Bio-equivalence tests in functional data by maximum deviation

Over-dispersed count data are frequently observed in clinical trials where the primary endpoint is occurrence of clinical events. Sample sizes of comparative clinical trials with these data are typically calculated under negative binomial models or quasi-Poisson models with specified variance functions, or under the assumption that the specified "working" variance functions are correctly specified. In this article, we propose a sample size formula anticipating misspecifications of the working variance function. We derived a method based on the asymptotic distribution of a Wald test statistic with a sandwich-type robust variance estimator under quasi-Poisson models. Under misspecifications of the working variance function, the asymptotic variance of the estimator of the treatment effect is expressed as a form involving both true and working variance functions. Our sample size formula includes several existing formulas as special cases when the working variance function is correctly specified as the true variance function. We also consider a sensitivity analysis for possible misspecifications of the "true" variance function when estimating sample sizes using our formula. A simulation study demonstrated the adequacy of our formulas in finite sample size settings. An application to a clinical trial to evaluate the treatment effect on prevention of COPD exacerbation is provided.

To evaluate the relationships between anatomical, functional, and metabolic parameters and distant metastasis in the primary staging of rectal adenocarcinoma. Seventy-three patients with rectal adenocarcinoma, who underwent pelvic MRI and whole-body 18 F-FDG PET/MRI for staging, were included. Anatomical [T and N stages, extramural venous invasion (EMVI) and circumferential resection margin (CRM) statuses] and functional parameters [apparent diffusion coefficient (ADC) mean (mm²/sn × 10 -6 )] of primary tumor were recorded from pelvic MRI, and metabolic data (maximum standard uptake value (SUV max ), mean SUV (SUV mean ), metabolic tumor volume (MTV), total lesion glycolysis (TLG), and total lesion quotient (TLQ) were recorded from 18 F-FDG PET/MRI. Quantitative parameters combining functional and metabolic data (SUV max /ADC mean , SUV mean /ADC mean , MTV/ADC mean , TLG/ADC mean , TLQ/ADCmean) were calculated. Distant metastases were recorded via 18 F-FDG PET/MRI. To detect lung nodules, supplementary 18 F-FDG PET/CT scans of the thorax were utilized. Relationship between these parameters and distant metastasis, and their ability to predict for distant metastatic disease, were statistically evaluated. In the univariate logistic regression analysis, the SUV max (1.04; 1.0-1.08; P = 0.031), TLG (1.0; 1.0-1.005; P = 0.044), TLG/ADC mean (8.12; 1.04-63.78; P = 0.046), and presence of EMVI (4.13; 1.31-12.98; P = 0.015) (OR; CI; P ) were found to predict distant metastasis. In multivariate regression analysis, SUV max (1.05; 1.0-1.1; P = 0.023) and the presence of EMVI (6.82; 1.64-28.48; P = 0.008) were identified as independent predictors for distant metastatic disease (OR; CI; P ). Significant associations were detected between distant lymph node metastasis and T stage and the presence of EMVI, whereas significant associations were detected between the size of distant lymph node metastases and the SUV max , SUV mean , SUV max /ADC mean , and SUV mean /ADC mean ( P < 0.05). Patients with lung and other organ metastases had significantly greater TLG and TLG/ADC mean values ( P < 0.05). 18 F-FDG PET/MRI allows obtaining anatomical, functional, and metabolic parameters related to the primary tumor in a single session and has the potential to predict information regarding tumor behavior, including distant metastatic spread.

We propose a double bootstrap procedure for reducing coverage error in the confidence intervals of descriptive statistics for independent and identically distributed functional data. Through a series of Monte Carlo simulations, we compare the finite sample performance of single and double bootstrap procedures for estimating the distribution of descriptive statistics for independent and identically distributed functional data. At the cost of longer computational time, the double bootstrap with the same bootstrap method reduces confidence level error and provides improved coverage accuracy than the single bootstrap. Illustrated by a Canadian weather station data set, the double bootstrap procedure presents a tool for visualizing the distribution of the descriptive statistics for the functional data.

Oracle-efficient estimation and global inferences for variance function of functional data

When dealing with very large datasets of functional data, survey sampling approaches are useful in order to obtain estimators of simple functional quantities, without being obliged to store all the data. We propose a Horvitz―Thompson estimator of the mean trajectory. In the context of a superpopulation framework, we prove, under mild regularity conditions, that we obtain uniformly consistent estimators of the mean function and of its variance function. With additional assumptions on the sampling design we state a functional central limit theorem and obtain asymptotic confidence bands. Stratified sampling is studied in detail, and we also obtain a functional version of the usual optimal allocation rule, considering a mean variance criterion. These techniques are illustrated by a test population of N = 18 902 electricity meters for which we have individual electricity consumption measures every 30 minutes over one week. We show that stratification can substantially improve both the accuracy of the estimators and reduce the width of the global confidence bands compared with simple random sampling without replacement.

In a series of recent articles, Bradley Efron has pointed out that in large-scale multiple testing problems, the observed distribution of the test statistics often does not match the theoretical null distribution (Efron, 2004, 2007a,b, 2008). The correction, which he termed “empirical null”, has been a subject of controversy in the statistical community. In Efron (2007a), he made the case that, even when the theoretical model is correct, the observed distribution of the test statistics can look different from the theoretical null distribution simply because of correlation between the test statistics. Efron’s present article represents an important step forward in the understanding of this problem. As opposed to previous papers, where the the effect of correlation was treated within the context of multiple testing problems and false discovery rates, Efron’s present article breaks through the confusion by separating these two concepts and focusing on the core issue, which is the behavior of a large collection of correlated normal variables. Only then, as applications, he presents the implications for false discovery rate analysis when the correlated normal variables are z-scores in a large-scale multiple testing problem. I think this separation is crucial and helps get us nearer a new theory of inference for high-dimensional data. In what follows, I present my own interpretation of Efron’s results on how correlation affects the empirical distribution of normal variables. As a shortcut, I work in the countinous domain directly rather than with histogram bins and avoid the inclusion of unnecessary constraints such as normalization, which applies very specifically to microarray data. For simplicity, I assume all the variables are standard normal rather than belonging to a mixture model, but may have an arbitrary correlation structure. Using these results, I hope to answer the question raised in Efron (2007a) of whether large-scale correlation can substantially widen the observed histogram, as in Figure 1 in that paper and Efron’s current one. The theoretical arguments below indicate that this is unlikely. On the contrary, large-scale correlation has to be mostly positive in order to satisfy positive definite contraints, and as a result, correlation will most likely narrow and shift the observed histogram rather than widen it. An important implication is that a wide histogram may be an indication of the presence of true signal, rather than an artifact of correlation. Having a model for the observed distribution under correlation, I will suggest a new way of fitting an empirical null, which may be more appropriate in cases where the observed widening is larger than could be explained by correlation alone. I will conclude commenting briefly on the possibility of performing this kind of analysis with χ2 variates rather than normal. I will try to keep the notation close to that of Efron, but some discrepancies in notation will be inevitable.

Purpose: To evaluate the correlation between MRC dyspnea scale and CAT (COPD assesment scale) and each of them with clinical and functional parameters. Method: The study included COPD outpatients in stable stage. Clinical (including comorbidities) and functional data were collected. In each patient was recorded the degree of dyspnea (MRC scale), and CAT questionnaire score. In addition to basic descriptive statistical study, Pearson correlation coefficient was used, and a multiple linear regression between factors that had shown a significant correlation. Statistical significance was assigned to p Results: 94 patients were studied (76 men), 23 were current smokers, 49 patients had comorbidities (cardiologic disease in 20.2% of all). They had an average of 1.62 exacerbations in previous year (SD 0.49). The average value of CAT was 15.8 (SD 8.5). The degree of dyspnea according to MRC scale was 0 in 11 patients, 1 in 44, 2 in 27, 3 in 10 y 4 in 2 patients. There was a significant correlation between degree of MCR and CAT (p Conclusion: There is a significant correlation between MRC scale and CAT score. The parameter wich shows more correlation with MRC scale was FEV1 as percentage. The data that is associated independently with CAT questionnaire score was the number of exacerbations in previous year.

A topic which is becoming more and more popular in Functional Data Analysis is local inference, i.e., the continuous statistical testing of a null hypothesis along a domain of interest. The principal issue in this topic is the infinite amount of tested hypotheses, which can be seen as an extreme case of multiple comparisons problem.Anumber of quantities have been introduced in the literature of multivariate analysis in relation to the multiple comparisons problem. Arguably the most popular one is the False Discovery Rate (FDR), that measures the expected proportion of false discoveries (rejected null hypotheses) among all discoveries.We define FDR in the setting of functional data defined on a compact set of Rd. A continuous version of the Benjamini-Hochberg procedure is introduced, along with a definition of adjusted 𝑝-value function. Some general conditions are stated, under which the functional Benjamini-Hochberg (fBH) procedure provides control of FDR. We show how the procedure can be plugged-in with every parametric or nonparametric pointwise test, given that such test is exact. Finally, the proposed method - together with a nonparametric test - is applied to the analysis of the benchmark dataset of Canadian temperatures.

The statistical analysis of change-point detection and estimation has received much attention recently. A time point such that observations follow a certain statistical distribution up to that point and a different distribution – commonly of the same functional form but different parameters after that point – is called a change-point. Multiple change-point problems arise when we have more than one change-point. This paper develops a method for multivariate normally distributed data to detect change-points and estimate within-segment parameters using maximum likelihood estimation.

Optimal estimation of Gaofen-3B satellite attitude deviation based on echo frequency domain features

The maximum indicators of the functionality of a multiuser communication system are investigated under a change in the capacity of network edges. Based on the transmission routes of the maximum flows of the same type, the minimum cuts of the network are determined. The influence of changes in the capacity of the cut edges on the maximum allowable internodal flows under monopoly control modes is studied. The maximum values of the internodal flows correspond to the corners of the set of allowable flows satisfying the constraints of the model. A convex combination of vectors corresponding to the corners is used to estimate the relative changes in network characteristics during deformation of the set of feasible flows. Multi-criteria guaranteed estimates of the maximum feasible deviations from the reference indicators of the network functioning are formulated. Summary diagrams for networks with various structural features are provided.

Background: Relationship between comorbidities and lung disorder could depend on the type of lung disorder (parenchymal vs airway). Aim: Determine whether CT scans available from clinical routine assessments can be made comparable for developing a prediction function to estimate the probability of lung disorder types from functional data. Methods: Within the COSYCONET cohort study, 2,741 patients with COPD were recruited in 30 study centers. Assessments included spirometry, body plethysmography and diffusing capacity for CO. CT scans from 24 centres were evaluated regarding the type of lung disorder. Using logistic/linear regression analyses, associations between categorical/continuous measures of CTs and lung function were assessed. Results: 342 CT scans could be used in patients of categories GOLD 0-IV (mean (SD) age 65 (8) y; 34% female; 8% GOLD 0; 40% I/II; 52% III/IV). Regarding the binary emphysema score, FEV1/FVC, TLCO%pred, TLC%pred, specific airway resistance sRaw and absolute FEV1 were identified as predictors, resulting in 76% of patients correctly categorized (sensitivity for emphysema 78%). Analyses of the continuous scores lung density, 15-percentile of density and emphysema index were consistent with these findings. Conclusion: Results indicate that rather heterogeneous chest CT scans can be brought to a level of comparability that is sufficient to reveal meaningful associations between emphysema scoring and functional parameters. The functions will be used to investigate the impact of the type of lung disorder in the total COPD cohort. Competence Network Asthma/COPD funded by German Federal Ministry of Education and Research.

Ebstein's anomaly (EA) involves a displaced and dysplastic tricuspid valve resulting in an atrialized portion of the right ventricle and an enlargement of the functional right ventricle and right atrium. Biomarkers targeting heart failure such as brain natriuretic peptide (BNP) or haematological parameters [haemoglobin (Hb) and haematocrit (Hct)] are upregulated in states of pulmonary hypoperfusion. We hypothesized that decreased pulmonary perfusion dependent on the stage of right heart failure is a possible mechanism in EA, and that it can be correlated with cardiac magnetic resonance (CMR) parameters. The aim of this study was to investigate the relationship between BNP and haematological parameters with functional parameters from CMR and exercise testing in patients with EA. Twenty-five patients with non-corrected EA were studied prospectively (mean age 26 ± 14 years). BNP level was increased (74 ± 127 ng/L), and in 16% markedly above the heart failure cut-off level of 100 ng/L. Hb and Hct were increased above normal levels in 20 and 24% of patients, respectively. BNP and Hct/Hb correlated with CMR [total right/left (R/L)-Volume-Index, right atrium-end-diastolic volume index (EDVi), functional right ventricle (fRV)-EDVi, fRV-ejection fraction (EF), tricuspid regurgitation, pulmonary artery flow, and left ventricular EF] and exercise testing [workload/kg, oxygen uptake (VO2), ventilatory response to carbon dioxide production (VE/VCO2), oxygen (O2) pulse, and heart rate reserve]. The higher BNP and haematological parameters, the higher was the disease severity and the more limited was the physical exercise capacity. In this EA cohort, BNP levels and haematological parameters correlated well with functional data from CMR and exercise testing. The total R/L-Volume-Index and BNP, and to some extent hematological parameters, may be useful as prognostic markers in patients with EA.

IntroductionThe aim of this observational study was to investigate the prevalence of endotoxemia after surgery and its association with ICU length of stay.Methods102 patients admitted to a university ICU after surgery were recruited. Within four hours of admission, functional data were collected and APACHE II severity score calculated. Arterial blood samples were taken and endotoxemia was measured by chemiluminescence (Endotoxin Activity (EA)). Patients were stratified according to their endotoxin levels (low, intermediate and high) and according to their surgical procedures. Differences between endotoxin levels were assessed by ANOVA, accepting P < 0.05 as significant. Data are expressed as mean ± SD.ResultsEA levels were low in 68 (66%) patients, intermediate in 17 (17%) and high in 17 (17%). Age (61 ± 17 years) and APACHE II score 8.3 ± 3.7 (P = 0.542) were not significantly different in the three EA groups. Functional parameters on admission were similar between EA groups: white blood cells 11093 ± 4605 cells/mm3 (P = 0.385), heart rate 76 ± 16 bpm (P = 0.898), mean arterial pressure 88.8 ± 13.6 mmHg (P = 0.576), lactate 1.18 ± 0.77 mmol/L (P = 0.370), PaO2/FiO2 383 ± 109 mmHg (P = 0.474). Patients with high levels of EA were characterized by longer length of stay in the ICU: 1.9 ± 3.0 days in the low EA group, 1.8 ± 1.4 days in intermediate and 5.2 ± 7.8 days in high group (P = 0.038).Conclusions17% of our patients were characterized by high levels of endotoxemia as assessed by EA assay, despite their low level of complexity on admission. High levels of endotoxin were associated with a longer ICU length of stay.

The performances of three statistical approaches for assessing in vitro equivalence was evaluated with a set of 55 scenarios of realistic test (T) and reference (R) cascade impactor (CI) profiles (originally employed by the Product Quality Research Institute to evaluate the chi-square ratio statistic: CSRS) by comparing the outcomes against experts' opinion (surrogate for the truth). The three methods were (A) a stepwise aerodynamic particle size distribution (APSD) equivalence test integrating population bioequivalence (PBE) testing of impactor-sized mass (ISM) with the CSRS (PBE-CSRS approach), previously suggested by the USFDA; (B) the combination of PBE testing of single actuation content and ISM with the newly suggested modified CSRS (PBE-mCSRS approach), a method employing reference variance scaling; and (C) EMA's average bioequivalence (ABE approach). Based on Monte-Carlo simulations, both PBE-CSRS and ABE approaches resulted in high misclassification rates, the former with highest false-pass rate and the latter with highest false-fail rate at both ≥ 50% and ≥ 80% classification threshold values (the % of simulations or experts necessary to judge a given scenario as equivalent). Based on DeLong's tests, the PBE-mCSRS approach showed significantly better overall agreement with experts' opinion compared to the other approaches. Comparison of CSRS with mCSRS (both without PBE) suggested that the more discriminatory characteristics of the mCSRS method is based on the integration of variance scaling into the mCSRS method. Contrary to the ABE approach, the application of PBE-mCSRS approach for assessing APSD profiles of three dry powder inhaler (DPI) formulations supported the pharmacokinetic bioequivalence assessment of these formulations.