The statistical analysis of functional data is a growing need in many research areas. We propose a new depth notion for functional observations based on the graphic representation of the curves. Given a collection of functions, it allows to establish the centrality of a function and provides a natural center-outward ordering of the sample curves. Robust statistics such as the median function or a trimmed mean function can be defined from this depth definition. Its finite-dimensional version provides a new depth for multivariate data that is computationally very fast and turns out to be convenient to study high-dimensional observations. The natural properties are established for the new depth and the uniform consistency of the sample depth is proved. Simulation results show that the trimmed mean presents a better behavior than the mean for contaminated models. Several real data sets are considered to illustrate this new concept of depth. Finally, we use this new depth to generalize to functions the Wilcoxon rank sum test. It allows to decide whether two groups of curves come from the same population. This functional rank test is applied to girls and boys growth curves concluding that they present different growth patterns.

Metastatic cancer patients experience a severe loss of skeletal muscle mass and function known as cachexia. Cachexia is associated with poor prognosis and accelerated death in cancer patients, yet its underlying mechanisms remain poorly understood. Here, we identify the metal transporter ZIP14 as a critical mediator of cancer-induced cachexia. ZIP14 is upregulated in cachectic muscles from mice and patients with metastatic cancer and can be induced by TNF-α and TGF-β cytokines.Strikingly, in vivo manipulation of Zip14 expression has profound impact on muscle atrophy in experimental models of metastasis.We find that ZIP14-mediated zinc uptake in muscle progenitor cells represses the expression of the key myogenic factors MyoD and Mef2c, and blocks muscle-cell differentiation. Importantly, ZIP14-mediated zinc accumulation in differentiated muscle cells induces myosin heavy chain loss. These results highlight a previously unrecognized role for altered zinc homeostasis in muscle during metastatic-cancer-induced cachexia, and implicate ZIP14 as a therapeutic target for its treatment.

Aims Troponin elevation is common in acute heart failure (AHF) and may be useful for prognostication; however, available data are mixed and many previous studies used older, less sensitive assays. We examined the association between serial measurements of high‐sensitivity cardiac troponin T (hs‐cTnT) and outcomes in RELAX‐AHF. Methods and results Hs‐cTnT was measured at baseline and days 2, 5, and 14. We assessed the relationship between baseline, peak and peak change hs‐cTnT with dyspnoea relief by visual analogue scale, cardiovascular death, or HF/renal hospitalization to 60 days and cardiovascular mortality to 180 days. Models were adjusted for clinical variables and treatment assignment. Whether baseline troponin status affected the treatment effect of serelaxin was assessed using interactions terms. In 1074 patients, the median baseline troponin was 0.033 µg/L, and 90% of patients were above the 99th upper reference limit (URL). Patients with hs‐cTnT >median were more likely to be men with ischaemic heart disease, worse renal function, and higher N‐terminal pro‐brain natriuretic peptide. Higher baseline or peak hs‐cTnT and greater peak change were associated with worse outcomes independent of adjustment for covariates, but relationships were generally strongest for 180‐day cardiovascular mortality (hazard ratio per doubling of baseline hs‐cTnT = 1.36, 95% confidence interval 1.15–1.60). Troponin was most strongly associated with death from heart failure or from other cardiovascular causes. The treatment effect of serelaxin did not differ by baseline troponin levels. Conclusion Hs‐cTnT was elevated above the 99% URL in the majority of AHF patients. Baseline, peak, and peak change hs‐cTnT were associated with worse outcomes, with the strongest relationship with 180‐day cardiovascular mortality.

Purpose To determine the rate of progression and optimal follow up time in patients with advanced stage retinitis pigmentosa (RP) comparing the use of fundus autofluorescence imaging and spectral domain optical coherence tomography. Design Retrospective analysis of progression rate. Methods Longitudinal imaging follow up in 71 patients with retinitis pigmentosa was studied using the main outcome measurements of hyperautofluoresent ring horizontal diameter and vertical diameter along with ellipsoid zone line width from spectral domain optical coherence tomography. Test-retest reliability and the rate of progression were calculated. The interaction between the progression rates was tested for sex, age, mode of inheritance, and baseline measurement size. Symmetry of left and right eye progression rate was also tested. Results Significant progression was observed in >75% of patients during the 2 year mean follow up. The mean annual progression rates of ellipsoid zone line, and hyperautofluorescent ring horizontal diameter and vertical diameter were 0.45° (4.9%), 0.51° (4.1%), and 0.42° (4.0%), respectively. The e llipsoid zone line width, and hyperautofluorescent ring horizontal diameter and vertical diameter had low test-retest variabilities of 8.9%, 9.5% and 9.6%, respectively. This study is the first to demonstrate asymmetrical structural progression rate between right and left eye, which was found in 19% of patients. The rate of progression was significantly slower as the disease approached the fovea, supporting the theory that RP progresses in an exponential fashion. No significant interaction between progression rate and patient age, sex, or mode of inheritance was observed. Conclusions Fundus autofluorescence and optical coherence tomography detect progression in patients with RP reliably and with strong correlation. These parameters may be useful alongside functional assessments as the outcome measurements for future therapeutic trials. Follow-up at 1 year intervals should be adequate to efficiently detect progression.