Multiscale methods for shape constraints in deconvolution: Confidence statements for qualitative features

We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We investigate the moderately ill-posed setting, where the Fourier transform of the error density in the deconvolution model is of polynomial decay. For multiscale testing, we consider a calibration, motivated by the modulus of continuity of Brownian motion. We investigate the performance of our results from both the theoretical and simulation based point of view. A major consequence of our work is that the detection of qualitative features of a density in a deconvolution problem is a doable task, although the minimax rates for pointwise estimation are very slow.

Reporting of statistical results in prosthodontic and implantology journals: p values or confidence intervals?

PURPOSE Confidence intervals (CIs) are integral to the interpretation of the precision and clinical relevance of research findings. The aim of this study was to ascertain the frequency of reporting of CIs in leading prosthodontic and dental implantology journals and to explore possible factors associated with improved reporting. MATERIALS AND METHODS Thirty issues of nine journals in prosthodontics and implant dentistry were accessed, covering the years 2005 to 2012: The Journal of Prosthetic Dentistry, Journal of Oral Rehabilitation, The International Journal of Prosthodontics, The International Journal of Periodontics & Restorative Dentistry, Clinical Oral Implants Research, Clinical Implant Dentistry and Related Research, The International Journal of Oral & Maxillofacial Implants, Implant Dentistry, and Journal of Dentistry. Articles were screened and the reporting of CIs and P values recorded. Other information including study design, region of authorship, involvement of methodologists, and ethical approval was also obtained. Univariable and multivariable logistic regression was used to identify characteristics associated with reporting of CIs. RESULTS Interrater agreement for the data extraction performed was excellent (kappa = 0.88; 95% CI: 0.87 to 0.89). CI reporting was limited, with mean reporting across journals of 14%. CI reporting was associated with journal type, study design, and involvement of a methodologist or statistician. CONCLUSIONS Reporting of CI in implant dentistry and prosthodontic journals requires improvement. Improved reporting will aid appraisal of the clinical relevance of research findings by providing a range of values within which the effect size lies, thus giving the end user the opportunity to interpret the results in relation to clinical practice.

Diagnostic confidence and image quality of CT pulmonary angiography at 100 kVp in overweight and obese patients.

AIM To compare image quality and diagnostic confidence of 100 kVp CT pulmonary angiography (CTPA) in patients with body weights (BWs) below and above 100kg. MATERIALS AND METHODS The present retrospective study comprised 216 patients (BWs of 75-99kg, 114 patients; 100-125kg, 88 patients; >125kg, 14 patients), who received 100 kVp CTPA to exclude pulmonary embolism. The attenuation was measured and the contrast-to-noise ratio (CNR) was calculated in the pulmonary trunk. Size-specific dose estimates (SSDEs) were evaluated. Three blinded radiologists rated subjective image quality and diagnostic confidence. Results between the BW groups and between three body mass index (BMI) groups (BMI <25kg/m(2), BMI = 25-29.9kg/m(2), and BMI ≥30kg/m(2), i.e., normal weight, overweight, and obese patients) were compared using the Kruskal-Wallis test. RESULTS Vessel attenuation was higher and SDDE was lower in the 75-99kg group than at higher BWs (p-values between <0.001 and 0.03), with no difference between the 100-125 and >125kg groups (p = 0.892 and 1). Subjective image quality and diagnostic confidence were not different among the BW groups (p = 0.225 and 1). CNR was lower (p < 0.006) in obese patients than in normal weight or overweight subjects. Diagnostic confidence was not different in the BMI groups (p = 0.105). CONCLUSION CTPA at 100 kVp tube voltage can be used in patients weighing up to 125kg with no significant deterioration of subjective image quality and confidence. The applicability of 100 kVp in the 125-150kg BW range needs further testing in larger collectives.

Prospective randomised comparison of diagnostic confidence and image quality with normal-dose and low-dose CT pulmonary angiography at various body weights.

OBJECTIVES To find a threshold body weight (BW) below 100 kg above which computed tomography pulmonary angiography (CTPA) using reduced radiation and a reduced contrast material (CM) dose provides significantly impaired quality and diagnostic confidence compared with standard-dose CTPA. METHODS In this prospectively randomised study of 501 patients with suspected pulmonary embolism and BW <100 kg, 246 were allocated into the low-dose group (80 kVp, 75 ml CM) and 255 into the normal-dose group (100 kVp, 100 ml CM). Contrast-to-noise ratio (CNR) in the pulmonary trunk was calculated. Two blinded chest radiologists independently evaluated subjective image quality and diagnostic confidence. Data were compared between the normal-dose and low-dose groups in five BW subgroups. RESULTS Vessel attenuation did not differ between the normal-dose and low-dose groups within each BW subgroup (P = 1.0). The CNR was higher with the normal-dose compared with the low-dose protocol (P < 0.006) in all BW subgroups except for the 90-99 kg subgroup (P = 0.812). Subjective image quality and diagnostic confidence did not differ between CT protocols in all subgroups (P between 0.960 and 1.0). CONCLUSIONS Subjective image quality and diagnostic confidence with 80 kVp CTPA is not different from normal-dose protocol in any BW group up to 100 kg. KEY POINTS • 80 kVp CTPA is safe in patients weighing <100 kg • Reduced radiation and iodine dose still provide high vessel attenuation • Image quality and diagnostic confidence with low-dose CTPA is good • Diagnostic confidence does not deteriorate in obese patients weighing <100 kg.

Optimal Confidence Bands for Shape-Restricted Curves

Let Y be a stochastic process on [0,1] satisfying dY(t)=n 1/2 f(t)dt+dW(t) , where n≥1 is a given scale parameter (`sample size'), W is standard Brownian motion and f is an unknown function. Utilizing suitable multiscale tests, we construct confidence bands for f with guaranteed given coverage probability, assuming that f is isotonic or convex. These confidence bands are computationally feasible and shown to be asymptotically sharp optimal in an appropriate sense.

Confidence Bands for Isotonic Median Curves using Sign-Tests

Suppose that one observes independent random variables (X1, Y1), (X2, Y2), …, (Xn, Yn) in R2 with unknown distributions, except that Median(Yi | Xi = M(x) for some unknown isotonic function M. We describe an explicit algorithm for the computation of confidence bands for the median function M whose running time is of order O(n2). The bands rely on multiscale sign tests and are shown to have desirable asymptotic properties.

Increasing Scientific Confidence in Adverse Outcome Pathways: Application of Tailored Bradford-Hill Considerations for Evaluating Weight of Evidence.

Systematic consideration of scientific support is a critical element in developing and, ultimately, using adverse outcome pathways (AOPs) for various regulatory applications. Though weight of evidence (WoE) analysis has been proposed as a basis for assessment of the maturity and level of confidence in an AOP, methodologies and tools are still being formalized. The Organization for Economic Co-operation and Development (OECD) Users' Handbook Supplement to the Guidance Document for Developing and Assessing AOPs (OECD 2014a; hereafter referred to as the OECD AOP Handbook) provides tailored Bradford-Hill (BH) considerations for systematic assessment of confidence in a given AOP. These considerations include (1) biological plausibility and (2) empirical support (dose-response, temporality, and incidence) for Key Event Relationships (KERs), and (3) essentiality of key events (KEs). Here, we test the application of these tailored BH considerations and the guidance outlined in the OECD AOP Handbook using a number of case examples to increase experience in more transparently documenting rationales for assigned levels of confidence to KEs and KERs, and to promote consistency in evaluation within and across AOPs. The major lessons learned from experience are documented, and taken together with the case examples, should contribute to better common understanding of the nature and form of documentation required to increase confidence in the application of AOPs for specific uses. Based on the tailored BH considerations and defining questions, a prototype quantitative model for assessing the WoE of an AOP using tools of multi-criteria decision analysis (MCDA) is described. The applicability of the approach is also demonstrated using the case example aromatase inhibition leading to reproductive dysfunction in fish. Following the acquisition of additional experience in the development and assessment of AOPs, further refinement of parameterization of the model through expert elicitation is recommended. Overall, the application of quantitative WoE approaches hold promise to enhance the rigor, transparency and reproducibility for AOP WoE determinations and may play an important role in delineating areas where research would have the greatest impact on improving the overall confidence in the AOP.

Szene, in: Hector Berlioz: Roméo et Juliette, Confidence à la nuit

Signatur des Originals: S 36/G03792

DISTRIBUTION FUNCTIONS, MEAN SQUARED ERRORS, AND CONFIDENCE LIMITS FOR RIDGE REGRESSION ESTIMATORS

A large number of ridge regression estimators have been proposed and used with little knowledge of their true distributions. Because of this lack of knowledge, these estimators cannot be used to test hypotheses or to form confidence intervals.^ This paper presents a basic technique for deriving the exact distribution functions for a class of generalized ridge estimators. The technique is applied to five prominent generalized ridge estimators. Graphs of the resulting distribution functions are presented. The actual behavior of these estimators is found to be considerably different than the behavior which is generally assumed for ridge estimators.^ This paper also uses the derived distributions to examine the mean squared error properties of the estimators. A technique for developing confidence intervals based on the generalized ridge estimators is also presented. ^

Robust effect sizes and their confidence intervals for group difference between trajectories in hierarchical linear growth model

Hierarchical linear growth model (HLGM), as a flexible and powerful analytic method, has played an increased important role in psychology, public health and medical sciences in recent decades. Mostly, researchers who conduct HLGM are interested in the treatment effect on individual trajectories, which can be indicated by the cross-level interaction effects. However, the statistical hypothesis test for the effect of cross-level interaction in HLGM only show us whether there is a significant group difference in the average rate of change, rate of acceleration or higher polynomial effect; it fails to convey information about the magnitude of the difference between the group trajectories at specific time point. Thus, reporting and interpreting effect sizes have been increased emphases in HLGM in recent years, due to the limitations and increased criticisms for statistical hypothesis testing. However, most researchers fail to report these model-implied effect sizes for group trajectories comparison and their corresponding confidence intervals in HLGM analysis, since lack of appropriate and standard functions to estimate effect sizes associated with the model-implied difference between grouping trajectories in HLGM, and also lack of computing packages in the popular statistical software to automatically calculate them. ^ The present project is the first to establish the appropriate computing functions to assess the standard difference between grouping trajectories in HLGM. We proposed the two functions to estimate effect sizes on model-based grouping trajectories difference at specific time, we also suggested the robust effect sizes to reduce the bias of estimated effect sizes. Then, we applied the proposed functions to estimate the population effect sizes (d ) and robust effect sizes (du) on the cross-level interaction in HLGM by using the three simulated datasets, and also we compared the three methods of constructing confidence intervals around d and du recommended the best one for application. At the end, we constructed 95% confidence intervals with the suitable method for the effect sizes what we obtained with the three simulated datasets. ^ The effect sizes between grouping trajectories for the three simulated longitudinal datasets indicated that even though the statistical hypothesis test shows no significant difference between grouping trajectories, effect sizes between these grouping trajectories can still be large at some time points. Therefore, effect sizes between grouping trajectories in HLGM analysis provide us additional and meaningful information to assess group effect on individual trajectories. In addition, we also compared the three methods to construct 95% confident intervals around corresponding effect sizes in this project, which handled with the uncertainty of effect sizes to population parameter. We suggested the noncentral t-distribution based method when the assumptions held, and the bootstrap bias-corrected and accelerated method when the assumptions are not met.^