Berry-Esseen bounds for nonlinear statistics, and asymptotic relative efficiency between correlation statistics

Four papers, written in collaboration with the author’s graduate school advisor, are presented. In the first paper, uniform and non-uniform Berry-Esseen (BE) bounds on the convergence to normality of a general class of nonlinear statistics are provided; novel applications to specific statistics, including the non-central Student’s, Pearson’s, and the non-central Hotelling’s, are also stated. In the second paper, a BE bound on the rate of convergence of the F-statistic used in testing hypotheses from a general linear model is given. The third paper considers the asymptotic relative efficiency (ARE) between the Pearson, Spearman, and Kendall correlation statistics; conditions sufficient to ensure that the Spearman and Kendall statistics are equally (asymptotically) efficient are provided, and several models are considered which illustrate the use of such conditions. Lastly, the fourth paper proves that, in the bivariate normal model, the ARE between any of these correlation statistics possesses certain monotonicity properties; quadratic lower and upper bounds on the ARE are stated as direct applications of such monotonicity patterns.

Development of record-breaking statistics for climatological time-series analysis

The number of record-breaking events expected to occur in a strictly stationary time-series depends only on the number of values in the time-series, regardless of distribution. This holds whether the events are record-breaking highs or lows and whether we count from past to present or present to past. However, these symmetries are broken in distinct ways by trends in the mean and variance. We define indices that capture this information and use them to detect weak trends from multiple time-series. Here, we use these methods to answer the following questions: (1) Is there a variability trend among globally distributed surface temperature time-series? We find a significant decreasing variability over the past century for the Global Historical Climatology Network (GHCN). This corresponds to about a 10% change in the standard deviation of inter-annual monthly mean temperature distributions. (2) How are record-breaking high and low surface temperatures in the United States affected by time period? We investigate the United States Historical Climatology Network (USHCN) and find that the ratio of record-breaking highs to lows in 2006 increases as the time-series extend further into the past. When we consider the ratio as it evolves with respect to a fixed start year, we find it is strongly correlated with the ensemble mean. We also compare the ratios for USHCN and GHCN (minus USHCN stations). We find the ratios grow monotonically in the GHCN data set, but not in the USHCN data set. (3) Do we detect either mean or variance trends in annual precipitation within the United States? We find that the total annual and monthly precipitation in the United States (USHCN) has increased over the past century. Evidence for a trend in variance is inconclusive.

Descriptive Statistics and Linear Regression

This morning Dr. Battle will introduce descriptive statistics and linear regression and how to apply these concepts in mathematical modeling. You will also learn how to use a spreadsheet to help with statistical analysis and to create graphs.

Circulating fibrinogen but not D-dimer level is associated with vital exhaustion in school teachers

Meta-analyses have established elevated fibrinogen and D-dimer levels in the circulation as biological risk factors for the development and progression of coronary artery disease (CAD). Here, we investigated whether vital exhaustion (VE), a known psychosocial risk factor for CAD, is associated with fibrinogen and D-dimer levels in a sample of apparently healthy school teachers. The teaching profession has been proposed as a potentially high stressful occupation due to enhanced psychosocial stress at the workplace. Plasma fibrinogen and D-dimer levels were measured in 150 middle-aged male and female teachers derived from the first year of the Trier-Teacher-Stress-Study. Log-transformed levels were analyzed using linear regression. Results yielded a significant association between VE and fibrinogen (p = 0.02) but not D-dimer controlling for relevant covariates. Further investigation of possible interaction effects resulted in a significant association between fibrinogen and the interaction term "VE x gender" (p = 0.05). In a secondary analysis, we reran linear regression models for males and females separately. Gender-specific results revealed that the association between fibrinogen and VE remained significant in males but not females. In sum, the present data support the notion that fibrinogen levels are positively related to VE. Elevated fibrinogen might be one biological pathway by which chronic work stress may impact on teachers' cardiovascular health in the long run.

Heart rate recovery after exercise in chronic heart failure: Role of vital exhaustion and type D personality

OBJECTIVE: Vital exhaustion and type D personality previously predicted mortality and cardiac events in patients with chronic heart failure (CHF). Reduced heart rate recovery (HRR) also predicts morbidity and mortality in CHF. We hypothesized that elevated levels of vital exhaustion and type D personality are both associated with decreased HRR. METHODS: Fifty-one patients with CHF (mean age 58+/-12 years, 82% men) and left ventricular ejection fraction (LVEF) Vital Exhaustion Questionnaire and the 14-item type D questionnaire asking about negative affectivity and social inhibition. HRR was calculated as the difference between heart rate at the end of exercise and 1min after abrupt cessation of exercise (HRR-1). Regression analyses were adjusted for gender, age, LVEF, and maximum exercise capacity. RESULTS: Vital exhaustion explained 8.4% of the variance in continuous HRR-1 (p=0.045). For each point increase on the vital exhaustion score (range 0-18) there was a mean+/-SEM decrease of 0.54+/-0.26bpm in HRR-1. Type D personality showed a trend toward statistical significance for being associated with lower levels of HRR-1 explaining 6.5% of the variance (p<0.08). The likelihood of having HRR-1vital exhaustion and type D personality were both independently associated with reduced HRR-1. The findings provide a hitherto not explored psychobiological explanation for poor cardiac outcome in patients with CHF.

Independent association of sleep quality, fatigue, and vital exhaustion with platelet count in patients with a previous venous thromboembolic event

Elevated platelet count might reflect increased inflammation as an etiological factor for venous thromboembolism (VTE). Poor sleep, fatigue, and exhaustion are all associated with inflammation and are also common sequelae of chronic psychological stress that previously predicted increased risk of VTE. We hypothesized that platelet count would be high in patients with VTE who sleep poorly and who are fatigued and exhausted. We investigated 205 patients scheduled for thrombophilia work-up > or =3 months after an objectively diagnosed venous thromboembolic event. They completed the Jenkins Sleep Questionnaire to rate subjective sleep quality and the short forms of the Multidimensional Fatigue Symptom Inventory and Maastricht Vital Exhaustion Questionnaire. Platelet count was determined by a mechanical Coulter counter. Analyses controlled for age, sex, body mass index, time since the index event, and medication. After taking into account these covariates, poorer sleep quality (p = 0.001; DeltaR(2)= 0.046), high fatigue (p = 0.008; DeltaR(2)= 0.032), and vital exhaustion (p = 0.050; DeltaR(2)= 0.017) were all associated with elevated platelet count. In addition, high level of fatigue mediated the relationship between poor sleep quality and elevated platelet count (p = 0.046). Poor sleep quality, high levels of fatigue, and vital exhaustion were identified as correlates of an elevated platelet count in patients with a previous episode of VTE. Given the emerging role of inflammatory processes in VTE, the findings suggest a mechanism through which behavioral and chronic psychological stressors might contribute to incident and recurrent venous thrombotic events.

Stroke events, and case fatalities in Switzerland based on hospital statistics and cause of death statistics

OBJECTIVE: In Switzerland there is a shortage of population-based information on stroke incidence and case fatalities (CF). The aim of this study was to estimate stroke event rates and both in- and out-of-hospital CF rates. METHODS: Data on stroke diagnoses, coded according to I60-I64 (ICD 10), were taken from the Federal Hospital Discharge Statistics database (HOST) and the Cause of Death database (CoD) for the year 2004. The number of total stroke events and of age- and gender-specific and agestandardised event rates were estimated; overall CF, in-hospital and out-of-hospital, were determined. RESULTS: Among the overall number of 13 996 hospital discharges from stroke (HOST) the number was lower in women (n = 6736) than in men (n = 7260). A total of 3568 deaths (2137 women and 1431 men) due to stroke were recorded in the CoD database. The number of estimated stroke events was 15 733, and higher in women (n = 7933) than in men (n = 7800). Men presented significantly higher age-specific stroke event rates and a higher age-standardised event rate (178.7/100 000 versus 119.7/100 000). Overall CF rates were significantly higher for women (26.9%) than for men (18.4%). The same was true of out-of-hospital CF but not of in-hospital CF rates. CONCLUSION: The data on estimated stroke events obtained indicate that stroke discharge rate underestimates the stroke event rate. Out-of-hospital deaths from stroke accounted for the largest proportion of total stroke deaths. Sex differences in both number of total stroke events and deaths could be explained by the higher proportion of women than men aged 55+ in the Swiss population.

Bayesian statistics in oncology: a guide for the clinical investigator

The rise of evidence-based medicine as well as important progress in statistical methods and computational power have led to a second birth of the >200-year-old Bayesian framework. The use of Bayesian techniques, in particular in the design and interpretation of clinical trials, offers several substantial advantages over the classical statistical approach. First, in contrast to classical statistics, Bayesian analysis allows a direct statement regarding the probability that a treatment was beneficial. Second, Bayesian statistics allow the researcher to incorporate any prior information in the analysis of the experimental results. Third, Bayesian methods can efficiently handle complex statistical models, which are suited for advanced clinical trial designs. Finally, Bayesian statistics encourage a thorough consideration and presentation of the assumptions underlying an analysis, which enables the reader to fully appraise the authors' conclusions. Both Bayesian and classical statistics have their respective strengths and limitations and should be viewed as being complementary to each other; we do not attempt to make a head-to-head comparison, as this is beyond the scope of the present review. Rather, the objective of the present article is to provide a nonmathematical, reader-friendly overview of the current practice of Bayesian statistics coupled with numerous intuitive examples from the field of oncology. It is hoped that this educational review will be a useful resource to the oncologist and result in a better understanding of the scope, strengths, and limitations of the Bayesian approach.

Association of vital exhaustion and depressive symptoms with changes in fibrin D-dimer to acute psychosocial stress

OBJECTIVE: Vital exhaustion and depression are psychosocial risk factors of coronary artery disease. A hypercoagulable state in response to acute psychosocial stress contributes to atherothrombotic events. We aimed to investigate the hypothesis that vital exhaustion and depression correlate with stress-induced changes in the hypercoagulability marker D-dimer. METHODS: Thirty-eight healthy and nonsmoking school teachers (mean age 50+/-8 years, 55% women) completed the nine-item Maastricht Vital Exhaustion Questionnaire and the seven-item depression subscale of the Hospital Anxiety and Depression Scale. Within 1 week, subjects twice underwent the Trier Social Stress Test (i.e., preparation phase, mock job interview, and mental arithmetic that totaled 13 min). Plasma D-dimer levels were determined at five time points during the protocol. RESULTS: Vital exhaustion (P=.022; eta(2)=.080) and depressive symptoms (P=.011; eta(2)=.090) were associated with stress-induced changes in D-dimer levels over time controlling for sex and age. Elevated levels of vital exhaustion (r=-.46, P=.005) and of depression (r=-.51, P=.002) correlated with reduced D-dimer increase from pre-stress to immediately post-stress. Also, elevated vital exhaustion (r=.34, P=.044) and depression (r=.41, P=.013) were associated with increase (i.e., attenuated recovery) of D-dimer levels between 20 and 45 min post-stress. Controlling for stress hormone and blood pressure reactivity did not substantially alter these results. CONCLUSION: The findings suggest an attenuated immediate D-dimer stress response and delayed recovery of D-dimer levels post-stress with elevated vital exhaustion and depressive symptoms. In particular, the prolonged hypercoagulability after stress cessation might contribute to the atherothrombotic risk previously observed with vital exhaustion and depression, even at subclinical levels.