Nonparametric Curve Fitting Research Articles

Learning Novelty Detection Outside a Class of Random Curves with Application to COVID-19 Growth

Abstract Let a class of proper curves is specified by positive examples only. We aim to propose a learning novelty detection algorithm that decides whether a new curve is outside this class or not. In opposite to the majority of the literature, two sources of a curve variability are present, namely, the one inherent to curves from the proper class and observations errors’. Therefore, firstly a decision function is trained on historical data, and then, descriptors of each curve to be classified are learned from noisy observations.When the intrinsic variability is Gaussian, a decision threshold can be established from T 2 Hotelling distribution and tuned to more general cases. Expansion coefficients in a selected orthogonal series are taken as descriptors and an algorithm for their learning is proposed that follows nonparametric curve fitting approaches. Its fast version is derived for descriptors that are based on the cosine series. Additionally, the asymptotic normality of learned descriptors and the bound for the probability of their large deviations are proved. The influence of this bound on the decision threshold is also discussed.The proposed approach covers curves described as functional data projected onto a finite-dimensional subspace of a Hilbert space as well a shape sensitive description of curves, known as square-root velocity (SRV). It was tested both on synthetic data and on real-life observations of the COVID-19 growth curves.

Simulation and analysis on the ship energy efficiency operational indicator for bulk carriers by Monte Carlo simulation method

The ship energy efficiency management is an important topic in the field of the energy management onboard and the exhaust gases emission nowadays. The advanced model plays a vital role to improve the ship energy efficiency management when considering the variable factors. The establishment of the ship energy efficiency model through energy efficiency operational indicator (EEOI) index has been conducted through Monte Carlo simulation method along with using the operation data of a bulk carrier. A bulk carrier is chosen, namely, M/V NSU JUSTICE 250,000 DWT of VINIC Shipping Transportation Company in Vietnam. This research uses the real operational data to perform a statistical methodology which calculates the various factors used to calculate EEOI. This method is supported by Matlab program through the curve fitting tool. The normal distribution estimation and the kernel density estimation method are used for the parametric curve fitting and non-parametric curve fitting, respectively. The average weather condition (wind speed and wave height) and the fouling condition of hull have been investigated and compared with the research results. The validation of the proposed methods has been conducted through the study of the external factors influencing the research results. The research result shows the optimal operational data for the fuel consumption at each certain voyage. This paper is useful for the ship-owners and the ship-operators in the field of the ship energy efficiency management.

A High-Throughput Phenotyping Pipeline for Image Processing and Functional Growth Curve Analysis.

High-throughput phenotyping system has become more and more popular in plant science research. The data analysis for such a system typically involves two steps: plant feature extraction through image processing and statistical analysis for the extracted features. The current approach is to perform those two steps on different platforms. We develop the package “implant” in R for both robust feature extraction and functional data analysis. For image processing, the “implant” package provides methods including thresholding, hidden Markov random field model, and morphological operations. For statistical analysis, this package can produce nonparametric curve fitting with its confidence region for plant growth. A functional ANOVA model to test for the treatment and genotype effects on the plant growth dynamics is also provided.

Penalized spline smoothing using Kaplan-Meier weights with censored data.

In this paper, we consider the problem of nonparametric curve fitting in the specific context of censored data. We propose an extension of the penalized splines approach using Kaplan-Meier weights to take into account the effect of censorship and generalized cross-validation techniques to choose the smoothing parameter adapted to the case of censored samples. Using various simulation studies, we analyze the effectiveness of the censored penalized splines method proposed and show that the performance is quite satisfactory. We have extended this proposal to a generalized additive models (GAM) framework introducing a correction of the censorship effect, thus enabling more complex models to be estimated immediately. A real dataset from Stanford Heart Transplant data is also used to illustrate the methodology proposed, which is shown to be a good alternative when the probability distribution for the response variable and the functional form are not known in censored regression models.

Impact of Early Salvage Radiation Therapy in Patients with Persistently Elevated or Rising Prostate-specific Antigen After Radical Prostatectomy

BackgroundSalvage radiation therapy (SRT) is a recommended treatment option for biochemical recurrence after radical prostatectomy (RP). However, its effectiveness may be limited to specific categories of patients. ObjectiveWe aimed to identify the optimal candidates for early SRT after RP. Design, setting, and participantsThe study included 925 node-negative patients treated with SRT after RP at seven institutions. Patients received SRT for either prostate-specific antigen (PSA) rising, or PSA persistence after RP that was defined as PSA level ≥0.1 ng/ml at 1 mo after surgery. All patients received local radiation to the prostate and seminal vesicle bed. Outcome measurements and statistical analysisThe primary outcome measured was distant metastasis after SRT. Regression tree analysis was used to develop a risk-stratification tool. Multivariable Cox regression analysis and nonparametric curve fitting methods were used to explore the relationship between PSA level at SRT and the probability of metastasis-free survival at 8 yr. Results and limitationsAt a median follow-up of 8.0 yr, 130 patients developed distant metastasis. At multivariable analysis, pre-SRT PSA level was significantly associated with distant metastasis (hazard ratio: 1.06, p<0.0001). However, when patients were stratified into five risk groups using regression tree analysis (area under the curve: 85%), early SRT administration provided better metastasis-free survival in three groups only: (1) low risk: undetectable PSA after RP, Gleason score ≤7, and tumour stage ≥pT3b, (2) intermediate risk: undetectable PSA after RP with Gleason score ≥8, (3) high risk: PSA persistence after RP with Gleason score ≤7. ConclusionsWe developed an accurate risk stratification tool to facilitate the individualised recommendation for early SRT based on prostate cancer characteristics. Early SRT proved to be beneficial only in selected groups of patients who are more likely to be affected by clinically significant but not yet systemic recurrence at the time of salvage treatment administration. Patient summaryIn patients affected by prostate cancer recurrence after radical prostatectomy, the early administration of salvage radiation therapy is beneficial only for selected subgroups of patients. In this study, these groups of patients were identified.

Impact of Postoperative Radiotherapy in Men with Persistently Elevated Prostate-specific Antigen After Radical Prostatectomy for Prostate Cancer: A Long-term Survival Analysis

BackgroundProstate cancer (PCa) patients with prostate-specific antigen (PSA) persistence after radical prostatectomy (RP) are at increased risk of mortality, although the natural history of these men is heterogeneous and the optimal management has not been established. ObjectiveTo develop a model to predict cancer-specific mortality (CSM) and to test the impact of radiotherapy (RT) on survival in this setting. Design, setting, and participantsWe identified 496 patients treated with RP and lymph node dissection at two referral centers between 1994 and 2014 who had PSA persistence, defined as a PSA level between 0.1 and 2 ng/ml at 6–8 wk after RP. Outcome measurements and statistical analysesA multivariable model predicting CSM was developed. We assessed whether the impact of postoperative PSA levels on survival differed according to baseline CSM risk. The nonparametric curve fitting method was then used to explore the relationship between baseline CSM risk and 10-yr CSM rates according to postoperative RT. Results and limitationsMedian follow-up for survivors was 110 mo. Overall, 49 patients experienced CSM. The 10-yr CSM-free survival was 88%. Pathologic grade group and pathologic stage were independent predictors of CSM (all p=0.01). The association between CSM-free survival and PSA at 6–8 wk differed by the baseline CSM risk, whereby the effect of increasing PSA was evident only in patients with a CSM risk of ≥10%. Postoperative RT was beneficial when the predicted risk of CSM was ≥30% (p=0.001 by an interaction test). Our study is limited by its retrospective design. ConclusionsIncreasing PSA levels should be considered as predictors of mortality exclusively in men with worse pathologic characteristics. Postoperative RT in this setting was associated with a survival benefit in patients with a CSM risk of ≥30%. Conversely, individuals with a CSM risk of <30% should be initially managed expectantly. Patient summaryNot all patients with prostate-specific antigen persistence have a poor prognosis. Pathologic characteristics should be used to estimate the risk of cancer-specific mortality in these individuals and to identify patients who could benefit from postoperative radiotherapy.

Locally Adaptive Smoothing with Markov Random Fields and Shrinkage Priors.

We present a locally adaptive nonparametric curve fitting method that operates within a fully Bayesian framework. This method uses shrinkage priors to induce sparsity in order-k differences in the latent trend function, providing a combination of local adaptation and global control. Using a scale mixture of normals representation of shrinkage priors, we make explicit connections between our method and kth order Gaussian Markov random field smoothing. We call the resulting processes shrinkage prior Markov random fields (SPMRFs). We use Hamiltonian Monte Carlo to approximate the posterior distribution of model parameters because this method provides superior performance in the presence of the high dimensionality and strong parameter correlations exhibited by our models. We compare the performance of three prior formulations using simulated data and find the horseshoe prior provides the best compromise between bias and precision. We apply SPMRF models to two benchmark data examples frequently used to test nonparametric methods. We find that this method is flexible enough to accommodate a variety of data generating models and offers the adaptive properties and computational tractability to make it a useful addition to the Bayesian nonparametric toolbox.

Evaluating the effect of time from prostate cancer diagnosis to radical prostatectomy on cancer control: Can surgery be postponed safely?

ObjectiveTo test the prognostic role of treatment delay in patients affected by prostate cancer (PCa). Materials and methodsThe study included 2,653 patients treated with radical prostatectomy (RP) at a single institution between 2006 and 2011. The evaluated outcomes were biochemical recurrence (BCR) and clinical recurrence (CR). Multivariable Cox regression analysis was used to test the association between time from diagnosis to RP and oncological outcomes. Nonparametric curve fitting methods were used to graphically explore the relationship between time from diagnosis to RP and oncological outcomes. Sensitivity analyses were repeated in the subgroups of low-, intermediate-, and high-risk patients. ResultsAt median follow-up of 56 months (interquartile range: 26, 92), 283 patients experienced BCR, and 84 patients developed CR. Median time from PCa diagnosis to surgery was 2.8 months (interquartile range: 1.6, 4.7). At multivariable Cox regression analysis, time from biopsy to RP was significantly associated with an increased risk of BCR (hazard ratio = 1.02, P = 0.0005) and CR (hazard ratio = 1.03, P = 0.0002). Using Nonparametric curve fitting methods, a significant increased risk of BCR and CR after approximately 18 months was observed. However, when sensitivity analyses were repeated according to risk groups, this effect was maintained in high-risk patients only, and such time interval was reduced to 12 months. ConclusionsDespite the overall trend on higher rate of cancer relapse after RP, the effect of treatment delay from biopsy to RP was significantly evident in high-risk patients only. Even in high-risk patients surgical treatment can be postponed safely, but not beyond the 12-month landmark.

Long-term Impact of Adjuvant Versus Early Salvage Radiation Therapy in pT3N0 Prostate Cancer Patients Treated with Radical Prostatectomy: Results from a Multi-institutional Series

BackgroundThree prospective randomised trials reported discordant findings regarding the impact of adjuvant radiation therapy (aRT) versus observation for metastasis-free survival (MFS) and overall survival (OS) among patients with pT3N0 prostate cancer treated with radical prostatectomy (RP). None of these trials systematically included patients who underwent early salvage radiation therapy (esRT). ObjectiveTo test the hypothesis that aRT was associated with better cancer control and survival compared with observation followed by esRT. Design, setting, and participantsUsing a multi-institutional cohort from seven tertiary referral centres, we retrospectively identified 510 pT3pN0 patients with undetectable prostate-specific antigen (PSA) after RP between 1996 and 2009. Patients were stratified into two groups: aRT (group 1) versus observation followed by esRT in case of PSA relapse (group 2). Specifically, esRT was administered at a PSA level ≤0.5ng/ml. InterventionWe compared aRT versus observation followed by esRT. Outcome measurements and statistical analysisThe evaluated outcomes were MFS and OS. Multivariable Cox regression analyses tested the association between groups (aRT vs observation followed by esRT) and oncologic outcomes. Covariates consisted of pathologic stage (pT3a vs pT3b or higher), pathologic Gleason score (≤6, 7, or ≥8), surgical margin status (negative vs positive), and year of surgery. An interaction with groups and baseline patient risk was tested for the hypothesis that the impact of aRT versus observation followed by esRT was different by pathologic characteristics. The nonparametric curve fitting method was used to explore graphically the relationship between MFS and OS at 8 yr and baseline patient risk (derived from the multivariable analysis). Results and limitationsOverall, 243 patients (48%) underwent aRT, and 267 (52%) underwent initial observation. Within the latter group, 141 patients experienced PSA relapse and received esRT. Median follow-up after RP was 94 mo (interquartile range [IQR]: 53–126) and 92 mo (IQR: 70–136), respectively (p=0.2). MFS (92% vs 91%; p=0.9) and OS (89% vs 92%; p=0.9) at 8 yr after surgery were not significantly different between the two groups. These results were confirmed in multivariable analysis, in which observation followed by esRT was not associated with a significantly higher risk of distant metastasis (hazard ratio [HR]: 1.35; p=0.4) and overall mortality (HR: 1.39; p=0.4) compared with aRT. Using the nonparametric curve fitting method, a comparable proportion of MFS and OS at 8 yr among groups was observed regardless of pathologic cancer features (p=0.9 and p=0.7, respectively). Limitations consisted of the retrospective nature of the study and the relatively small size of the patient population. ConclusionsAt long-term follow-up, no significant differences between aRT and esRT were observed for MFS and OS. Our study, although based on retrospective data, suggests that esRT does not compromise cancer control and potentially reduces overtreatment associated with aRT. Patient summaryAt long-term follow-up, no significant differences in terms of distant metastasis and mortality were observed between immediate postoperative adjuvant radiation therapy (aRT) and initial observation followed by early salvage radiation therapy (esRT) in case of prostate-specific antigen relapse. Our study suggests that esRT does not compromise cancer control and potentially reduces overtreatment associated with aRT.

Exploring Curvilinearity Through Fractional Polynomials in Management Research

Imprecise theories do not give enough guidelines for empirical analyses. A paradigmatic shift from linear to curvilinear relationships is necessary to advance management theories. Within the framework of the abductive generation of theories, the authors present a data exploratory technique for the identification of functional relationships between variables. Originating in medical research, the method uses fractional polynomials to test for alternative curvilinear relationships. It is a compromise between nonparametric curve fitting and conventional polynomials. The multivariable fractional polynomial (MFP) technique is a good tool for exploratory research when theoretical knowledge is nonspecific and thus very useful in phenomena discovery. The authors conduct simulations to demonstrate MFP’s performance in various scenarios. The technique’s major benefit is the uncovering of nontraditional shapes that cannot be modeled by logarithmic or quadratic functions. While MFP is not suitable for small samples, there does not seem to be a downside of overfitting the data as the fitted curves are very close to the true ones. The authors call for a routine application of the procedure in exploratory studies involving medium to large sample sizes.

Bayesian Scale Space Analysis of Differences in Images

This article considers the detection of image features in different spatial scales. The main focus is on capturing the scale-dependent differences in a pair of noisy images, but the technique developed can also be applied to the analysis of single images. The approach proposed uses Bayesian statistical modeling and simulation-based inference, and it can be viewed as a further development of SiZer technology, originally designed for nonparametric curve fitting. Numerical examples include artificial test images and a preliminary analysis of a pair of Landsat images used in satellite-based forest inventory. This article has supplementary material online.

Cockpit Protection Analysis for Digital Pilot against Soft Kill from High Power Microwave

A body finite difference time domain (FDTD) grid modeling engineering method and a simplified parallel FDTD algorithm are brought forward based on frequency-dependence electromagnetic equation by nonparametric curve fitting. By a shielded construction designed soft kill analysis against high power microwave (HPM) is carried out respectively on 3D simple and digital pilot in fighter model with a scale of 1:1, which is electrically huge and very complex in geometry and electromagnetic characteristics. The simulation tests show that the protective effectiveness to soft kill is good with shielded construction at 0.3-6GHz, HPM protective efficiency evaluation on digital pilot model is more optimistic and complex than that on simple pilot model, and speedup ratio of the presented approach can compare with that of the conventional method.

Extending the working calibration ranges of four hexachlorocyclohexane isomers in gas chromatography–electron capture detector by radial basis function neural network

A radial basis function neural network (RBFNN) method was developed for the first time to model the nonlinear calibration curves of four hexachlorocyclohexane (HCH) isomers, aiming to extend their working calibration ranges in gas chromatography–electron capture detector (GC–ECD). Other 14 methods, including seven parametric curve fitting methods, two nonparametric curve fitting methods, and five other artificial neural network (ANN) methods, were also developed and compared. Only the RBFNN method, with logarithm-transform and normalization operation on the calibration data, was able to model the nonlinear calibration curves of the four HCH isomers adequately. The RBFNN method accurately predicted the concentrations of HCH isomers within and out of the linear ranges in certified test samples. Furthermore, no significant difference (p>0.05) was found between the results of HCH isomers concentrations in water samples calculated with RBFNN method and ordinary least squares (OLS) method (R2>0.9990). Conclusively, the working calibration ranges of the four HCH isomers were extended from 0.08–60ng/ml to 0.08–1000ng/ml without sacrificing accuracy and precision by means of RBFNN. The outstanding nonlinear modeling capability of RBFNN, along with its universal applicability to various problems as a “soft” modeling method, should make the method an appealing alternative to traditional modeling methods in the calibration analyses of various systems besides the GC–ECD.

Discussion generale : quels enjeux pour l’imagerie?

To test the prognostic role of treatment delay in patients affected by prostate cancer (PCa).The study included 2,653 patients treated with radical prostatectomy (RP) at a single institution between 2006 and 2011. The evaluated outcomes were biochemical recurrence (BCR) and clinical recurrence (CR). Multivariable Cox regression analysis was used to test the association between time from diagnosis to RP and oncological outcomes. Nonparametric curve fitting methods were used to graphically explore the relationship between time from diagnosis to RP and oncological outcomes. Sensitivity analyses were repeated in the subgroups of low-, intermediate-, and high-risk patients.At median follow-up of 56 months (interquartile range: 26, 92), 283 patients experienced BCR, and 84 patients developed CR. Median time from PCa diagnosis to surgery was 2.8 months (interquartile range: 1.6, 4.7). At multivariable Cox regression analysis, time from biopsy to RP was significantly associated with an increased risk of BCR (hazard ratio = 1.02, P = 0.0005) and CR (hazard ratio = 1.03, P = 0.0002). Using Nonparametric curve fitting methods, a significant increased risk of BCR and CR after approximately 18 months was observed. However, when sensitivity analyses were repeated according to risk groups, this effect was maintained in high-risk patients only, and such time interval was reduced to 12 months.Despite the overall trend on higher rate of cancer relapse after RP, the effect of treatment delay from biopsy to RP was significantly evident in high-risk patients only. Even in high-risk patients surgical treatment can be postponed safely, but not beyond the 12-month landmark.

The impact of changes to heroin supply on blood-borne virus notifications and injecting related harms in New South Wales, Australia

BackgroundIn early 2001 Australia experienced a sudden and unexpected disruption to heroin availability, know as the 'heroin shortage'. This 'shortage has been linked to a decrease in needle and syringe output and therefore possibly a reduction in injecting drug use. We aimed to examine changes, if any, in blood-borne viral infections and presentations for injecting related problems related to injecting drug use following the reduction heroin availability in Australia, in the context of widespread harm reduction measures.MethodsTime series analysis of State level databases on HIV, hepatitis B, hepatitis C notifications and hospital and emergency department data. Examination of changes in HIV, hepatitis B, hepatitis C notifications and hospital and emergency department admissions for injection-related problems following the onset of the heroin shortage; non-parametric curve-fitting of number of hepatitis C notifications among those aged 15–19 years.ResultsThere were no changes observed in hospital visits for injection-related problems. There was no change related to the onset heroin shortage in the number of hepatitis C notifications among persons aged 15–19 years, but HCV notifications have subsequently decreased in this group. No change occurred in HIV and hepatitis B notifications.ConclusionA marked reduction in heroin supply resulted in no increase in injection-related harm at the community level. However, a delayed decrease in HCV notifications among young people may be related. These changes occurred in a setting with widespread, publicly funded harm reduction initiatives.

The study of anaemia-related haemostasis impairment in haemodialysis patients by in vitro closure time test

It is known that anaemia in haemodialysis patients could contribute to haemostasis impairment. However, the precise relation between the degree of anaemia and the degree of haemostasis impairment is not known, nor the optimal level of hematocrit above which anaemia no longer disturbs haemostasis. Our study addresses these clinically relevant questions by employing in vitro closure time test, a new method in which the process of platelet adhesion and aggregation following vascular injury is simulated in vitro in samples of whole blood. We studied 63 haemodialysis patients, with 30 age-matched, healthy controls. Results show that patients with hematocrit below 0.32 (N=28) had significantly impaired primary haemostasis, in contrast to patients with hematocrit above 0.32 (N=35), as measured by both types of closure time test. A significant negative association was found between hematocrit values and closure time (CEPI cartridges: rho=-0.41, p<0.001; CADP cartridges: rho=-0.47, p<0.001). A multiple logistic regression model for predicting prolonged closure time confirmed this finding. Nonparametric curve fitting enabled estimation of the level of hematocrit at which the values of in vitro closure time in haemodialysis patients do not differ from those in the controls at approximately 0.35. ROC analysis confirmed this to be the optimal threshold for predicting prolonged closure time for both cartridges. By using in vitro closure time test, we confirmed that anaemia correlates with the severity of haemostasis impairment. We estimated the target level of hematocrit above which anaemia no longer affects haemostasis to be about 0.35. These new results (and new assay) appear to have clinical value for treating haemodialysis patients.

A note on methods of restoring consistency to the bootstrap

SUMMARY We consider the property of consistency and its relevance for determining the performance of the bootstrap. We analyse various parametric bootstrap approximations to the distributions of the Hodges and Stein estimators, whose behaviour is typical of that of super-efficient estimators employed in wavelet regression, kernel density estimation and nonparametric curve fitting. Our results reveal not only some of the difficulties in selecting good modifications to the intuitive bootstrap, but also that inconsistent bootstrap approximations may perform better than consistent versions even in large samples.

Predicting basal metabolic rate in the obese is difficult.

To reassess the validity of the Schofield equations for predicting basal metabolic rate (BMR) in the obese. The data collection compiled from many studies by Schofield in 1985. Nonparametric curve fitting and comparison of groups. BMR increases more slowly at heavier weights in men (above about 75 kg) and women (above about 65 kg), and to ignore this is to predict overestimates of BMR. Data obtained from studies of different populations show substantial differences, which are influential when data are combined. The Schofield equations are unsuitable for obese populations. Given that current Western populations exhibit prevalences of obesity many times greater than those in the Schofield database, this indicates the need for further study of suitable predictors for these individuals.

Standardization and Validation of the Body Weight Adjustment Regression Equations in Olympic Weightlifting

The problems in comparing the performances of Olympic weightlifters arise from the fact that the relationship between body weight and weightlifting results is not linear. In the present study, this relationship was examined by using a nonparametric curve fitting technique of robust locally weighted regression (LOWESS) on relatively large data sets of the weightlifting results made in top international competitions. Power function formulas were derived from the fitted LOWESS values to represent the relationship between the 2 variables in a way that directly compares the snatch, clean-and-jerk, and total weightlifting results of a given athlete with those of the world-class weightlifters (golden standards). A residual analysis of several other parametric models derived from the initial results showed that they all experience inconsistencies, yielding either underestimation or overestimation of certain body weights. In addition, the existing handicapping formulas commonly used in normalizing the performances of Olympic weightlifters did not yield satisfactory results when applied to the present data. It was concluded that the devised formulas may provide objective means for the evaluation of the performances of male weightlifters, regardless of their body weights, ages, or performance levels.

Standardization and Validation of the Body Weight Adjustment Regression Equations in Olympic Weightlifting

The problems in comparing the performances of Olympic weightlifters arise from the fact that the relationship between body weight and weightlifting results is not linear. In the present study, this relationship was examined by using a nonparametric curve fitting technique of robust locally weighted regression (LOWESS) on relatively large data sets of the weightlifting results made in top international competitions. Power function formulas were derived from the fitted LOWESS values to represent the relationship between the 2 variables in a way that directly compares the snatch, clean-and-jerk, and total weightlifting results of a given athlete with those of the world-class weightlifters (golden standards). A residual analysis of several other parametric models derived from the initial results showed that they all experience inconsistencies, yielding either underestimation or overestimation of certain body weights. In addition, the existing handicapping formulas commonly used in normalizing the performances of Olympic weightlifters did not yield satisfactory results when applied to the present data. It was concluded that the devised formulas may provide objective means for the evaluation of the performances of male weightlifters, regardless of their body weights, ages, or performance levels.