Revisiting the disabilities of the arm, shoulder and hand (DASH) and QuickDASH in rheumatoid arthritis

Background Limitations in upper limb functioning are common in Musculoskeletal disorders and the Disabilities of the Arm, Shoulder and Hand scale (DASH) has gained widespread use in this context. However, various concerns have been raised about its construct validity and so this study seeks to examine this and other psychometric aspects of both the DASH and QuickDASH from a modern test theory perspective. Methods Participants in the study were eligible if they had a confirmed diagnosis of Rheumatoid Arthritis (RA). They were mailed a questionnaire booklet which included the DASH. Construct validity was examined by fit to the Rasch measurement model. The degree of precision of both the DASH and QuickDASH were considered through their Standard Error of Measurement (SEM). Results Three hundred and thirty-seven subjects with confirmed RA took part, with a mean age of 62.0 years (SD12.1); 73.6% (n = 252) were female. The median standardized score on the DASH was 33 (IQR 17.5–55.0). Significant misfit of the DASH and QuickDASH was observed but, after accommodating local dependency among items in a two-testlet solution, satisfactory fit was obtained, supporting the unidimensionality of the total sets and the sufficiency of the raw (ordinal or standardized) scores. Conclusion Having accommodated local response dependency in the DASH and QuickDASH item sets, their total scores are shown to be valid, given they satisfy the Rasch model assumptions. The Rasch transformation should be used whenever all items are used to calculate a change score, or to apply parametric statistics within an RA population. Significance and innovations Most previous modern psychometric analyses of both the DASH and QuickDASH have failed to fully address the effect of a breach of the local independence assumption upon construct validity. Accommodating this problem by creating ‘super items’ or testlets, removes this effect and shows that both versions of the scale are valid and unidimensional, as applied with a bi-factor equivalent solution to an RA population. The Standard Error of Measurement of a scale can be biased by failing to take into account the local dependency in the data which inflates reliability and thus making the SEM appear better (i.e. smaller) than the true value without bias. </ul

Tur\'an Graphs, Stability Number, and Fibonacci Index

The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and the order of general graphs and connected graphs. Tur\'an graphs frequently appear in extremal graph theory. We show that Tur\'an graphs and a connected variant of them are also extremal for these particular problems.Comment: 11 pages, 3 figure

Trees with Given Stability Number and Minimum Number of Stable Sets

We study the structure of trees minimizing their number of stable sets for given order $n$ and stability number $\alpha$. Our main result is that the edges of a non-trivial extremal tree can be partitioned into $n-\alpha$ stars, each of size $\lceil \frac{n-1}{n-\alpha} \rceil$ or $\lfloor \frac{n-1}{n-\alpha}\rfloor$, so that every vertex is included in at most two distinct stars, and the centers of these stars form a stable set of the tree.Comment: v2: Referees' comments incorporate

Sclerosing Epithelioid Fibrosarcoma of the Bone: A Case Report of High Resistance to Chemotherapy and a Survey of the Literature

Sclerosing epithelioid fibrosarcoma (SEF) is a rare soft tissue sarcoma mostly occurring in extraosseous sites. SEF represents a clinically challenging entity especially because no standardized treatment regimens are available. Intraosseous localization is an additional challenge with respect to the therapeutical approach. We report on a 16-year-old patient with SEF of the right proximal tibia. The patient underwent standardized neoadjuvant chemotherapy analogous to the EURAMOS-1 protocol for the treatment of osteosarcoma followed by tumor resection and endoprosthetic reconstruction. Histopathological analysis of the resected tumor showed >90% vital tumor cells suggesting no response to chemotherapy. Therefore, therapy was reassigned to the CWS 2002 High-Risk protocol for the treatment of soft tissue sarcoma. To date (22 months after diagnosis), there is no evidence of relapse or metastasis. Our data suggest that SEF may be resistant to a chemotherapy regimen containing Cisplatin, Doxorubicin, and Methotrexate, which should be considered in planning treatment for patients with SEF

Statistical properties of the Burgers equation with Brownian initial velocity

We study the one-dimensional Burgers equation in the inviscid limit for Brownian initial velocity (i.e. the initial velocity is a two-sided Brownian motion that starts from the origin x=0). We obtain the one-point distribution of the velocity field in closed analytical form. In the limit where we are far from the origin, we also obtain the two-point and higher-order distributions. We show how they factorize and recover the statistical invariance through translations for the distributions of velocity increments and Lagrangian increments. We also derive the velocity structure functions and we recover the bifractality of the inverse Lagrangian map. Then, for the case where the initial density is uniform, we obtain the distribution of the density field and its $n$-point correlations. In the same limit, we derive the $n-$point distributions of the Lagrangian displacement field and the properties of shocks. We note that both the stable-clustering ansatz and the Press-Schechter mass function, that are widely used in the cosmological context, happen to be exact for this one-dimensional version of the adhesion model.Comment: 42 pages, published in J. Stat. Phy

Gorlin syndrome associated with small bowel carcinoma and mesenchymal proliferation of the gastrointestinal tract: case report and review of literature

<p>Abstract</p> <p>Background and Case Presentation</p> <p>A patient with nevoid basal cell carcinoma syndrome (Gorlin syndrome) presented with two unusual clinical features, i.e. adenocarcinoma of the small bowel and extensive mesenchymal proliferation of the lower gastrointestinal tract.</p> <p>Conclusions</p> <p>We discuss the possibility that these two features are pathogenetically linked to the formerly undescribed patient's <it>PTCH </it>germ line mutation.</p

Super congruences and Euler numbers

Let $p>3$ be a prime. We prove that $$\sum_{k=0}^{p-1}\binom{2k}{k}/2^k=(-1)^{(p-1)/2}-p^2E_{p-3} (mod p^3),$$ $$\sum_{k=1}^{(p-1)/2}\binom{2k}{k}/k=(-1)^{(p+1)/2}8/3*pE_{p-3} (mod p^2),$$ $$\sum_{k=0}^{(p-1)/2}\binom{2k}{k}^2/16^k=(-1)^{(p-1)/2}+p^2E_{p-3} (mod p^3)$$, where E_0,E_1,E_2,... are Euler numbers. Our new approach is of combinatorial nature. We also formulate many conjectures concerning super congruences and relate most of them to Euler numbers or Bernoulli numbers. Motivated by our investigation of super congruences, we also raise a conjecture on 7 new series for $\pi^2$, $\pi^{-2}$ and the constant $K:=\sum_{k>0}(k/3)/k^2$ (with (-) the Jacobi symbol), two of which are $$\sum_{k=1}^\infty(10k-3)8^k/(k^3\binom{2k}{k}^2\binom{3k}{k})=\pi^2/2$$ and $$\sum_{k>0}(15k-4)(-27)^{k-1}/(k^3\binom{2k}{k}^2\binom{3k}k)=K.$