Longitudinal data from factorial experiments frequently arise in various fields of study, ranging from medicine and biology to public policy and sociology. In most practical situations, the distribution of observed data is unknown and there may exist a number of atypical measurements and outliers. Hence, use of parametric and semiparametric procedures that impose restrictive distributional assumptions on observed longitudinal samples becomes questionable. This, in turn, has led to a substantial demand for statistical procedures that enable us to accurately and reliably analyze longitudinal measurements in factorial experiments with minimal conditions on available data, and robust nonparametric methodology offering such a possibility becomes of particular practical importance. In this article, we introduce a new R package nparLD which provides statisticians and researchers from other disciplines an easy and user-friendly access to the most up-todate robust rank-based methods for the analysis of longitudinal data in factorial settings. We illustrate the implemented procedures by case studies from dentistry, biology, and medicine.

D-RaCe instruments were associated with significantly less residual filling material than ProTaper Universal Retreatment instruments and hand files. Hedström files removed significantly less dentine than both rotary NiTi systems. Retreatment with rotary NiTi systems resulted in a high incidence of procedural errors.

One-way layouts, i.e., a single factor with several levels and multiple observations at each level, frequently arise in various fields. Usually not only a global hypothesis is of interest but also multiple comparisons between the different treatment levels. In most practical situations, the distribution of observed data is unknown and there may exist a number of atypical measurements and outliers. Hence, use of parametric and semiparametric procedures that impose restrictive distributional assumptions on observed samples becomes questionable. This, in turn, emphasizes the demand on statistical procedures that enable us to accurately and reliably analyze one-way layouts with minimal conditions on available data. Nonparametric methods offer such a possibility and thus become of particular practical importance. In this article, we introduce a new R package nparcomp which provides an easy and user-friendly access to rank-based methods for the analysis of unbalanced one-way layouts. It provides procedures performing multiple comparisons and computing simultaneous confidence intervals for the estimated effects which can be easily visualized. The special case of two samples, the nonparametric Behrens-Fisher problem, is included. We illustrate the implemented procedures by examples from biology and medicine.

Background Fatigue, exertion intolerance and post-exertional malaise are among the most frequent symptoms of Post-COVID Syndrome (PCS), with a subset of patients fulfilling criteria for Myalgic Encephalomyelitis/Chronic Fatigue Syndrome (ME/CFS). As SARS-CoV-2 infects endothelial cells, causing endotheliitis and damaging the endothelium, we investigated endothelial dysfunction (ED) and endothelial biomarkers in patients with PCS. Methods We studied the endothelial function in 30 PCS patients with persistent fatigue and exertion intolerance as well as in 15 age- and sex matched seronegative healthy controls (HCs). 14 patients fulfilled the diagnostic criteria for ME/CFS. The other patients were considered to have PCS. Peripheral endothelial function was assessed by the reactive hyperaemia index (RHI) using peripheral arterial tonometry (PAT) in patients and HCs. In a larger cohort of patients and HCs, including post-COVID reconvalescents (PCHCs), Endothelin-1 (ET-1), Angiopoietin-2 (Ang-2), Endocan (ESM-1), IL-8, Angiotensin-Converting Enzyme (ACE) and ACE2 were analysed as endothelial biomarkers. Results Five of the 14 post-COVID ME/CFS patients and five of the 16 PCS patients showed ED defined by a diminished RHI (< 1.67), but none of HCs exhibited this finding. A paradoxical positive correlation of RHI with age, blood pressure and BMI was found in PCS but not ME/CFS patients. The ET-1 concentration was significantly elevated in both ME/CFS and PCS patients compared to HCs and PCHCs. The serum Ang-2 concentration was lower in both PCS patients and PCHCs compared to HCs. Conclusion A subset of PCS patients display evidence for ED shown by a diminished RHI and altered endothelial biomarkers. Different associations of the RHI with clinical parameters as well as varying biomarker profiles may suggest distinct pathomechanisms among patient subgroups.