Nonparametric Alternatives Research Articles

Maximum Marginal Likelihood Estimation of a Monotonic Polynomial Generalized Partial Credit Model with Applications to Multiple Group Analysis.

We present a semi-parametric approach to estimating item response functions (IRF) useful when the true IRF does not strictly follow commonly used functions. Our approach replaces the linear predictor of the generalized partial credit model with a monotonic polynomial. The model includes the regular generalized partial credit model at the lowest order polynomial. Our approach extends Liang's (A semi-parametric approach to estimate IRFs, Unpublished doctoral dissertation, 2007) method for dichotomous item responses to the case of polytomous data. Furthermore, item parameter estimation is implemented with maximum marginal likelihood using the Bock-Aitkin EM algorithm, thereby facilitating multiple group analyses useful in operational settings. Our approach is demonstrated on both educational and psychological data. We present simulation results comparing our approach to more standard IRF estimation approaches and other non-parametric and semi-parametric alternatives.

Impact of Being Overweight on Factor VIII Dosing in 72 Children with Severe Hemophilia a Treated with Advate®, Kogenate® FS or Refacto AF®/Xyntha®

▪Introduction: The treatment of hemophilia A (HA) requires infusions of factor VIII (FVIII) concentrates. The number of FVIII units infused in order to obtain a specific circulating FVIII level is calculated with the formula: [body weight (BW) (kg) × desired FVIII increase (%)] / 2, with the assumption that each unit of FVIII infused per kg of BW increases the circulating FVIII level by 2 % 1. The aim of the present study was to evaluate the impact of several morphometrical parameters (BW, body mass index (BMI), BMI-for-age, fat mass index (FMI), height), age and type of coagulation factor concentrate on the FVIII recovery in a large group of children with severe haemophilia A who had previously taken part in pharmacokinetic studies using Advate®, Kogenate FS® or ReFacto AF/Xyntha®.Methods: A total of 72 children aged between 6 and 17 with severe HA carefully selected from 7 pharmacokinetic clinical trials using three recombinant FVIII concentrates were included in the analysis. The FVIII recovery was calculated using the maximum FVIII concentration measured at 15 and 30 minutes after infusion. Regression tree (RT) was used to identify predictors of FVIII recovery. RT-based models are non-linear and non-parametric alternatives to linear models for regression problems 2.Results: The median age was 14.5 years with a median FVIII recovery of 2.09 for all patients. The median FVIII recovery was not significantly different between the 3 coagulation factor groups (p=0.542) but was significantly different between BMI-for-age percentiles groups (p<0.001) with a median FVIII recovery of 1.53, 1.93, 2.15 and 2.59 for underweight, normal, overweight and obese children, respectively (Fig. 1). The median age was similar in these 4 groups (p=0.930). In multivariate analysis, 2 groups were created by RT (Fig. 2): patients with a BMI-for-age percentile < P95 (Group 1; Median [P25; P75] FVIII recovery: 1.94 [1.57; 2.21]) and patients with a BMI-for-age percentile ≥ P95 (Group 2; Median [P25; P75] FVIII recovery: 2.59 [2.39; 2.75]). The FVIII recovery was significantly different between these two groups (P<0.001) (Fig. 3).Conclusions: The BMI-for-age emerged as the strongest predictor of FVIII recovery in children aged between 6 and 17, with a cut-off value at the 95th percentile. Our findings support that dose calculation of FVIII to reach a specific FVIII target level should be adapted in overweight children since only a small fraction of FVIII distributes outside the vascular system 6. These results are consistent with previous studies conducted in adults with HA 4;5, and confirm that the long-held and current practice of applying an arbitrary and universal recovery of 2 to the calculations of FVIII dosage should be abolished. [Display omitted] [Display omitted] [Display omitted]

Nonparametric estimation of pair-copula constructions with the empirical pair-copula

A pair-copula construction is a decomposition of a multivariate copula into a structured system, called regular vine, of bivariate copulae or pair-copulae. The standard practice is to model these pair-copulae parametrically, inducing a model risk, with errors potentially propagating throughout the vine structure. The empirical pair-copula provides a nonparametric alternative, which is conjectured to still achieve the parametric convergence rate. Its main advantage for the user is that it does not require the choice of parametric models for each of the pair-copulae constituting the construction. It can be used as a basis for inference on dependence measures, for selecting an appropriate vine structure, and for testing for conditional independence.

Non-Normal Random Effects Models for Immunogenicity Assay Cut Point Determination

Administration of biological therapeutics can generate undesirable immune responses that may induce anti-drug antibodies (ADAs). Immunogenicity can negatively affect patients, ranging from mild reactive effect to hypersensitivity reactions or even serious autoimmune diseases. Assessment of immunogenicity is critical as the ADAs can adversely impact the efficacy and safety of the drug products. Well-developed and validated immunogenicity assays are required by the regulatory agencies as tools for immunogenicity assessment. Key to the development and validation of an immunogenicity assay is the determination of a cut point, which serves as the threshold for classifying patients as ADA positive(reactive) or negative. In practice, the cut point is determined as either the quantile of a parametric or nonparametric empirical distribution. The parametric method, which is often based on a normality assumption, may lead to biased cut point estimates when the normality assumption is violated. The non-parametric method, which yields unbiased estimates of the cut point, may have low efficiency when the sample size is small. As the distribution of immune responses are often skewed and sometimes heavy-tailed, we propose two non-normal random effects models for cut point determination. The random effects, following a skew-t or log-gamma distribution, can incorporate the skewed and heavy-tailed responses and the correlation among repeated measurements. Simulation study is conducted to compare the proposed method with the current normal and nonparametric alternatives. The proposed models are also applied to a real dataset generated from assay validation studies.

A Goodness-of-Fit Test for a Class of Autoregressive Conditional Duration Models

This article develops a method for testing the goodness-of-fit of a given parametric autoregressive conditional duration model against unspecified nonparametric alternatives. The test statistics are functions of the residuals corresponding to the quasi maximum likelihood estimate of the given parametric model, and are easy to compute. The limiting distributions of the test statistics are not free from nuisance parameters. Hence, critical values cannot be tabulated for general use. A bootstrap procedure is proposed to implement the tests, and its asymptotic validity is established. The finite sample performances of the proposed tests and several other competing ones in the literature, were compared using a simulation study. The tests proposed in this article performed well consistently throughout, and they were either the best or close to the best. None of the tests performed uniformly the best. The tests are illustrated using an empirical example.

Specification testing for transformation models with an application to generalized accelerated failure-time models

This paper provides a nonparametric test of the specification of a transformation model. Specifically, we test whether an observable outcome Y is monotonic in the sum of a function of observable covariates X plus an unobservable error U. Transformation models of this form are commonly assumed in economics, including, e.g., standard specifications of duration models and hedonic pricing models. Our test statistic is asymptotically normal under local alternatives and consistent against nonparametric alternatives violating the implied restriction. Monte Carlo experiments show that our test performs well in finite samples. We apply our results to test for specifications of generalized accelerated failure-time (GAFT) models of the duration of strikes.

Likelihood- and residual-based evaluation of medium-term earthquake forecast models for California

Seven competing models for forecasting medium-term earthquake rates in California are quantitatively evaluated using the framework of the Collaboratory for the Study of Earthquake Predictability (CSEP). The model class consists of contrasting versions of the Every Earthquake a Precursor According to Size (EEPAS) and Proximity to Past Earthquakes (PPE) modelling approaches. Models are ranked by their performance on likelihood-based tests, which measure the consistency between a model forecast and observed earthquakes. To directly compare one model against another, we run a classical paired t-test and its non-parametric alternative on an information gain score based on the forecasts. These test scores are complemented by several residual-based methods, which offer detailed spatial information. The experiment period covers 2009 June–2012 September, when California experienced 23 earthquakes above the magnitude threshold. Though all models fail to capture seismicity during an earthquake sequence, spatio-temporal differences between models also emerge. The overall best-performing model has strong time- and magnitude-dependence, weights all earthquakes equally as medium-term precursors of larger events and has a full set of fitted parameters. Models with this time- and magnitude-dependence offer a statistically significant advantage over simpler baseline models. In addition, models that down-weight aftershocks when forecasting larger events have a desirable feature in that they do not overpredict following an observed earthquake sequence. This tendency towards overprediction differs between the simpler model, which is based on fewer parameters, and more complex models that include more parameters.

Goodness-of-fit test for Gaussian regression with block correlated errors

We propose a procedure to test that the expectation of a Gaussian vector is linear against a nonparametric alternative. We consider the case where the covariance matrix of the observations has a block diagonal structure. This framework encompasses regression models with autocorrelated errors, heteroscedastic regression models, mixed-effects models and growth curves. Our procedure does not depend on any prior information about the alternative. We prove that the test is asymptotically of the nominal level and consistent. We characterize the set of vectors on which the test is powerful and prove the classical √log log (n)/n convergence rate over directional alternatives. We propose a bootstrap version of the test as an alternative to the initial one and provide a simulation study in order to evaluate both procedures for small sample sizes when the purpose is to test goodness of fit in a Gaussian mixed-effects model. Finally, we illustrate the procedures using a real data set.

Commentary

Background: An important factor in the functional results after total knee arthroplasty is the achieved maximal flexion. The main purpose of this study was to compare the maximal knee flexion one year after surgery in patients who received either the bicruciate substituting knee system or the conventional posterior stabilized system. Methods: In a prospective randomized controlled trial, 124 patients presenting with osteoarthritis received the bicruciate substituting or the conventional posterior stabilized prosthesis. The primary outcome was the maximum flexion angle at one year postoperatively on a lateral radiograph made with the supine patient using manual force to bend the knee. Secondary outcomes were active flexion (lying and standing), the Knee Society Score, the Patella Scoring System score, the University of California Los Angeles score, the number and type of adverse device effects, and visual analog scale satisfaction up to two years postoperatively. The outcome measures of both groups were compared using one-sided t tests and non-parametric alternatives, with a significance level of p < 0.05. Results: No significant differences between the two groups were observed in maximal flexion on radiographs and in active flexion at baseline. The median maximal flexion on radiographs was 127° (range, 83° to 150°) for the bicruciate substituting group and 125° (range, 74° to 145°) for the conventional posterior stabilized group. The two groups showed comparable two-year results with respect to the Knee Society Score, the Patella Scoring System, the University of California Los Angeles score, and visual analog scale satisfaction. In the bicruciate substituting group, forty-one adverse device effects in twenty-six patients were reported, including three total system revisions and fourteen manipulations under anesthesia, compared with the conventional posterior stabilized group, in which sixteen adverse device effects were observed in thirteen patients, including six manipulations under anesthesia (p = 0.012). Conclusions: Patients who receive a bicruciate substituting system compared with those who receive a conventional posterior stabilized system have comparable knee flexion characteristics and clinical and functional outcomes but more complications by two years after total knee arthroplasty. Level of Evidence: Therapeutic Level I. See Instructions for Authors for a complete description of levels of evidence.

Assessing calibration of multinomial risk prediction models

Calibration, that is, whether observed outcomes agree with predicted risks, is important when evaluating risk prediction models. For dichotomous outcomes, several tools exist to assess different aspects of model calibration, such as calibration-in-the-large, logistic recalibration, and (non-)parametric calibration plots. We aim to extend these tools to prediction models for polytomous outcomes. We focus on models developed using multinomial logistic regression (MLR): outcome Y with k categories is predicted using k - 1 equations comparing each category i (i = 2, … ,k) with reference category 1 using a set of predictors, resulting in k - 1 linear predictors. We propose a multinomial logistic recalibration framework that involves an MLR fit where Y is predicted using the k - 1 linear predictors from the prediction model. A non-parametric alternative may use vector splines for the effects of the linear predictors. The parametric and non-parametric frameworks can be used to generate multinomial calibration plots. Further, the parametric framework can be used for the estimation and statistical testing of calibration intercepts and slopes. Two illustrative case studies are presented, one on the diagnosis of malignancy of ovarian tumors and one on residual mass diagnosis in testicular cancer patients treated with cisplatin-based chemotherapy. The risk prediction models were developed on data from 2037 and 544 patients and externally validated on 1107 and 550 patients, respectively. We conclude that calibration tools can be extended to polytomous outcomes. The polytomous calibration plots are particularly informative through the visual summary of the calibration performance.

Testing for Monotonicity in Unobservables Under Unconfoundedness

Monotonicity in a scalar unobservable is a now common assumption when modeling heterogeneity in structural models. Among other things, it allows one to recover the underlying structural function from certain conditional quantiles of observables. Nevertheless, monotonicity is a strong assumption and in some economic applications unlikely to hold, e.g., random coefficient models. Its failure can have substantive adverse consequences; having a test for this hypothesis is hence desirable. This paper provides such a test for cross-section data. We show how to exploit an exclusion restriction together with a conditional independence assumption, which in the binary treatment literature is commonly called unconfoundedness, to construct a test. Our statistic is asymptotically normal under local alternatives and consistent against nonparametric alternatives. Monte Carlo experiments show that a suitable bootstrap procedure yields tests with reasonable level behavior and useful power. We apply our test to study the role of unobserved ability in determining Black-White wage differences and to study whether Engel curves are monotonically driven by a scalar unobservable.

Comparison of the Short-Term Results of the First and Last 50 Scandinavian Total Ankle Replacements

Total ankle replacement (TAR) is presently considered to be an acceptable alternative to ankle fusion for patients with debilitating conditions of the ankle. The placing of a total ankle prosthesis is a technically demanding procedure. We hypothesized that the challenging conditions could cause a longer learning curve (>30 cases), and therefore the short-term results of the first and the last 50 cases in a consecutive series of 134 cases were compared. The first and last consecutive 50 cases by a single surgeon in a series of 134 Scandinavian Total Ankle Replacements (STAR; Waldemar Link, Hamburg, Germany), inserted between May 1999 and May 2008, were evaluated. Operation characteristics, clinical outcome (Foot Function Index [FFI], Kofoed score), complications, and the component alignment on X-rays were assessed. The outcome measures for both groups were compared using independent Student t tests, chi-square tests, and nonparametric alternatives (P < .05). Surgery time decreased from a median of 125 (83-160) to 100 (65-170) minutes (P < .001), and fewer perioperative complications were observed (12 vs 4, P = .04). The sagittal alignment of the tibial component was closer to normal in the last series (P < .001). The clinical outcome did not differ between the 2 series (median FFI: 32 [0-74] vs 25 [0-75], Kofoed score: median 71 [21-96] vs 80.5 [23-100]). The major underlying pathology did change from rheumatoid arthritis (60%) to osteoarthritis (44%; P = .002). No differences in type and number of complications were reported. The surgery time did decrease, there were fewer perioperative fractures, and the tibial component orientation improved, suggesting the presence of a learning curve. Operative experience and a shift in major underlying pathology did not influence clinical outcome. In view of this learning curve we suggest more restrictive patient selection for at least the first 50 TARs. Level III, comparative series.

Model checking in Tobit regression via nonparametric smoothing

This paper proposes a class of lack-of-fit tests for checking the adequacy of a presumed parametric form of the regression function in Tobit regression models. This class of tests is a weighted adaptation of the Zheng’s test for fitting a parametric regression model. The asymptotic null distributions of the underlying test statistics are shown to be normal. Moreover, the consistency of these tests against some fixed alternatives and asymptotic power against some local nonparametric alternatives are also derived. An optimal test within the proposed class of tests against a given sequence of nonparametric local alternatives is identified. A finite sample simulation shows some superiority of some of the proposed tests, compared to some of the existing tests.

Testing if a mixture is from a given location–scale family

Suppose we observe a random sample from . Here, to the best of our knowledge, we provide the first parametric test that F 0 is any given cumulative distribution function. The test is based on the first four sample moments and is most practicable when F 0 is symmetric. Simulation studies suggest that the test compares well with non-parametric alternatives and that it is consistent. A real data application is also presented.

Maximum-Likelihood Estimation of the Discrete Coefficient of Determination in Stochastic Boolean Systems

The discrete Coefficient of Determination (CoD) has become a key component of inference methods for stochastic Boolean models. We develop a parametric maximum-likelihood (ML) method for the inference of the discrete CoD for static Boolean systems and for dynamical Boolean systems in the steady state. Using analytical and numerical approaches, we compare the performance of the parametric ML approach against that of common nonparametric alternatives for CoD estimation, which show that the parametric approach has the least bias, variance, and root mean-square (RMS) error, provided that the system noise level is not too high. Next we consider the application of the proposed estimation approach to the problem of system identification, where only partial knowledge about the system is available. Inference procedures are proposed for both the static and dynamical cases, and their performance in logic gate and wiring identification is assessed through numerical experiments. The results indicate that identification rates converge to 100% as sample size increases, and that the convergence rate is much faster as more prior knowledge is available. For wiring identification, the parametric ML approach is compared to the nonparametric approaches, and it produced superior identification rates, though as the amount of prior knowledge is reduced, its performance approaches that of the nonparametric ML estimator, which was generally the best nonparametric approach in our experiments.

Improved survival modeling in cancer research using a reduced piecewise exponential approach

Statistical models for survival data are typically nonparametric, for example, the Kaplan-Meier curve. Parametric survival modeling, such as exponential modeling, however, can reveal additional insights and be more efficient than nonparametric alternatives. A major constraint of the existing exponential models is the lack of flexibility due to distribution assumptions. A flexible and parsimonious piecewise exponential model is presented to best use the exponential models for arbitrary survival data. This model identifies shifts in the failure rate over time based on an exact likelihood ratio test, a backward elimination procedure, and an optional presumed order restriction on the hazard rate. Such modeling provides a descriptive tool in understanding the patient survival in addition to the Kaplan-Meier curve. This approach is compared with alternative survival models in simulation examples and illustrated in clinical studies.

Robustness and Power of the Kornbrot Rank Difference, Signed Ranks, and Dependent Samples T-test

The purpose of the study was to compare the power and accuracy of the Kornbrot rank difference test to classical parametric and nonparametric alternatives when the assumption of normality is not met, the data are ordinal, and the sample size is small. Although the procedure is robust, there was no evidence the rank difference test had power advantages over Wilcoxon Signed-Ranks test.

Grip Kinetic Profile Variability in Adult Signature Writing

Previous studies of handwriting grip kinetics have demonstrated the ability to classify writers based on the topography of grip forces associated with signature writing. However, the topographic representation requires a large array of individual sensors in practice. The possibility of differentiating participants on the basis of a summative, temporal force profile is yet unknown. In this study, we investigated the variability of features derived from a time-evolving total grip force profile. Using an instrumented writing utensil, twenty adult participants provided 600 samples of a well-practised bogus signature over a period of 10 days. Deploying a combination of temporal, spectral and information-theoretic features, a linear discriminant analysis classifier outperformed nonparametric and nonlinear classifier alternatives and discriminated among participants with an average misclassification rate of 5.8% as estimated by cross-validation. These results suggest the existence of a unique kinetic profile for each writer even when generating the same written product. Our findings highlight the potential of using grip kinetics as a biometric measure.

Major Impact of Underweight and Overweight On Factor VIII Dosing in 201 Patients with Severe Haemophilia A Treated with Advate, Kogenate or Refacto AF/Xyntha

AbstractAbstract ▪626▪This icon denotes a clinically relevant abstract Introduction:The treatment of hemophilia A (HA) requires infusions of factor VIII (FVIII) concentrates. The number of FVIII units infused in order to obtain a specific circulating FVIII level is calculated with the formula: [body weight (BW) (kg) × desired FVIII increase (%)]/2, with the assumption that each unit of FVIII infused per kg of BW increases the circulating FVIII level by 2 %. The aim of the present study was to evaluate the impact of several morphometrical parameters (BW, body mass index (BMI), fat mass index (FMI), difference between BW and ideal BW, height), age and type of coagulation factor concentrate on the FVIII recovery in a large group of patients with severe haemophilia who had previously taken part in pharmacokinetic studies using Advate®, Kogenate FS® or ReFacto AF/Xyntha®. Methods:A total of 201 adults (> 18 yr) with severe HA carefully selected from 8 clinical trials using three recombinant FVIII concentrates were included in the analysis (Fig. 1). The FVIII recovery was calculated using the maximum FVIII concentration measured at 15 or 30 minutes after infusion. Regression tree (RT) was used to identify predictors of FVIII recovery. RT-based models are non-linear and non-parametric alternatives to linear models for regression problems. Continuous variables were compared using the Kruskal-Wallis test. Results:The median FVIII recovery was 2.16 for all patients and was significantly different between the 3 coagulation factor groups in univariate analysis. However, the BW, difference between BW and IBW, BMI and FMI were also significantly different between coagulation factor groups. In multivariate analysis, 5 groups were created by RT (Fig. 2 and Fig. 3): patients with a BMI < 20.3 kg/m2 (Group 2; Median FVIII recovery: 1.60), patients with a BMI between 20.3 and 29.5 kg/m2 (Group 4; Median FVIII recovery: 2.14) and patients with a BMI ≥ 29.6 kg/m2 (Group 5; Median FVIII recovery: 2.70). Group 1 and group 3 were made up of 2 outlier patients. The FVIII recovery was significantly different between group 2, group 4 and group 5 (P<0.001) (Fig. 2 and Fig. 3). The random forest associated with this RT shows that the age and the type of coagulation factor concentrate had no influence on FVIII recovery. Conclusions:The type of coagulation factor concentrate first emerged as a univariate predictor of FVIII recovery in our study. It later appeared to have no influence in the multivariate model, as opposed to the BMI which emerged as the strongest predictor of FVIII recovery. These results are consistent with previous crossover studies which have demonstrated comparable FVIII recovery of different concentrates (Haemophilia 2007;13:124–30, Haemophilia 2009;15(4):869–80). Our findings also support that dose calculation of FVIII to reach a specific FVIII target level should be adapted in underweight and overweight patients. Taking the ideal BW instead of the actual BW in the dose calculation should be implemented since only a small fraction of FVIII distributes outside the vascular system. [Display omitted] [Display omitted] [Display omitted] Disclosures:No relevant conflicts of interest to declare.

A restricted b‐spline basis for S‐shaped calibration curves

S‐shaped curves arise in many calibration assays. They are typically modeled using an empirically chosen nonlinear function. Nonparametric alternatives usually perform poorly because there are often insufficient data points and there are difficulties in enforcing the required asymptotic behavior. We propose an alternative approach using a b‐spline basis adapted to produce lower and upper asymptotes in the fitted curves. Its main advantage is that, with pre‐determined knot positions, the model is linear in the parameters and so is more numerically stable than a nonlinear model; this has advantages in, for example, fitting a mixed model to multiple curves. We explore the performance of this approach using data from a single radioimmunoassay for cortisol and from a set of 96 ELISA assays for the herbicide atrazine. Copyright © 2012 John Wiley &amp; Sons, Ltd.