10 research outputs found

    Vicious walkers, friendly walkers and Young tableaux II: With a wall

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    We derive new results for the number of star and watermelon configurations of vicious walkers in the presence of an impenetrable wall by showing that these follow from standard results in the theory of Young tableaux, and combinatorial descriptions of symmetric functions. For the problem of nn-friendly walkers, we derive exact asymptotics for the number of stars and watermelons both in the absence of a wall and in the presence of a wall.Comment: 35 pages, AmS-LaTeX; Definitions of n-friendly walkers clarified; the statement of Theorem 4 and its proof were correcte

    A clinical decision support tool may help to optimise vedolizumab therapy in Crohn's disease

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    International audienceBackground A clinical decision support tool (CDST) has been validated for predicting treatment effectiveness of vedolizumab (VDZ) in Crohn's disease. Aim To assess the utility of this CDST for predicting exposure-efficacy and disease outcomes. Methods Using data from three independent datasets (GEMINI, GETAID and VICTORY), we assessed clinical remission rates and measured VDZ exposure, rapidity of onset of action, response to dose optimisation and progression to surgery by CDST-defined response groups (low, intermediate and high). Results A linear relationship existed between CDST-defined groups, measured VDZ exposure, rapidity of onset of action and efficacy in GEMINI through week 52 (P < 0.001 at all time points across three CDST-defined groups). In GETAID, CDST predicted differences in clinical remission at week 14 (AUC = 0.68) and rapidity of onset of action (P = 0.04) between probability groups. The high-probability patients did not benefit from shortening of infusion intervals, and differences in onset of action between the high-intermediate and low-probability groups within GETAID were no longer significant when including low-probability patients who received a week 10 infusion. CDST predicted a twofold increase in surgery risk over 12 months of VDZ therapy among low- to intermediate-probability vs high-probability patients (adjusted HR 2.06, 95% CI 1.33-3.21). Conclusions We further extended the clinical utility of a previously validated VDZ CDST, which accurately predicts at baseline exposure-efficacy relationships and rapidity of onset of action and could be used to help identify patients who would most benefit from interval shortening and those most likely to require surgery while on active therapy
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