Linear combinations come alive in crossover designs.

BackgroundCLIPPER2 was an 8-year, open-label extension of the phase 3b, 2-year CLIPPER study of the safety and efficacy of etanercept (ETN) in patients (pts) with juvenile idiopathic arthritis (JIA), categorized...

The use of the repeated Cauchy principal value affords greater facility in the application of inversion formulae involving characteristic functions. Formula (2) below is especially useful in obtaining the inversion formula (1) for the distribution of the ratio of linear combinations of random variables which may be correlated. Formulae (1), (10), (12) generalize the special cases considered by Cramer [2], Curtiss [4], Geary [6], and are free of some restrictions they impose. The results are further generalized in section 6, where inversion formulae are given for the joint distribution of several ratios. In section 7, the joint distribution of several ratios of quadratic forms in random variables $X_1, X_2,\cdots,X_n$ having a multivariate normal distribution is considered.

In this paper, we analyze the average-case performance of the Modified Harmonic algorithm for bin packing. We first analyze the average-case performance for arbitrary distribution of item sizes over (0, 1]. This analysis is based on the following result. Let f1 and f2 be two linear combinations of random variables {ni} n=1 k , where the Nis have a joint multinomial distribution for each \(n = \sum\limits_{i = 1}^k {N_i }\). Let E(f1)≠0, and E(f2)↮0. Then \(\mathop {\lim }\limits_{n \to \infty }\)E(max(f1, f2))/n=\(\mathop {\lim }\limits_{n \to \infty }\)max(E(f1), E(f2))/n. We then consider the special case when the item sizes are uniformly distributed over (0, 1], and obtain optimal values for the parameters of the algorithm. For these values of the parameters, the average-case performance ratio is less than 1.19. This compares well with the performance ratio 1.2865... of the Harmonic algorithm.

The extended Gini is a family of measures of variability which is mainly used in the areas of finance and income distribution. Each index in the family is defined by specifying one parameter, which reflects the social evaluation of the marginal utility of income. The higher the parameter, the more weight is attached to the lower portion of the cumulative distribution, reflecting higher concern for poverty. In this paper we list and investigate the properties of the equivalents of the correlation coefficient that are associated with the extended Gini family. In addition, we show that the extended Gini of a linear combination of random variables can be decomposed, in a way which is equivalent to the decomposition of the variance, with, in addition, terms that reflect additional properties of the random variables. The implication of these properties is that any decomposition that is performed with the coefficient of variation can be replicated by an infinite number of indices that are based on the Extended Gini coefficient.

CHAPTER III - NUMERICAL CHARACTERISTICS OF PROBABILITY DISTRIBUTIONS

Supplementary Appendix to: A Coskewness Shrinkage Approach for Estimating the Skewness of Linear Combinations of Random Variables

This paper presents a framework for an error correction decoding algorithm which can perform soft-input/soft-output decoding on arbitrary linear block codes over arbitrary finite fields. The algorithm produces estimates of individual symbols by detecting the symbol as a scalar multiple of a column of the generator matrix for the code, with other columns forming an interfering "noise" which is probabilistically modeled. Only the generator matrix is used for the decoder; the parity check matrix is not employed. The posterior probability so obtained is iteratively fed back as a prior input for turbo-like operation. Methods of incorporating statistical dependence among symbols are presented. The decoder can be used for channels with arbitrary noise distributions. Computation over larger fields is achieved through the use of an extended Hadamard transform, which is used to compute the distribution of arbitrary linear combinations of random variables distributed over the field. Results are presented for some codes of various lengths and design distances.

This work investigates the use of the tolerance limits on the treatment couch position to detect mistakes in patient positioning and warn users of possible treatment errors. Computer controlled radiotherapy systems use the position of the treatment couch as a surrogate for patient position, and a tolerance limit is applied against a planned position. When the couch is out of tolerance, a warning is sent to a user to indicate a possible mistake in setup. A tight tolerance may catch all positioning mistakes while at the same time sending too many warnings; a loose tolerance will not catch all mistakes. We developed a statistical model of the absolute position for the three translational axes of the couch. The couch position for any fraction is considered a random variable xi. The ideal planned couch position xp is unknown before a patient starts treatment and must be estimated from the daily positions of xi. As such, xp is also a random variable. The tolerance, tol, is applied to the difference between the daily and planned position, di=xi−xp. The di is a linear combination of random variables and therefore the density of di is the convolution of distributions of xi and xp. Tolerance limits are based on the standard deviation of di such that couch positions that are more than two standard deviations away are considered out of tolerance. Using this framework, we investigated two methods of setting xp and tolerance limits. The first, called first day acquire (FDA), is to take couch position on the first day as the planned position. The second is to use the cumulative average (CumA) over previous fractions as the planned position. The standard deviation of di shrinks as more samples are used to determine xp and, as a result, the tolerance limit shrinks as a function of fraction number when a CumA technique is used. The metrics of sensitivity and specificity were used to characterize the performance of the two methods to correctly identify a couch position as in‐ or out‐of‐tolerance. These two methods were tested using simulated and real patient data. Five clinical sites with different indexed immobilization were tested. These were whole brain, head and neck, breast, thorax, and prostate. Analysis of the head and neck data shows that it is reasonable to model the daily couch position as a random variable in this treatment site. Using an average couch position for xp increased the sensitivity of the couch interlock and reduced the chances of acquiring a couch position that was a statistical outlier. Analysis of variation in couch position for different sites allowed the tolerance limit to be set specifically for a site and immobilization device. The CumA technique was able to increase the sensitivity of detecting out‐of‐tolerance positions while shrinking tolerance limits for a treatment course. Making better use of the software interlock on the couch positions could have a positive impact on patient safety and reduce mistakes in treatment delivery.PACS number: 87.55.Ne, 87.55.Qr, 87.55.tg, 87.55.tm

ABSTRACTDistance learning can be useful for bridging geographical barriers to education in rural settings. However, empirical evidence on the equivalence of distance education and traditional face-to-face (F2F) instruction in statistics and biostatistics is mixed. Despite the difficulty in randomization, we minimized intra-instructor variation between F2F and online sections in seven graduate-level biostatistics service courses in a synchronous (live, real time) fashion; that is, for each course taught in a traditional F2F setting, a separate set of students were taught simultaneously via online learning technology, allowing for two-way interaction between instructor and students. Our primary objective was to compare student performance in the two courses that use these two teaching modes. We used a Bayesian hierarchical model to test equivalence of modes. The frequentist mixed model approach was also conducted for reference. The results of Bayesian and frequentist methods agree and suggest a difference of less than 1% in average final grades. Finally, we discuss barriers to instruction and learning using the applied online teaching technology.

Purpose: CCX282-B represents a new class of highly specific chemokine receptor antagonists. It targets chemokine receptor 9 (CCR9), a key homing signal for intestine-specific T cells. In a 28-day phase 2 study, CCX282-B induced clinical responses (CDAIΔ70) in 58% of Crohn's disease (CD) patients with a baseline CDAI >250 and elevated CRP, vs. 31% on placebo. CRP decreased 11 mg/L in the CCX282-B group relative to placebo. These results prompted PROTECT-1, a large, randomized, placebo-controlled trial in CD. Methods: This study involves >100 sites in 16 countries. The primary efficacy endpoint is CDAI decrease over 12 weeks. Maintenance of response is assessed over 36 weeks. Adults with moderate to severe CD (CDAI 250–450), are randomized 3:2:2:2 to receive placebo, CCX282-B 250 mg/day, 500 mg/day, or 250 mg twice daily (bid) for 12 weeks followed by a 4-week Active Treatment period (250 mg CCX282-B bid). CDAIΔ70 responders are then re-randomized 2:3 to receive either placebo or 250 mg CCX282-B bid for 36 weeks (Maintenance period). Results: As of May 2007, 163 subjects have been enrolled into the Induction Period. 56 subjects have enrolled into the Active Treatment period. 39 subjects have completed the Active Treatment period, of which 29 (74%) have achieved a CDAIΔ70 response, 27 (69%) a CDAIΔ100 response, and 16 subjects (41%) were in remission (CDAI < 150). No serious unexpected adverse events related to CCX282-B have been observed, and overall more than 250 subjects have received CCX282-B in clinical trials, with no adverse safety concerns. Conclusion: CCX282-B, a highly specific, oral CCR9 antagonist, and the first chemokine-based inhibitor of leukocyte trafficking tested in IBD, shows promise in CD.

Cladribine (CLAD) is a purine nucleoside analog approved in tablet form to treat highly active multiple sclerosis (MS). CLAD tablets are the first oral therapy with an infrequent dosing schedule, administered in two annual treatment courses, each divided into two treatment cycles comprising 4–5 days of treatment. The efficacy and safety of CLAD tablets have been verified in randomized controlled clinical trials. Clinical observational studies are performed in more representative populations and over more extended periods, and thus provide valuable complementary insights. Here, we summarize the available evidence for CLAD tablets from post-marketing trials, including two observational, four long-term extensions, and two comparative studies. The patients in the post-marketing setting differed from the cohort recruited in the pivotal phase III trials regarding demographics and MS-related disability. The limited number of studies with small cohorts corroborate the disease-modifying capacity of oral CLAD and report on a durable benefit after active treatment periods. Skin-related adverse events were common in the studies focusing on safety aspects. In addition, single cases of CLAD-associated autoimmune events have been reported. Lastly, CLAD tablets appear safe regarding COVID-19 concerns, and patients mount a robust humoral immune response to SARS-CoV‑2 vaccination. We conclude that the current real-world evidence for CLAD tablets as immune reconstitution therapy for treatment of MS is based on a small number of studies and a population distinct from the cohorts randomized in the pivotal phase III trials. Further research should advance the understanding of long-term disease control after active treatment periods and the mitigation of adverse events.

The aim of the study was to evaluate the effects of a beta 1-selective (atenolol 50 mg q.d.) and a non-selective (propranolol 80 mg b.i.d.) beta-adrenoceptor antagonists on human stimulated parotid and submandibular-sublingual (SM-SL) gland secretion. A randomized double-blind, placebo-controlled cross-over ("Latin square") design was used in 19 healthy male volunteers. Stimulated parotid and SM-SL saliva were sampled immediately before and 7 days after the start of each treatment period. Stimulation of salivary secretion was achieved by use of a 3% citric acid solution. Plasma concentrations of propranolol and atenolol were determined from blood samples. The salivary secretion of both glands was assessed for flow rate, amylase, lysozyme, and salivary peroxidase activity and for concentrations of total protein, hexosamine, sialic acid, Ca2+, Cl-, K+, Mg2+, Na+, and PO4(3-). In both parotid and SM-SL secretions, the total protein and phosphate concentrations and amylase activity were significantly decreased during the two active treatment periods. In SM-SL gland secretion, there were significant changes in potassium and calcium concentrations during active treatment as compared with baseline, with potassium showing a decreased and calcium an increased concentration. During atenolol treatment, salivary peroxidase activity decreased significantly in SM-SL secretion. In parotid secretion, the hexosamine/total protein ratio decreased and the sialic acid/hexosamine ratio increased during atenolol treatment, which may indicate an effect on protein synthesis. No significant effects on salivary secretion rates were disclosed.

Background: Most of the DNP programs provide only one Biostatistics course for the students, which means instructors have limited time to prepare DNP students in mastering the statistics skills they need to complete their scholarly project. Methods: Quantitative content analysis was conduct on 100 DNP projects to retrieve information regarding the subjects, sample size, sampling strategies, and statistics methods used. These projects were selected from two online DNP projects repositories, where DNP graduates uploaded their projects voluntarily. Results: Almost half of the projects had a sample size less than 50, majority of the studies adopted convenience sampling strategy, and the most often used statistics methods discovered were descriptive analysis, t Test, and Chi square analysis. Conclusion: Small sample size is an intrinsic problem of most DNP projects. The results of this study give DNP students and faculty a more clear teaching map that focuses on skills used most often.

Effect of Ivabradine vs Atenolol on Heart Rate and Effort Tolerance in Patients With Mild to Moderate Mitral Stenosis and Normal Sinus Rhythm

Little is known about the mechanisms of the effect og exogeneous glucocorticosteroids. The aim of the present study was to assesss whether low doses of oral prednisolone affect serum levels of ICF-1, ICF binding protein-3, the carboxyterminal propeptide of type III procollagen (PICP) and the aminoterminal propeptide of type III procollarjen (PIIINP). A group of 10 children with asthma aged 7-11 years was studied. The design was a randomised double-blind cross-over trial with run-in, wash-out and two active periods of 15 days. During run-in and wash-out placebo was given. During active treatment periods 2.5 or 5 mg prednisolono were given per day. Blood samplus were taken at the end of the periods. ICF-1 and 1GFBP-3 were not statistically significantly influenced by the treatments. PICP (ng/ml) was 345 (run-in;, 319 (2.5 mg) and 275 (5 mg); Pages test :P<0.05. PIIINP (ng/ml) was 7.84 (run-in), 5.96 (2.3 my) and 4.69 (5.0 mg); Pages tetst :P<0.01. Oral prediusolone Causes a dose related reduction of procollagen I and III indicating a suppression of collagen synthesis. Thus may explain the growth retarding effect of systemic glucocorticosteroids.