Squared Extrapolation Methods (SQUAREM): A New Class of Simple and Efficient Numerical Schemes for Accelerating the Convergence of the EM Algorithm

We derive a new class of iterative schemes for accelerating the convergence of the EM algorithm, by exploiting the connection between fixed point iterations and extrapolation methods. First, we present a general formulation of one-step iterative schemes, which are obtained by cycling with the extrapolation methods. We, then square the one-step schemes to obtain the new class of methods, which we call SQUAREM. Squaring a one-step iterative scheme is simply applying it twice within each cycle of the extrapolation method. Here we focus on the first order or rank-one extrapolation methods for two reasons, (1) simplicity, and (2) computational efficiency. In particular, we study two first order extrapolation methods, the reduced rank extrapolation (RRE1) and minimal polynomial extrapolation (MPE1). The convergence of the new schemes, both one-step and squared, is non-monotonic with respect to the residual norm. The first order one-step and SQUAREM schemes are linearly convergent, like the EM algorithm but they have a faster rate of convergence. We demonstrate, through five different examples, the effectiveness of the first order SQUAREM schemes, SqRRE1 and SqMPE1, in accelerating the EM algorithm. The SQUAREM schemes are also shown to be vastly superior to their one-step counterparts, RRE1 and MPE1, in terms of computational efficiency. The proposed extrapolation schemes can fail due to the numerical problems of stagnation and near breakdown. We have developed a new hybrid iterative scheme that combines the RRE1 and MPE1 schemes in such a manner that it overcomes both stagnation and near breakdown. The squared first order hybrid scheme, SqHyb1, emerges as the iterative scheme of choice based on our numerical experiments. It combines the fast convergence of the SqMPE1, while avoiding near breakdowns, with the stability of SqRRE1, while avoiding stagnations. The SQUAREM methods can be incorporated very easily into an existing EM algorithm. They only require the basic EM step for their implementation and do not require any other auxiliary quantities such as the complete data log likelihood, and its gradient or hessian. They are an attractive option in problems with a very large number of parameters, and in problems where the statistical model is complex, the EM algorithm is slow and each EM step is computationally demanding.

Impact of viral E2-gene status on outcome after radiotherapy for patients with human papillomavirus 16-positive cancer of the uterine cervix

PURPOSE: Integration of high-risk papillomavirus DNA has been considered an important step in oncogenic progression to cervical carcinoma. Disruption of the human papillomavirus (HPV) genome within the E2 gene is frequently a consequence. This study investigated the influence of episomal viral DNA on outcome in patients with advanced cervical cancer treated with primary radiotherapy. METHODS AND MATERIALS: Paraffin-embedded biopsies of 82 women with locally advanced cervical cancer could be analyzed for HPV infection by multiplex polymerase chain reaction (PCR) by use of SPF1/2 primers. E2-gene intactness of HPV-16-positive samples was analyzed in 3 separate amplification reactions by use of the E2A, E2B, E2C primers. Statistical analyses (Kaplan-Meier method; log-rank test) were performed for overall survival (OS), disease-free survival (DFS), local progression-free survival (LPFS), and distant metastases-free survival (DMFS). RESULTS: Sixty-one (75%) of 82 carcinomas were HPV positive, 44 of them for HPV-16 (72%). Seventeen of the 44 HPV-16-positive tumors (39%) had an intact E2 gene. Patients with a HPV-16-positive tumor and an intact E2 gene showed a trend for a better DFS (58% vs. 38%, p = 0.06) compared with those with a disrupted E2 gene. A nonsignificant difference occurred regarding OS (87% vs. 66%, p = 0.16) and DMFS (57% vs. 48%, p = 0.15). CONCLUSION: E2-gene status may be a promising new target, but more studies are required to elucidate the effect of the viral E2 gene on outcome after radiotherapy in HPV-positive tumors.

Designed Extension of Survival Studies: Application to Clinical Trials with Unrecognized Heterogeneity

It is well known that unrecognized heterogeneity among patients, such as is conferred by genetic subtype, can undermine the power of randomized trial, designed under the assumption of homogeneity, to detect a truly beneficial treatment. We consider the conditional power approach to allow for recovery of power under unexplained heterogeneity. While Proschan and Hunsberger (1995) confined the application of conditional power design to normally distributed observations, we consider more general and difficult settings in which the data are in the framework of continuous time and are subject to censoring. In particular, we derive a procedure appropriate for the analysis of the weighted log rank test under the assumption of a proportional hazards frailty model. The proposed method is illustrated through application to a brain tumor trial.

DECOMPOSITION OF REGRESSION ESTIMATORS TO EXPLORE THE INFLUENCE OF "UNMEASURED" TIME-VARYING CONFOUNDERS

In environmental epidemiology, exposure X and health outcome Y vary in space and time. We present a method to diagnose the possible influence of unmeasured confounders U on the estimated effect of X on Y and to propose several approaches to robust estimation. The idea is to use space and time as proxy measures for the unmeasured factors U. We start with the time series case where X and Y are continuous variables at equally-spaced times and assume a linear model. We define matching estimator b(u)s that correspond to pairs of observations with specific lag u. Controlling for a smooth function of time, St, using a kernel estimator is roughly equivalent to estimating the association with a linear combination of the b(u)s with weights that involve two components: the assumptions about the smoothness of St and the normalized variogram of the X process. When an unmeasured confounder U exists, but the model otherwise correctly controls for measured confounders, the excess variation in b(u)s is evidence of confounding by U. We use the plot of b(u)s versus lag u, lagged-estimator-plot (LEP), to diagnose the influence of U on the effect of X on Y. We use appropriate linear combination of b(u)s or extrapolate to b(0) to obtain novel estimators that are more robust to the influence of smooth U. The methods are extended to time series log-linear models and to spatial analyses. The LEP plot gives us a direct view of the magnitude of the estimators for each lag u and provides evidence when models did not adequately describe the data.

COVARIATE-ADJUSTED NONPARAMETRIC ANALYSIS OF MAGNETIC RESONANCE IMAGES USING MARKOV CHAIN MONTE CARLO

Permutation tests are useful for drawing inferences from imaging data because of their flexibility and ability to capture features of the brain that are difficult to capture parametrically. However, most implementations of permutation tests ignore important confounding covariates. To employ covariate control in a nonparametric setting we have developed a Markov chain Monte Carlo (MCMC) algorithm for conditional permutation testing using propensity scores. We present the first use of this methodology for imaging data. Our MCMC algorithm is an extension of algorithms developed to approximate exact conditional probabilities in contingency tables, logit, and log-linear models. An application of our non-parametric method to remove potential bias due to the observed covariates is presented.

Anemia is associated with abdominal aortic aneurysm (AAA) size and decreased long-term survival after endovascular AAA repair

OBJECTIVE: Anemia is a common comorbid condition in various inflammatory states and an established predictor of mortality in patients with chronic heart failure, ischemic heart disease, and end-stage renal disease. The present study of patients with abdominal aortic aneurysm (AAA) undergoing endovascular repair (EVAR) assessed the relationships between baseline hemoglobin concentration and AAA size, as well as anemia and long-term survival. METHODS: Between March 1994 and November 2006, 711 patients (65 women, mean age 75.8 +/- 7.8 years) underwent elective EVAR. Anemia was defined as a hemoglobin level <13 g/dL in men and <12 g/dL in women. Post-EVAR mean follow-up was 48.3 +/- 32.0 months. Association of hemoglobin level with AAA size was assessed with multiple linear regression. Mortality was determined with use of the internet-based Social Security Death Index and the electronic hospital record. Kaplan-Meier survival curves of anemic and nonanemic patient groups were compared by the log-rank method. Multivariable logistic regression models were used to determine the influence of anemia on vital status after EVAR. RESULTS: A total of 218/711 (30.7%) of AAA patients undergoing EVAR had anemia at baseline. After adjustment for various risk factors, hemoglobin level was inversely related to maximum AAA diameter (beta: - .144, 95%-CI: -1.482 - .322, P = .002). Post-EVAR survival was 65.5% at 5 years and 44.4% at 10 years. In long-term follow-up, survival was significantly lower in patients with anemia as compared to patients without anemia (P < .0001 by log-rank). Baseline hemoglobin levels were independently related to long-term mortality in multivariable Cox regression analysis adjusted for various risk factors (adjusted HR: 0.866, 95% CI: .783 to .958, P = .005). Within this model, statin use (adjusted HR: .517, 95% CI: .308 to .868, P = .013) was independently related to long-term survival, whereas baseline AAA diameter (adjusted HR: 1.022, 95% CI: 1.009 to 1.036, P = .001) was an independently associated with increased mortality. CONCLUSIONS: Baseline hemoglobin concentration is independently associated with AAA size and reduced long-term survival following EVAR. Thus, the presence or absence of anemia offers a potential refinement of existing risk stratification instruments.

Synergy between trovafloxacin and ceftriaxone against penicillin-resistant pneumococci in the rabbit meningitis model and in vitro

The bactericidal activities of monotherapy with trovafloxacin (-0.37 +/- 0.15 Delta log(10) CFU/ml. h), vancomycin (-0.32 +/- 0.12 Delta log(10) CFU/ml. h), and ceftriaxone (-0.36 +/- 0.19 Delta log(10) CFU/ml. h) for the treatment of experimental meningitis in rabbits due to a clinical penicillin-resistant pneumococcal strain (MIC, 4 mg/liter) were similar. The combination of ceftriaxone with trovafloxacin considerably improved the killing rates (-0.67 +/- 0.16 Delta log(10) CFU/ml. h) and was slightly superior to ceftriaxone with vancomycin (killing rate, -0.53 +/- 0. 22 Delta log(10) CFU/ml. h), the regimen most commonly used in clinical practice. In vitro, synergy was demonstrated between ceftriaxone and trovafloxacin by the checkerboard method (fractional inhibitory concentration index, 0.5) and by time-killing assays over 8 h.

Statins are associated with decreased mortality in abdominal, but not in thoracic aortic aneurysm patients undergoing endovascular repair: propensity score-adjusted analysis

BACKGROUND: Purpose of this study was to compare the correlation of statin use with long-term mortality in patients with abdominal (AAA) and thoracic aortic aneurysm (TAA). PATIENTS AND METHODS: We compared long-term survival of 731 AAA and 59 TAA patients undergoing elective endovascular repair (EVAR). Kaplan-Meier survival curves were compared by the log-rank method. Propensity score-adjusted multivariable logistic regression models were used to determine independent associations of statin use on vital status after EVAR. RESULTS: Statin use was associated with decreased long-term mortality in AAA patients in bivariate and multivariable regression analysis, in which the effect of propensity to receive a statin was considered (adjusted HR: .613, 95%-CI: .379- .993, p = .047) whereas mortality of TAA patients was not associated with use of statins (adjusted HR: 1.795, 95%-CI: .147 -21.942, p = .647). CONCLUSIONS: Use of statins is an independent predictor of decreased mortality after elective EVAR in AAA, but not in TAA patients. These findings indirectly support the concept of a distinct pathogenesis of AAA and TAA.

Fading pdf of free-space optical communication system with pointing error

A free-space optical (FSO) laser communication system with perfect fast-tracking experiences random power fading due to atmospheric turbulence. For a FSO communication system without fast-tracking or with imperfect fast-tracking, the fading probability density function (pdf) is also affected by the pointing error. In this thesis, the overall fading pdfs of FSO communication system with pointing errors are calculated using an analytical method based on the fast-tracked on-axis and off-axis fading pdfs and the fast-tracked beam profile of a turbulence channel. The overall fading pdf is firstly studied for the FSO communication system with collimated laser beam. Large-scale numerical wave-optics simulations are performed to verify the analytically calculated fading pdf with collimated beam under various turbulence channels and pointing errors. The calculated overall fading pdfs are almost identical to the directly simulated fading pdfs. The calculated overall fading pdfs are also compared with the gamma-gamma (GG) and the log-normal (LN) fading pdf models. They fit better than both the GG and LN fading pdf models under different receiver aperture sizes in all the studied cases. Further, the analytical method is expanded to the FSO communication system with beam diverging angle case. It is shown that the gamma pdf model is still valid for the fast-tracked on-axis and off-axis fading pdfs with point-like receiver aperture when the laser beam is propagated with beam diverging angle. Large-scale numerical wave-optics simulations prove that the analytically calculated fading pdfs perfectly fit the overall fading pdfs for both focused and diverged beam cases. The influence of the fast-tracked on-axis and off-axis fading pdfs, the fast-tracked beam profile, and the pointing error on the overall fading pdf is also discussed. At last, the analytical method is compared with the previous heuristic fading pdf models proposed since 1970s. Although some of previously proposed fading pdf models provide close fit to the experiment and simulation data, these close fits only exist under particular conditions. Only analytical method shows accurate fit to the directly simulated fading pdfs under different turbulence strength, propagation distances, receiver aperture sizes and pointing errors.

Effectiveness of a nondestructive evaluation technique for assessing standing timber quality

The research presented in this thesis was conducted to further the development of the stress wave method of nondestructively assessing the quality of wood in standing trees. The specific objective of this research was to examine, in the field, use of two stress wave nondestructive assessment techniques. The first technique examined utilizes a laboratory-built measurement system consisting of commercially available accelerometers and a digital storage oscilloscope. The second technique uses a commercially available tool that incorporates several technologies to determine speed of stress wave propagation in standing trees. Field measurements using both techniques were conducted on sixty red pine trees in south-central Wisconsin and 115 ponderosa pine trees in western Idaho. After in-situ measurements were taken, thirty tested red pine trees were felled and a 15-foot-long butt log was obtained from each tree, while all tested ponderosa pine trees were felled and an 8 1/2 -foot-long butt log was obtained, respectively. The butt logs were sent to the USDA Forest Products Laboratory and nondestructively tested using a resonance stress wave technique. Strong correlative relationships were observed between stress wave values obtained from both field measurement techniques. Excellent relationships were also observed between standing tree and log speed-of-sound values.

A PETROPHYSICAL EVALUATION OF THE TRENTON-BLACK RIVER FORMATION OF THE MICHIGAN BASIN

This work is conducted to study the geological and petrophysical features of the Trenton- Black River limestone formation. Log curves, crossplots and mineral identification methods using well-log data are used to determine the components and analyze changes in lithology. Thirty-five wells from the Michigan Basin are used to define the mineralogy of Trenton-Black River limestone. Using the different responses of a few log curves, especially gamma-ray, resistivity and neutron porosity, the formation tops for the Utica shale, the Trenton limestone, the Black River limestone and the Prairie du Chien sandstone are identified to confirm earlier authors’ work and provide a basis for my further work. From these, an isopach map showing the thickness of Trenton-Black River formation is created, indicating that its maximum thickness lies in the eastern basin and decreases gradually to the west. In order to obtain more detailed lithological information about the limestone formations at the thirty-five wells, (a) neutron-density and neutron-sonic crossplots, (b) mineral identification methods, including the M-N plot, MID plot, ϱmaa vs. Umaa MID plot, and the PEF plot, and (c) a modified mineral identification technique are applied to these wells. From this, compositions of the Trenton-Black River formation can be divided into three different rock types: pure limestone, partially dolomitized limestone, and shaly limestone. Maps showing the fraction of dolomite and shale indicate their geographic distribution, with dolomite present more in the western and southwestern basin, and shale more common in the north-central basin. Mineral identification is an independent check on the distribution found from other authors, who found similar distributions based on core descriptions. The Thomas Stieber method of analysis is best suited to sand-shale sequences, interpreting hree different distributions of shale within sand, including dispersed, laminated and structural. Since this method is commonly applied in clastic rocks, my work using the Thomas Stieber method is new, as an attempt to apply this technique, developed for clastics, to carbonate rocks. Based on the original assumption and equations with a corresponding change to the Trenton-Black River formation, feasibility of using the Thomas Stieber method in carbonates is tested. A graphical display of gamma-ray versus density porosity, using the properties of clean carbonate and pure shale, suggests the presence of laminated shale in fourteen wells in this study. Combined with Wilson’s study (2001), it is safe to conclude that when shale occurs in the Trenton-Black River formation, it tends to be laminated shale.

Social-Software-Portfolios im Einsatz

Die Dissertationsschrift widmet sich der Erforschung des Online-Lernens mittels Weblogs unter Anwendung der E-Portfolio Methode als einer seit mehreren Jahren verstärkt aufkommenden Lern- und Präsentationsform im Bildungskontext. Über mehrere Lehrveranstaltungen des Studiengangs "Angewandte Medien- und Kommunikationswissenschaft" an der Technischen Universität Ilmenau hinweg wurden drei Fallstudien gebildet. Innerhalb dieser wurde das Führen von eigenen E-Portfolio Blogs durch Studierende über einen Zeitraum von etwa drei Jahren evaluiert. Als Evaluationsziel wurde anhand spezifischer Fragestellungen ermittelt, wie das damit einhergehende selbstgesteuert-konnektive Lernen zu entsprechendem Erfolg führen kann. Hierbei wurde insbesondere die Teildimension Medienkompetenz im Spannungsfeld von Lernaktivität, Wissenserwerb und Informations-/Wissensmanagement betrachtet sowie weitere intervenierende Variablen, wie zum Beispiel Aufwand oder Akzeptanz, berücksichtigt. Inhaltlich wurden zunächst begriffliche Grundlagen dargestellt, die Nutzung von E-Portfolios in Theorie und Praxis beschrieben, Medienkompetenz-Ansätze detailliert aufgezeigt sowie in den Kontext von E-Portfolios gebracht und schließlich eine umfangreiche Analyse des Forschungsstandes aufbereitet. Diese gingen mit Erkenntnissen aus einer qualitativen Vorstudie in Form von fünf leitfadengestützten Experteninterviews einher. Die darauf aufbauende Hauptstudie widmete sich anschließend der Erhebung und Auswertung quantitativer Daten anhand von Online-Befragungen mit den Studierenden zu fünf Zeitpunkten aus intra- und interindividueller Perspektive. Als markanteste empirische Erkenntnis der Arbeit kann festgehalten werden, dass es durch das selbstgesteuert-konnektive Lernen mit E-Portfolio Blogs zu einer nachhaltigen Förderung der Medienkompetenz kommt, die sich auch in signifikanten Zusammenhängen mit den anderen Teildimensionen und intervenierenden Variablen widerspiegelt. Darüber hinaus bieten sich aber auch Potenziale für eine steigende Lernaktivität, einen ansteigenden Wissenserwerb und ein verbessertes Informations-/Wissensmanagement, die es aber noch weiterführend zu erforschen gilt. Demgegenüber können allerdings der entstehende und kontinuierlich hohe Aufwand sowie die erforderliche (Eigen-) Motivation als entscheidende Herausforderungen dieser Lernmethode identifiziert werden.

Stochastic search for semiparametric linear regression models

This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar [Ann. Statist. 15(3) (1987) 1131–1154]. The idea is to generate a random finite subset of a parameter space which will automatically contain points which are very close to an unknown true parameter. The motivation for this procedure comes from recent work of Dümbgen et al. [Ann. Statist. 39(2) (2011) 702–730] on regression models with log-concave error distributions.

Dose–effect relationship in routine outpatient psychotherapy: Does treatment duration matter?

Objective: There is an ongoing debate concerning how outcome variables change during the course of psychotherapy. We compared the dose–effect model, which posits diminishing effects of additional sessions in later treatment phases, against a model that assumes a linear and steady treatment progress through termination. Method: Session-by-session outcome data of 6,375 outpatients were analyzed, and participants were categorized according to treatment length. Linear and log-linear (i.e., negatively accelerating) latent growth curve models (LGCMs) were estimated and compared for different treatment length categories. Results: When comparing the fit of the various models, the log-linear LGCMs assuming negatively accelerating treatment progress consistently outperformed the linear models irre- spective of treatment duration. The rate of change was found to be inversely related to the length of treatment. Conclusion: As proposed by the dose–effect model, the expected course of improvement in psychotherapy appears to follow a negatively accelerated pattern of change, irrespective of the duration of the treatment. However, our results also suggest that the rate of change is not constant across various treatment lengths. As proposed by the “good enough level” model, longer treatments are associated with less rapid rates of change.

Feeding mastitis milk to organic dairy calves: effect on health and performance during suckling and on udder health at first calving

BackgroundInfection pathways of S. aureus udder infections in heifers are still not well understood. One hypothesis is that calves become infected with S. aureus via feeding mastitis milk. Especially on small-scale farms, pasteurisers are not economic. The purpose of this randomised comparative study was to investigate the influence of feeding milk containing S. aureus genotype B (SAGTB) on the health and development of calves and udder health of the respective heifers. Additionally, a method reducing the bacterial load to obtain safer feeding milk was tested. Thirty-four calves were fed mastitis milk from cows with subclinical SAGTB mastitis. One group was fed untreated milk (UMG). For the other group, milk was thermised at 61°C for one minute (heat treated milk group¿=¿HMG). After weaning, calves were followed up until first calving. A milk sample of these heifers was taken at first milking to compare udder health of both groups.ResultsThermisation of milk led to an effective reduction of S. aureus in the feeding milk. 78% of the analysed pools were free of S. aureus, a reduction of at least one log was obtained in the other pools.Quarter milk samples revealed that two heifers had a S. aureus intramammary infection, but caused by a genotype different from genotype B.During the suckling period, the UMG had a significantly higher incidence rate of 1.09 diarrhoea cases per 100 calf days at risk compared to 0.26 cases per 100 calf days in the HMG (p¿<¿0.05).ConclusionsUnder the conditions of this study, no effects of feeding milk containing SAGTB on udder health after first calving were observed. But a power analysis indicated that the sample size in the current setup is insufficient to allow for assessment on mastitis risk after SAGTB exposition, as a minimal number of 4 calves infected (vs. 0 in the HMG) would have shown significant effects. High bacterial load, however, was associated with an increased incidence rate of diarrhoea. Thus, thermisation as a minimal preventive measure before feeding mastitis milk to calves might be beneficial for maintaining calf health.