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BACKGROUND: The efficacy of vedolizumab, an α4β7 integrin antibody, in Crohn's disease is unknown. METHODS: In an integrated study with separate induction and maintenance trials, we assessed intravenous vedolizumab therapy (300 mg) in adults with active Crohn's disease. In the induction trial, 368 patients were randomly assigned to receive vedolizumab or placebo at weeks 0 and 2 (cohort 1), and 747 patients received open-label vedolizumab at weeks 0 and 2 (cohort 2); disease status was assessed at week 6. In the maintenance trial, 461 patients who had had a response to vedolizumab were randomly assigned to receive placebo or vedolizumab every 8 or 4 weeks until week 52. RESULTS: At week 6, a total of 14.5% of the patients in cohort 1 who received vedolizumab and 6.8% who received placebo were in clinical remission (i.e., had a score on the Crohn's Disease Activity Index [CDAI] of ≤150, with scores ranging from 0 to approximately 600 and higher scores indicating greater disease activity) (P=0.02); a total of 31.4% and 25.7% of the patients, respectively, had a CDAI-100 response (≥100-point decrease in the CDAI score) (P=0.23). Among patients in cohorts 1 and 2 who had a response to induction therapy, 39.0% and 36.4% of those assigned to vedolizumab every 8 weeks and every 4 weeks, respectively, were in clinical remission at week 52, as compared with 21.6% assigned to placebo (P<0.001 and P=0.004 for the two vedolizumab groups, respectively, vs. placebo). Antibodies against vedolizumab developed in 4.0% of the patients. Nasopharyngitis occurred more frequently, and headache and abdominal pain less frequently, in patients receiving vedolizumab than in patients receiving placebo. Vedolizumab, as compared with placebo, was associated with a higher rate of serious adverse events (24.4% vs. 15.3%), infections (44.1% vs. 40.2%), and serious infections (5.5% vs. 3.0%). CONCLUSIONS: Vedolizumab-treated patients with active Crohn's disease were more likely than patients rec

Kernel type density estimators are studied for random fields. It is proved that the estimators are asymptotically normal if the set of locations of observations become more and more dense in an increasing sequence of domains. It turns out that in our setting the covariance structure of the limiting normal distribution can be a combination of those of the continuous parameter and the discrete parameter cases. The proof is based on a new central limit theorem for α-mixing random fields. Simulation results support our theorems. © Springer 2006.

Almost sure versions of limit theorems by Kruglov for the Pearson χ2-statistic are obtained.

A central limit theorem is proved for α-mixing random fields. The sets of locations where the random field is observed become more and more dense in an increasing sequence of domains. The central limit theorem concerns these observations. The limit theorem is applied to obtain asymptotic normality of kernel type density estimators. It turns out that in our setting the covariance structure of the limiting normal distribution can be a combination of those of the continuous parameter and the discrete parameter cases.

A central limit theorem is proved for α-mixing random fields. The sets of locations where the random field is observed become more and more dense in an increasing sequence of domains. The central limit theorem concerns these observations. The limit theorem is applied to obtain asymptotic normality of kernel type density estimators. It turns out that in our setting the covariance structure of the limiting normal distribution can be a combination of those of the continuous parameter and the discrete parameter cases.

Kernel type density estimators are studied for random fields. It is proved that the estimators are asymptotically normal if the set of locations of observations become more and more dense in an increasing sequence of domains. It turns out that in our setting the covariance structure of the limiting normal distribution can be a combination of those of the continuous parameter and the discrete parameter cases. The proof is based on a new central limit theorem for α-mixing random fields. Simulation results support our theorems. © Springer 2006.

Almost sure versions of limit theorems by Kruglov for the Pearson χ2-statistic are obtained.

An exponential inequality for the tail of the conditional expectation of sums of centered independent random variables is obtained. This inequality is applied to prove analogues of the Law of the Iterated Logarithm and the Strong Law of Large Numbers for conditional expectations. As corollaries we obtain certain strong theorems for the generalized allocation scheme and for the nonuniformly distributed allocation scheme. © 2010 Akadémiai Kiadó, Budapest, Hungary.

An inequality for conditional moments of centered random variables is proved. This inequality is applied to the generalized allocation scheme. For the generalized allocation scheme an exponential inequality is obtained. The exponential inequality is applied to prove (partial) analogues of the Law of the Iterated Logarithm and an analogue of Prokhorov's Law of Large Numbers.

The generalized allocation scheme is studied. Its extension for coloured balls is defined. Some analogues of the Law of the Iterated Logarithm and the Strong Law of Large Numbers are obtained for the number of boxes containing fixed numbers of balls.

An almost sure functional limit theorem is obtained for variables being in the domain of geometric partial attraction of a semistable law. © Springer Science+Business Media, LLC 2007.

An integral analogue of the general almost sure limit theorem is presented. In the theorem, instead of a sequence of random elements, a continuous time random process is involved, moreover, instead of the logarithmical average, the integral of delta-measures is considered. Then the general theorem is applied to obtain almost sure versions of limit theorems for semistable and max-semistable processes, moreover for processes being in the domain of attraction of a stable law or being in the domain of geometric partial attraction of a semistable or a max-semistable law. © Akadémiai Kiadó, Budapest.

Almost sure versions of some functional limit theorems for random step lines and random broken lines defined by sums of independent identically distributed random variables with replacements are obtained.

Almost sure limit theorems are presented for random allocations. A general almost sure limit theorem is proved for arrays of random variables. It is applied to obtain almost sure versions of the central limit theorem for the number of empty boxes when the parameters are in the central domain. Almost sure versions of the Poisson limit theorem in the left domain are also proved. © 2005 Akadémiai Kiadó, Budapest.

The paper deals with random step-line processes defined by sums of independent identically distributed random variables multiplied by independent indicators. These processes describe some models in which random variables are replaced with other ones. We prove the convergence in distribution of such processes to the weighted Ornstein-Uhlenbeck process. ©1998 Plenum Publishing Corporation.

© 2017 Taylor & Francis Group, LLC The conditional maxima of independent Poisson random variables are studied. A triangular array of row-wise independent Poisson random variables is considered. If condition is given for the row-wise sums, then the limiting distribution of the row-wise maxima is concentrated onto two points. The result is in accordance with the classical result of Anderson. The case of general power series distributions is also covered. The model studied in Theorems 2.1 and 2.2 is an analogue of the generalized allocation scheme. It can be considered as a non homogeneous generalized scheme of allocations of at most n balls into N boxes. Then the maximal value of the contents of the boxes is studied.

© 2017 Taylor & Francis Group, LLC The conditional maxima of independent Poisson random variables are studied. A triangular array of row-wise independent Poisson random variables is considered. If condition is given for the row-wise sums, then the limiting distribution of the row-wise maxima is concentrated onto two points. The result is in accordance with the classical result of Anderson. The case of general power series distributions is also covered. The model studied in Theorems 2.1 and 2.2 is an analogue of the generalized allocation scheme. It can be considered as a non homogeneous generalized scheme of allocations of at most n balls into N boxes. Then the maximal value of the contents of the boxes is studied.

An integral analogue of the general almost sure limit theorem is presented. In the theorem, instead of a sequence of random elements, a continuous time random process is involved, moreover, instead of the logarithmical average, the integral of delta-measures is considered. Then the general theorem is applied to obtain almost sure versions of limit theorems for semistable and max-semistable processes, moreover for processes being in the domain of attraction of a stable law or being in the domain of geometric partial attraction of a semistable or a max-semistable law. © Akadémiai Kiadó, Budapest.

The paper deals with random step-line processes defined by sums of independent identically distributed random variables multiplied by independent indicators. These processes describe some models in which random variables are replaced with other ones. We prove the convergence in distribution of such processes to the weighted Ornstein-Uhlenbeck process. ©1998 Plenum Publishing Corporation.

An almost sure functional limit theorem is obtained for variables being in the domain of geometric partial attraction of a semistable law. © Springer Science+Business Media, LLC 2007.

Random forests are studied. A moment inequality and a strong law of large numbers are obtained for the number of trees having a fixed number of nonroot vertices. © Akadémiai Kiadó, Budapest, Hungary, 2009.