dengan tingkat kemiskinan tertinggi di Pulau Sumatera, padahal memiliki jumlah penduduk terbanyak di Pulau Sumatera. Penelitian ini bertujuan untuk melakukan pemodelan kemiskinan dengan faktor yang mempengaruhinya yaitu IPM di Provinsi Sumatera Utara dengan regresi nonparametrik dan regresi kuantil karena sifatnya yang fleksibel dan dapat memodelkan data dengan level yang berbeda. Regresi nonparametrik yang digunakan pada penelitian ini dalah regresi kernel dan smoothing splines. Hasil pemodelan regresi nonparametrik kernel diperoleh bandwith optimal dari fungsi kernel gaussian dengan NWE adalah 2,13512 dengan GCV 11,78793, pemodelan dengan smoothing splines diperoleh nilai parameter pemulus optimal yaitu 0,00544 dengan GCV 47,29301, dan pemodelan dengan regresi kuantil smoothing splines diperoleh nilai parameter pemulus optimal yaitu 0,11 dengan GCV 3,81497. Hasil perbandingan model diperoleh bahwa metode regresi kuantil smoothing splines merupakan metode terbaik karena memiliki kurva regresi yang lebih mengikuti sebaran hubungan data dan nilai GCV dan RMSE yang lebih rendah.

Smoothing Splines of Apex Predator Movement: Functional modeling strategies for exploring animal behavior and social interactions

The collection of animal position data via GPS tracking devices has increased in quality and usage in recent years. Animal position and movement, although measured discretely, follows the same principles of kinematic motion, and as such, the process is inherently continuous and differentiable. I demonstrate the functionality and visual elegance of smoothing spline models. I discuss the challenges and benefits of implementing such an approach, and I provide an analysis of movement and social interaction of seven jaguars inhabiting the Taiamã Ecological Station, Pantanal, Brazil. In the analysis, I derive measures for pairwise distance, cooccurence and spatiotemporal associaton between jaguars, borrowing ideas from density estimation and information theory. These measures are feasible as a result of spline model estimation, and they provide a critical tool for a deeper investigation of cooccurence duration, frequency, and localized spatio-temporal relationships between animals.

Low myocardial energetic efficiency is associated with increased mortality in aortic stenosis

ObjectivesIn hypertension, low myocardial energetic efficiency (MEEi) has been documented as an integrated marker of metabolic and left ventricular (LV) myocardial dysfunction. We tested the predictive performance of MEEi in initially asymptomatic aortic stenosis (AS) patients free from diabetes and known cardiovascular disease.MethodsData from 1703 patients with mostly moderate AS enrolled in the Simvastatin and Ezetimibe in Aortic Stenosis study followed for 4.3 years was used. MEE was calculated from Doppler stroke volume/([heart rate/60]) and indexed to LV mass (MEEi). The threshold value for MEEi associated with increased mortality was identified in generalised additive model with smoothing splines. Covariables of MEEi were identified in logistic regression analysis. Outcome was assessed in Cox regression analysis and reported as HR and 95% CI.ResultsMEEi <0.34 mL/s per gram was associated with increased cardiovascular mortality (n=80) (HR 2.53 (95% CI 1.50 to 4.28)) and all-cause mortality (n=155) (HR 1.74 (95% CI 1.20 to 2.52)) (both p<0.01). The association was independent of confounders of low MEEI (<0.34 mL/s per gram) identified in multivariable logistic regression analysis, including more severe AS, higher body mass index, lower LV midwall shortening and ejection fraction and presence of hypertension. Comparison of the Cox models with and without MEEi among the covariables demonstrated that MEEi significantly improved the prognostic yield (both p<0.01).ConclusionsIn patients with initially asymptomatic AS, low MEEi was associated with clustering of cardiometabolic risk factors, lower LV myocardial function and subsequent increased mortality during 4.3 years follow-up, independent of known prognosticators.Trial registration numberNCT00092677.