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.

Noninvasive measurement of cardiac output during exercise by inert gas rebreathing technique

Reduced exercise tolerance and dyspnea during exercise are hallmarks of heart failure syndrome. Exercise capacity and various parameters of cardiopulmonary response to exercise are of important prognostic value. All the available parameters only indirectly reflect left ventricular dysfunction and hemodynamic adaptation to an increased demand. Noninvasive assessment of cardiac output, especially during an incremental exercise stress test, would allow the direct measure of cardiac reserve and may become the gold standard for prognostic evaluation in the future.

Corticospinal output and loss of force during motor fatigue

The objective of this study was to analyze central motor output changes in relation to contraction force during motor fatigue. The triple stimulation technique (TST, Magistris et al. in Brain 121(Pt 3):437-450, 1998) was used to quantify a central conduction index (CCI = amplitude ratio of central conduction response and peripheral nerve response, obtained simultaneously by the TST). The CCI removes effects of peripheral fatigue from the quantification. It allows a quantification of the percentage of the entire target muscle motor unit pool driven to discharge by a transcranial magnetic stimulus. Subjects (n = 23) performed repetitive maximal voluntary contractions (MVC) of abductor digiti minimi (duration 1 s, frequency 0.5 Hz) during 2 min. TST recordings were obtained every 15 s, using stimulation intensities sufficient to stimulate all cortical motor neurons (MNs) leading to the target muscle, and during voluntary contractions of 20% of the MVC to facilitate the responses. TST was also repetitively recorded during recovery. This basic exercise protocol was modified in a number of experiments to further characterize influences on CCI of motor fatigue (4 min exercise at 50% MVC; delayed fatigue recovery during local hemostasis, "stimulated exercise" by 20 Hz trains of 1 s duration at 0.5 Hz during 2 min). In addition, the cortical silent period was measured during the basic exercise protocol. Force fatigued to approximately 40% of MVC in all experiments and in all subjects. In all subjects, CCI decreased during exercise, but this decrease varied markedly between subjects. On average, CCI reductions preceded force reductions during exercise, and CCI recovery preceded force recovery. Exercising at 50% for 4 min reduced muscle force more markedly than CCI. Hemostasis induced by a cuff delayed muscle force recovery, but not CCI recovery. Stimulated exercise reduced force markedly, but CCI decreased only marginally. Summarized, force reduction and reduction of the CCI related poorly quantitatively and in time, and voluntary drive was particularly critical to reduce the CCI. The fatigue induced reduction of CCI may result from a central inhibitory phenomenon. Voluntary muscle activation is critical for the CCI reduction, suggesting a primarily supraspinal mechanism.

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.