Curve crossing for random walks reflected at their maximum

Let $R_n=\max_{0\leq j\leq n}S_j-S_n$ be a random walk $S_n$ reflected in its maximum. Except in the trivial case when $P(X\ge0)=1$, $R_n$ will pass over a horizontal boundary of any height in a finite time, with probability 1. We extend this by giving necessary and sufficient conditions for finiteness of passage times of $R_n$ above certain curved (power law) boundaries, as well. The intuition that a degree of heaviness of the negative tail of the distribution of the increments of $S_n$ is necessary for passage of $R_n$ above a high level is correct in most, but not all, cases, as we show. Conditions are also given for the finiteness of the expected passage time of $R_n$ above linear and square root boundaries.Comment: Published at http://dx.doi.org/10.1214/009117906000000953 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Local asymptotics for the time of first return to the origin of transient random walk

We consider a transient random walk on $Z^d$ which is asymptotically stable, without centering, in a sense which allows different norming for each component. The paper is devoted to the asymptotics of the probability of the first return to the origin of such a random walk at time $n$

Passage time and fluctuation calculations for subexponential L\'evy processes

We consider the passage time problem for L\'evy processes, emphasising heavy tailed cases. Results are obtained under quite mild assumptions, namely, drift to $-\infty$ a.s. of the process, possibly at a linear rate (the finite mean case), but possibly much faster (the infinite mean case), together with subexponential growth on the positive side. Local and functional versions of limit distributions are derived for the passage time itself, as well as for the position of the process just prior to passage, and the overshoot of a high level. A significant connection is made with extreme value theory via regular variation or maximum domain of attraction conditions imposed on the positive tail of the canonical measure, which are shown to be necessary for the kind of convergence behaviour we are interested in.Comment: Published at http://dx.doi.org/10.3150/15-BEJ700 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Local behaviour of the remainder in Renewal theory

Several terms in an asynptotic estimate for the renewal mass function ina discrete random walk which has positive mean and regularly varying right-hand tail are given. Similar results are given for the renewal density function in the absolutely continuous case.Comment: 16 page

Impact of EMA regulatory label changes on systemic diclofenac initiation, discontinuation, and switching to other pain medicines in Scotland, England, Denmark, and The Netherlands

Purpose: In June 2013 a European Medicines Agency referral procedure concluded that diclofenac was associated with an elevated risk of acute cardiovascular events and contraindications, warnings, and changes to the product information were implemented across the European Union. This study measured the impact of the regulatory action on the prescribing of systemic diclofenac in Denmark, The Netherlands, England, and Scotland. Methods: Quarterly time series analyses measuring diclofenac prescription initiation, discontinuation and switching to other systemic nonsteroidal anti-inflammatory (NSAIDs), topical NSAIDs, paracetamol, opioids, and other chronic pain medication in those who discontinued diclofenac. Absolute effects were estimated using interrupted time series regression. Results: Overall, diclofenac prescription initiations fell during the observation periods of all countries. Compared with Denmark where there appeared to be amore limited effect, the regulatory action was associated with significant immediate reductions in diclofenac initiation in The Netherlands (−0.42%, 95% CI, −0.66% to −0.18%), England (−0.09%, 95% CI, −0.11% to −0.08%), and Scotland (−0.67%, 95% CI, −0.79% to −0.55%); and falling trends in diclofenac initiation in the Netherlands (−0.03%, 95% CI, −0.06% to −0.01% per quarter) and Scotland (−0.04%, 95% CI, −0.05% to −0.02% per quarter). There was no significant impact on diclofenac discontinuation in any country. The regulatory action was associated with modest differences in switching to other pain medicines following diclofenac discontinuation. Conclusions: The regulatory action was associated with significant reductions in overall diclofenac initiation which varied by country and type of exposure. There was no impact on discontinuation and variable impact on switching

Impact of EMA regulatory label changes on systemic diclofenac initiation, discontinuation, and switching to other pain medicines in Scotland, England, Denmark, and The Netherlands

PURPOSE: In June 2013 a European Medicines Agency referral procedure concluded that diclofenac was associated with an elevated risk of acute cardiovascular events and contraindications, warnings, and changes to the product information were implemented across the European Union. This study measured the impact of the regulatory action on the prescribing of systemic diclofenac in Denmark, The Netherlands, England, and Scotland. METHODS: Quarterly time series analyses measuring diclofenac prescription initiation, discontinuation and switching to other systemic nonsteroidal anti‐inflammatory (NSAIDs), topical NSAIDs, paracetamol, opioids, and other chronic pain medication in those who discontinued diclofenac. Absolute effects were estimated using interrupted time series regression. RESULTS: Overall, diclofenac prescription initiations fell during the observation periods of all countries. Compared with Denmark where there appeared to be a more limited effect, the regulatory action was associated with significant immediate reductions in diclofenac initiation in The Netherlands (−0.42%, 95% CI, −0.66% to −0.18%), England (−0.09%, 95% CI, −0.11% to −0.08%), and Scotland (−0.67%, 95% CI, −0.79% to −0.55%); and falling trends in diclofenac initiation in the Netherlands (−0.03%, 95% CI, −0.06% to −0.01% per quarter) and Scotland (−0.04%, 95% CI, −0.05% to −0.02% per quarter). There was no significant impact on diclofenac discontinuation in any country. The regulatory action was associated with modest differences in switching to other pain medicines following diclofenac discontinuation. CONCLUSIONS: The regulatory action was associated with significant reductions in overall diclofenac initiation which varied by country and type of exposure. There was no impact on discontinuation and variable impact on switching

Impact of EMA regulatory label changes on hydroxyzine initiation, discontinuation and switching to other medicines in Denmark, Scotland, England and the Netherlands:an interrupted time series regression analysis

Background: Hydroxyzine is indicated for the management of anxiety, skin and sleep disorders. In 2015, the European Medicines Agency (EMA) concluded that hydroxyzine was pro-arrhythmogenic and changes to the product information were implemented in Europe. This study aimed to evaluate their impact in Denmark, Scotland, England and the Netherlands. Method: Quarterly time series analyses measuring hydroxyzine initiation, discontinuation, and switching to other antihistamines, benzodiazepines and antidepressants in Denmark, England, Scotland and the Netherlands from 2009 to 2018. Data were analysed using interrupted time series regression. Results: Hydroxyzine initiation in quarter one 2010 in Denmark, Scotland, England and the Netherlands per 100 000 was: 23.5, 91.5, 35.9 and 34.4 respectively. Regulatory action was associated with a significant: immediate fall in hydroxyzine initiation per 100 000 in England (−12.05, 95%CI −18.47 to −5.63) and Scotland (−19.01, 95%CI −26.99 to −11.02); change to a negative trend in hydroxyzine initiation per 100 000/quarter in England (−1.72, 95%CI −2.69 to −0.75) and Scotland (−2.38, 95%CI −3.32 to −1.44). Regulatory action was associated with a significant: immediate rise in hydroxyzine discontinuation per 100 000 in England (3850, 95%CI 440-7240). No consistent changes were observed in the Netherlands or Denmark. Regulatory action was associated with no switching to other antihistamines, benzodiazepines or antidepressants following hydroxyzine discontinuation in any country. Conclusion: The 2015 EMA regulatory action was associated with heterogeneous impact with reductions in hydroxyzine initiation varying by country. There was limited impact on discontinuation with no strong evidence suggesting unintended consequences of major switching to other antihistamines, benzodiazepines or antidepressants