Alla Sikorskii

Stochastic Models for Fractional Calculus

Preface: 1 Introduction 1.1 The traditional diffusion model 1.2 Fractional diffusion 2 Fractional Derivatives 2.1 The Grunwald formula 2.2 More fractional derivatives 2.3 The Caputo derivative 2.4 Time-fractional diffusion 3 Stable Limit Distributions 3.1 Infinitely divisible laws 3.2 Stable characteristic functions 3.3 Semigroups 3.4 Poisson approximation 3.5 Shifted Poisson approximation 3.6 Triangular arrays 3.7 One-sided stable limits 3.8 Two-sided stable limits 4 Continuous Time Random Walks 4.1 Regular variation 4.2 Stable Central Limit Theorem 4.3 Continuous time random walks 4.4 Convergence in Skorokhod space 4.5 CTRW governing equations 5 Computations in R 5.1 R codes for fractional diffusion 5.2 Sample path simulations 6 Vector Fractional Diffusion 6.1 Vector random walks 6.2 Vector random walks with heavy tails 6.3 Triangular arrays of random vectors 6.4 Stable random vectors 6.5 Vector fractional diffusion equation 6.6 Operator stable laws 6.7 Operator regular variation 6.8 Generalized domains of attraction 7 Applications and Extensions 7.1 LePage Series Representation 7.2 Tempered stable laws 7.3 Tempered fractional derivatives 7.4 Pearson Diffusion 7.5 Classification of Pearson diffusions 7.6 Spectral representations of the solutions of Kolmogorov equations 7.7 Fractional Brownian motion 7.8 Fractional random fields 7.9 Applications of fractional diffusion 7.10 Applications of.

Development of a New Knee Society Scoring System

BackgroundThe Knee Society Clinical Rating System was developed in 1989 and has been widely adopted. However, with the increased demand for TKA, there is a need for a new, validated scoring system to better characterize the expectations, satisfaction, and physical activities of the younger, more diverse population of TKA patients.Questions/purposesWe developed and validated a new Knee Society Scoring System.MethodsWe developed the new knee scoring system in two stages. Initially, a comprehensive survey of activities was developed and administered to 101 unilateral TKA patients (53 women, 48 men). A prototype knee scoring instrument was developed from the responses to the survey and administered to 497 patients (204 men, 293 women; 243 postoperatively, 254 preoperatively) at 15 medical institutions within the United States and Canada. Objective and subjective data were analyzed using standard statistical and psychometric procedures and compared to the Knee Injury and Osteoarthritis Score and SF-12 scores for validation. Based on this analysis, minor modifications led to the new Knee Society Scoring System.ResultsWe found the new Knee Society Scoring System to be broadly applicable and to accurately characterize patient outcomes after TKA. Statistical analysis confirmed the internal consistency, construct and convergent validity, and reliability of the separate subscale measures.ConclusionsThe new Knee Society Scoring System is a validated instrument based on surgeon- and patient-generated data, adapted to the diverse lifestyles and activities of contemporary patients with TKA. This assessment tool allows surgeons to appreciate differences in the priorities of individual patients and the interplay among function, expectation, symptoms, and satisfaction after TKA.

Depressive symptoms in mid-pregnancy, lifetime stressors and the 5-HTTLPR genotype

Few studies of gene–environment interactions for the serotonin transporter promoter polymorphism (5‐HTTLPR), life stressors and depression have considered women separately or examined specific types of stressful life events. None have looked at depression during pregnancy. In the Pregnancy Outcomes and Community Health (POUCH) Study, women were queried about history of stressful life events and depressive symptoms at the time of enrollment (15–27 weeks gestation). Stressful life events were grouped a priori into “subconstructs” (e.g. economic, legal, abuse, loss) and evaluated by subconstruct, total subconstruct score and total stressful life event score. The effect of genotype on the association between stressful life events and elevated depressive symptoms was assessed in 568 white non‐Hispanic participants. The relationship between exposure to abuse and elevated depressive symptoms was more pronounced in the s/s group (OR = 24.5) than in the s/l group (OR = 3.0) and the l/l group (OR = 7.7), but this significant interaction was detected only after excluding 73 (13%) women with recent use of psychotropic medications. There was no evidence of gene–environment interaction in analytic models with other stressful life events subconstructs, total subconstruct score or total stressful life events score. These data offer modest support to other reports of gene–environment interaction and highlight the importance of considering specific stressful life events.

United States Birth Weight Reference Corrected For Implausible Gestational Age Estimates

OBJECTIVES: To provide an updated US birth weight for gestational age reference corrected for likely errors in last menstrual period (LMP)-based gestational age dating, as well as means and SDs, to enable calculation of continuous and categorical measures of birth weight for gestational age. METHODS: From the 2009–2010 US live birth files, we abstracted singleton births between 22 and 44 weeks of gestation with at least 1 nonmissing estimate of gestational age (ie, LMP or obstetric/clinical) and birth weight. Using an algorithm based on birth weight and the concordance between these gestational age estimates, implausible LMP-based gestational age estimates were either excluded or corrected by using the obstetric/clinical estimate. Gestational age– and sex-specific birth weight means, SDs, and smoothed percentiles (3rd, 5th, 10th, 90th, 95th, 97th) were calculated, and the 10th and 90th percentiles were compared with published population-based references. RESULTS: A total of 7 818 201 (99% of eligible) births were included. The LMP-based estimate of gestational age comprised 85% of the dataset, and the obstetric/clinical estimate comprised the remaining 15%. Cut points derived from the current reference identified ∼10% of births as ≤10th and ≥90th percentiles at all gestational weeks, whereas cut points derived from previous US-based references captured variable proportions of infants at these thresholds within the preterm and postterm gestational age ranges. CONCLUSIONS: This updated US-based birth weight for gestational age reference corrects for likely errors in gestational age dating and allows for the calculation of categorical and continuous measures of birth size.

Complementary and Alternative Medicine Use, Spending, and Quality of Life in Early Stage Breast Cancer

Background: Up to 80% of women with breast cancer use complementary and alternative medicine (CAM) therapies to improve quality of life (QOL) during treatment. Objective: The objective of this study was to explore the association between CAM therapy use, spending on CAM therapies, demographic variables, surgical treatment, and QOL. Methods: A secondary analysis was conducted for women with early stage breast cancer (N = 222) who were enrolled in a nursing intervention study after breast surgery. The complementary therapy utilization instrument included specific CAM therapies used, number of treatments, and spending. The number of major categories of CAM and the specific CAM therapies used were analyzed in relation to study variables using proportional odds logistic regression models. The outcome of spending for major CAM categories was analyzed using linear mixed effects modeling. Results: A majority of women (56.8%) used at least one CAM therapy, and the biologically based therapies category was most frequently used (43.7%). Women with less than a college level of education were less likely to use CAM (odds ratio [OR] = 0.36, 95% confidence interval [CI] = 0.15-0.86, p < .01). Women who were employed were more likely to use therapies from multiple CAM categories (OR = 2.42, 95% CI = 1.00-5.88, p < .05), and those with lower QOL were more likely to use CAM (OR = 0.97, 95% CI = 0.95-0.99, p < .01). The results support that women with early stage breast cancer, especially those with lower QOL, are highly likely to use CAM therapies. Further research is needed on CAM interventions to enhance supportive care for breast cancer.

An Intervention to Improve Adherence and Management of Symptoms for Patients Prescribed Oral Chemotherapy Agents: An Exploratory Study

Background: Use of oral chemotherapy agents to treat cancer has increased. Patients are responsible for adhering to complex regimens while managing symptoms from adverse effects of the chemotherapy. Objective: This study examined an intervention to manage symptoms and adherence to oral agents. Methods: A 3-group pilot study determined how an Automated Voice Response (AVR) system alone (n = 40), or the AVR with strategies to manage symptoms and adherence (n = 40), or the AVR with strategies to manage adherence (n = 39) reduced symptom severity and improved adherence. Participants received a Symptom Management Toolkit, completed a baseline interview, and were randomized to receive 8 weekly AVR calls. An exit interview occurred at 10 weeks. Results: Mean age was 59.6 years, with 70% female and 76% white, and 42% were nonadherent, with missed doses increasing with regimen complexity. Symptom severity declined over time in all groups. No difference was found in adherence rates, and higher adherence was related with lower symptom severity across groups. Conclusions: Adherence, a significant clinical problem, can affect efficacy of the cancer treatment. The AVR intervention alone was just as effective as the AVR plus the nurse intervention at promoting adherence and managing symptoms from adverse effects. Implications for Practice: Nurses need to focus on patient education by ensuring patient understanding of oral agent regimen and the need to adhere to the oral agent for efficacious cancer treatment. Nurses can promote the use of medication reminders and self-management of symptoms from adverse effects, to support adherence to the oral agent.

Health-related quality-of-life outcomes: a reflexology trial with patients with advanced-stage breast cancer.

PURPOSE/OBJECTIVES To evaluate the safety and efficacy of reflexology, a complementary therapy that applies pressure to specific areas of the feet. DESIGN Longitudinal, randomized clinical trial. SETTING Thirteen community-based medical oncology clinics across the midwestern United States. SAMPLE A convenience sample of 385 predominantly Caucasian women with advanced-stage breast cancer receiving chemotherapy and/or hormonal therapy. METHODS Following the baseline interview, women were randomized into three primary groups: reflexology (n = 95), lay foot manipulation (LFM) (n = 95), or conventional care (n = 96). Two preliminary reflexology (n = 51) and LFM (n = 48) test groups were used to establish the protocols. Participants were interviewed again postintervention at study weeks 5 and 11. MAIN RESEARCH VARIABLES Breast cancer-specific health-related quality of life (HRQOL), physical functioning, and symptoms. FINDINGS No adverse events were reported. A longitudinal comparison revealed significant improvements in physical functioning for the reflexology group compared to the control group (p = 0.04). Severity of dyspnea was reduced in the reflexology group compared to the control group (p < 0.01) and the LFM group (p = 0.02). No differences were found on breast cancer-specific HRQOL, depressive symptomatology, state anxiety, pain, and nausea. CONCLUSIONS Reflexology may be added to existing evidence-based supportive care to improve HRQOL for patients with advanced-stage breast cancer during chemotherapy and/or hormonal therapy. IMPLICATIONS FOR NURSING Reflexology can be recommended for safety and usefulness in relieving dyspnea and enhancing functional status among women with advanced-stage breast cancer.

Managing Symptoms Among Patients With Breast Cancer During Chemotherapy: Results of a Two-Arm Behavioral Trial

PURPOSE In this study, we compare symptom response and times to response among patients with breast cancer who were assigned to either a cognitive behavioral Nurse-Administered Symptom Management intervention or an Automated Telephone Symptom Management (ATSM) intervention. PATIENTS AND METHODS Patients with breast cancer were identified from a larger trial. Baseline equivalence existed between arms, and there was no differential attrition by arm. Anchor-based definition of response using mild, moderate, and severe categories of symptom severity were used. Responses and times to response for 15 symptoms were investigated in relation to trial arm, comorbid conditions, treatment protocols, and metastatic versus localized disease. RESULTS The ATSM arm was more effective among patents with metastatic disease. Compared with patients receiving combination chemotherapy protocols, those treated with single agents had greater response and shorter time to response. CONCLUSION An educational information intervention delivered via an automated voice response system that assesses symptoms and refers patients to a Symptom Management Guide is more effective than a complex cognitive behavioral approach in terms of producing greater symptom responses in shorter time intervals among patients with metastatic disease.

Do Older Adults With Cancer Fall More Often? A Comparative Analysis of Falls in Those With and Without Cancer

PURPOSE/OBJECTIVES To examine whether a history of cancer increased the likelihood of a fall in community-dwelling older adults, and if cancer type, stage, or time since diagnosis increased falls. DESIGN A longitudinal, retrospective, cohort study. SETTING A home- and community-based waiver program in Michigan. SAMPLE 862 older adults aged 65 years or older with cancer compared to 8,617 older adults without cancer using data from the Minimum Data Set-Home Care and Michigan cancer registry. METHODS Reports of falls were examined for 90-180 days. Generalized estimating equations were used to compare differences between the groups. MAIN RESEARCH VARIABLES Cancer, falls, patient characteristics, comorbidities, medications, pain, weight loss, vision, memory recall, and activities, as well as cancer type, stage, and time since diagnosis. FINDINGS A fall occurred at a rate of 33% in older adults with cancer compared to 29% without cancer (p < 0.00). Those with a history of cancer were more likely to fall than those without cancer (adjusted odds ratio 1.16; 95% confidence interval [1.02, 1.33]; p = 0.03). No differences in fall rates were determined by cancer type or stage, and the odds of a fall did not increase when adding time since cancer diagnosis. CONCLUSIONS The fall rate was higher in older adults with cancer than in older adults without cancer. IMPLICATIONS FOR NURSING Nurses need to assess fall risk and initiate fall prevention measures for older adults at the time of cancer diagnosis. KNOWLEDGE TRANSLATION When caring for older adults with cancer, nurses should be aware of an increased risk for falls. Healthcare staff also should be aware of an increased risk for falls in that population during cancer treatment. Evidence-based fall prevention measures should be included in care plans for older adult cancer survivors.

Sex differences in depressive symptoms and their correlates after mild-to-moderate traumatic brain injury

The purpose of this secondary data analysis, guided by allostatic load theory, was to compare depressive symptoms and their correlates in men and women following mild or moderate traumatic brain injury (n = 159). Using general linear modeling procedures in the Statistical Analysis Software, women reported significantly higher Center for Epidemiological Studies-Depression scores compared with men. According to the Neurobehavioral Functioning Inventory subscales, women also reported higher somatic and motor symptoms and difficulties with memory and cognition. Further, women within the first 6 months of their injury reported higher levels of depressive and depressive-somatic symptoms, perceived chronic stress, pain, memory difficulties, and somatic symptoms. These findings were no longer present at the 6- to 12-month or >12-month cutoffs. Womens depressive symptoms during the early recovery period are explained by higher symptom loads and perceived stress, yet mechanisms responsible for these differences remain to be elucidated. Future research is needed to describe hormonal, perceptual, or brain structure differences that may account for these findings. Findings from such research will most likely to contribute to our understanding of postconcussion syndrome.