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BackgroundAdult asthma is phenotypically heterogeneous with unclear aetiology. We aimed to evaluate the potential contribution of environmental exposure and its ensuing response to asthma and its heterogeneity.MethodsEnvironmental risk was evaluated by assessing the records of National Health Insurance Research Database (NHIRD) and residence-based air pollution (particulate matter with diameter less than 2.5 micrometers (PM2.5) and PM2.5-bound polycyclic aromatic hydrocarbons (PAHs)), integrating biomonitoring analysis of environmental pollutants, inflammatory markers and sphingolipid metabolites in case–control populations with mass spectrometry and ELISA. Phenotypic clustering was evaluated by t-distributed stochastic neighbor embedding (t-SNE) integrating 18 clinical and demographic variables.FindingsIn the NHIRD dataset, modest increase in the relative risk with time-lag effect for emergency (N=209 837) and outpatient visits (N=638 538) was observed with increasing levels of PM2.5and PAHs. Biomonitoring analysis revealed a panel of metals and organic pollutants, particularly metal Ni and PAH, posing a significant risk for current asthma (ORs=1.28–3.48) and its severity, correlating with the level of oxidative stress markers, notably Nε-(hexanoyl)-lysine (r=0.108–0.311, p2.5exposure. Further, levels of circulating sphingosine-1-phosphate and ceramide-1-phosphate were found to discriminate asthma (pInterpretationThese results suggest the potential contribution of environmental factors from multiple sources, their ensuing oxidative stress and sphingolipid remodeling to adult asthma and its phenotypic heterogeneity.

Motivated by two examples concerning global warming and monthly total import and export by China, we study time series that contain a nonparametric periodic component with an unknown period, a nonp...

Background Inflammation is a potential risk factor of mental disturbance. FKBP5 that encodes FK506-binding protein 51 (FKBP51), a negative cochaperone of glucocorticoid receptor (GR), is a stress-inducible gene and has been linked to psychiatric disorders. Yet, the role of FKBP51 in the inflammatory stress-associated mental disturbance remained unclear. Methods Fkbp5-deficient (Fkbp5-KO) mice were used to study inflammatory stress by a single intraperitoneal injection of lipopolysaccharide (LPS). The anxiety-like behaviors, neuroimaging, immunofluorescence staining, immunohistochemistry, protein and mRNA expression analysis of inflammation- and neurotransmission-related mediators were evaluated. A dexamethasone drinking model was also applied to examine the effect of Fkbp5-KO in glucocorticoid-induced stress. Results LPS administration induced FKBP51 elevation in the liver and hippocampus accompanied with transient sickness. Notably, Fkbp5-KO but not wild-type (WT) mice showed anxiety-like behaviors 7 days after LPS injection (LPS-D7). LPS challenge rapidly increased peripheral and central immune responses and hippocampal microglial activation followed by a delayed GR upregulation on LPS-D7, and these effects were attenuated in Fkbp5-KO mice. Whole-brain [18F]-FEPPA neuroimaging, which target translocator protein (TSPO) to indicate neuroinflammation, showed that Fkbp5-KO reduced LPS-induced neuroinflammation in various brain regions including hippocampus. Interestingly, LPS elevated glutamic acid decarboxylase 65 (GAD65), the membrane-associated GABA-synthesizing enzyme, in the hippocampus of WT but not Fkbp5-KO mice on LPS-D7. This FKBP51-dependent GAD65 upregulation was observed in the ventral hippocampal CA1 accompanied by the reduction of c-Fos-indicated neuronal activity, whereas both GAD65 and neuronal activity were reduced in dorsal CA1 in a FKBP51-independent manner. GC-induced anxiety was also examined, which was attenuated in Fkbp5-KO and hippocampal GAD65 expression was unaffected. Conclusions These results suggest that FKBP51/FKBP5 is involved in the systemic inflammation-induced neuroinflammation and hippocampal GR activation, which may contribute to the enhancement of GAD65 expression for GABA synthesis in the ventral hippocampus, thereby facilitating resilience to inflammation-induced anxiety.

Motivated by an ischemic heart screening problem, a new global test for one-way ANOVA in functional data analysis is studied. The test statistic is taken as the maximum of the pointwise F -test statistic over the interval the functional responses are observed. Nonparametric bootstrap, which is applicable in more general situations and easier to implement than parametric bootstrap, is employed to approximate the null distribution and to obtain an approximate critical value. Under mild conditions, asymptotically our test has the correct level and is root- n consistent in detecting local alternatives. Simulation studies show that the proposed test outperforms several existing tests in terms of both size control and power when the correlation between observations at any two different points is high or moderate, and it is comparable with the competitors otherwise. Application to an ischemic heart dataset suggests that resting electrocardiogram signals may contain enough information for ischemic heart screening at outpatient clinics, without the help of stress tests required by the current standard procedure.

Varying-coefficient models are widely used to model nonparametric interaction and recently adopted to analyze longitudinal data measured repeatedly over time. We focus on high-dimensional longitudinal observations in this article. A novel two-step sparse boosting approach is proposed to carry out the variable selection and the model-based prediction. As a new machine learning tool, boosting provides seamless integration of model estimation and variable selection for complicated regression functions. Specifically, in the first step the sparse boosting technique assuming independence is applied to facilitate an initial estimate of the correlation structure while in the second step the estimated correlation structure is incorporated in the loss function of the sparse boosting algorithm. Extensive numerical examples illustrate the advantage of the two-step sparse boosting method. An application of yeast cell cycle gene expression data is further provided to demonstrate the proposed methodology.

Background: Adult asthma is phenotypically heterogeneous with unclear etiology. We aimed to evaluate the potential contribution of environmental exposure and its ensuing response to asthma and its heterogeneity. Methods: Environmental risk was evaluated by assessing the records of National Health Insurance Research database (NHIRD) and residence-based air pollution [PM2.5 and PM2.5-bound polycyclic aromatic hydrocarbons (PAHs)], integrating biomonitoring analysis of environmental pollutants, inflammatory markers and sphingolipid metabolites in case-control populations with mass spectrometry and ELISA. Phenotypic clustering was evaluated by t-SNE integrating 18 clinical and demographic variables. Findings: In the NHIRD dataset, a modest increase in the relative risk with time-lag effect for emergency (N=209,837) and outpatient visits (N=638,538) was observed with increasing levels of PM2.5 and PAHs. Biomonitoring analysis revealed a panel of metals and organic pollutants, particularly metal Ni and PAH originated from multiple sources, posing a significant risk for current asthma and its severity, correlating with the level of oxidative stress markers, notably Ne-(hexanoyl)-lysine (HEL) as a marker of response in both cases and controls. Further, levels of circulating sphingosine-1-phosphate (S1P) and ceramide-1-phosphate (C1P) were found to discriminate asthma, correlating with the levels of exposure to PAH and metals, respectively, and both correlating with a panel of circulating inflammatory markers. Stratification of the combined datasets by 6 phenotypic clusters among 1,163 asthmatic subjects and those with comorbid T2DM revealed cluster-selective environmental risks and biosignatures. Interpretation: These results suggest the potential contribution of environmental factors, their ensuing oxidative stress and sphingolipid remodeling to adult asthma and its phenotypic heterogeneity. Funding Information: This work was supported, in part, by grants from National Health Research Institutes, Taiwan (EOPP10-014, EOSP07-014 and NHRI-102A1-PDCO-03010201) and Ministry of Health, Taiwan (EODOH01), National Science Council (NSC 102-2314-B-037-052), Ministry of Health (EODOH01), Ministry of Science and Technology (MOST 103-2320-B-110-001), and Academic Sinica (BM-102021170), Taiwan. Declaration of Interests: We declare no competing interests. Ethics Approval Statement: All eligible subjects were enrolled in the study after signing the informed consent approved by the respective recruitment hospitals.

Testing the equality of two means is a fundamental inference problem. For high-dimensional data, the Hotelling’s T2-test either performs poorly or becomes inapplicable. Several modifications have been proposed to address this issue. However, most of them are based on asymptotic normality of the null distributions of their test statistics which inevitably requires strong assumptions on the covariance. We study this problem thoroughly and propose an L2-norm based test that works under mild conditions and even when there are fewer observations than the dimension. Specially, to cope with general nonnormality of the null distribution we employ the Welch–Satterthwaite χ2-approximation. We derive a sharp upper bound on the approximation error and use it to justify that χ2-approximation is preferred to normal approximation. Simple ratio-consistent estimators for the parameters in the χ2-approximation are given. Importantly, our test can cope with singularity or near singularity of the covariance which is commonly seen in high dimensions and is the main cause of nonnormality. The power of the proposed test is also investigated. Extensive simulation studies and an application show that our test is at least comparable to and often outperforms several competitors in terms of size control, and the powers are comparable when their sizes are. Supplementary materials for this article are available online.

Nonparametric and semiparametric regression models are useful statistical regression models to discover nonlinear relationships between the response variable and predictor variables. However, optimal efficient estimators for the nonparametric components in the models are biased which hinders the development of methods for further statistical inference. In this paper, based on the local linear fitting, we propose a simple bias reduction approach for the estimation of the nonparametric regression model. Our approach does not need to use higher-order local polynomial regression to estimate the bias, and hence avoids the double bandwidth selection and design sparsity problems suffered by higher-order local polynomial fitting. It also does not inflate the variance. Hence it can be easily applied to complex statistical inference problems. We extend our approach to varying coefficient models, to estimate the variance function, and to construct simultaneous confidence band for the nonparametric regression function. Simulations are carried out for comparisons with existing methods, and a data example is used to investigate the performance of the proposed method.

Summary Periodicity and trend are features describing an observed sequence, and extracting these features is an important issue in many scientific fields. However, it is not an easy task for existing methods to analyse simultaneously the trend and dynamics of the periodicity such as time varying frequency and amplitude, and the adaptivity of the analysis to such dynamics and robustness to heteroscedastic dependent errors are not guaranteed. These tasks become even more challenging when there are multiple periodic components. We propose a non-parametric model to describe the dynamics of multicomponent periodicity and investigate the recently developed synchro-squeezing transform in extracting these features in the presence of a trend and heteroscedastic dependent errors. The identifiability problem of the non-parametric periodicity model is studied, and the adaptivity and robustness properties of the synchro-squeezing transform are theoretically justified in both discrete and continuous time settings. Consequently we have a new technique for decoupling the trend, periodicity and heteroscedastic, dependent error process in a general non-parametric set-up. Results of a series of simulations are provided, and the incidence time series of varicella and herpes zoster in Taiwan and respiratory signals observed from a sleep study are analysed.

Peter Hall made wide-ranging and far-reaching contributions to nonparametric modeling. He was one of the leading figures in the developments of nonparametric techniques with over 300 published papers in the field alone. This article gives a selective overview on the contributions of Peter Hall to nonparametric function estimation and modeling. The focuses are on density estimation, nonparametric regression, bandwidth selection, boundary corrections, inference under shape constraints, estimation of residual variances, analysis of wavelet estimators, multivariate regression and applications of nonparametric methods.

We develop a variance reduction method for the seemingly unrelated (SUR) kernel estimator of Wang (2003). We show that the quadratic interpolation method introduced in Cheng et al. (2007) works for the SUR kernel estimator. For a given point of estimation, Cheng et al. (2007) define a variance reduced local linear estimate as a linear combination of classical estimates at three nearby points. We develop an analogous variance reduction method for SUR kernel estimators in clustered/longitudinal models and perform simulation studies which demonstrate the efficacy of our variance reduction method in finite sample settings.

Multiparameter likelihood models (MLMs) with multiple covariates have a wide range of applications; however, they encounter the “curse of dimensionality” problem when the dimension of the covariates is large. We develop a generalized multiparameter likelihood model that copes with multiple covariates and adapts to dynamic structural changes well. It includes some popular models, such as the partially linear and varying-coefficient models, as special cases. We present a simple, effective two-step method to estimate both the parametric and the nonparametric components when the model is fixed. The proposed estimator of the parametric component has the n −1/2convergence rate, and the estimator of the nonparametric component enjoys an adaptivity property. We suggest a data-driven procedure for selecting the bandwidths, and propose an initial estimator in profile likelihood estimation of the parametric part to ensure stability of the approach in general settings. We further develop an automatic procedure to ide...

First, we propose a new method for estimating the conditional variance in heteroscedasticity regression models. For heavy tailed innovations, this method is in general more efficient than either of the local linear and local likelihood estimators. Secondly, we apply a variance reduction technique to improve the inference for the conditional variance. The proposed methods are investigated through their asymptotic distributions and numerical performances.

In this article we propose an implementation of the so-called zero-crossing-time detection technique specifically designed for estimating the location of jump-points in the first derivative (kinks) of a regression function f. Our algorithm relies on a new class of kernel functions having a second derivative with vanishing moments and an asymmetric first derivative steep enough near the origin. We provide a software package which, for a sample of size n, produces estimators with an accuracy of order, at least, O(n−2/5). This contrasts with current algorithms for kink estimation which at best provide an accuracy of order O(n−1/3). In the software, the kernel statistic is standardized and compared to the universal threshold to test the existence of a kink. A simulation study shows that our algorithm enjoys very good finite sample properties even for low sample sizes. The method reveal skink features in real data sets with high noise levels at places where traditional smoothers tend to over smooth the data.

Local likelihood modeling is a unified and effective approach to establishing the dependence of a response variable, which can be of various types, on independent variables. Therefore, these models have become popular in a wide range of applications. There is an increasing interest in employing multiparameter local likelihood models to investigate trends of sample extremes in environmental statistics. When sample maxima are modeled by a generalized extreme value distribution, the sample size is small in general and local likelihood estimation exhibits a large variation. In this article variance reduction techniques are employed to improve the efficiency of the inference. A simulation study and an application to annual maximum temperatures show that our methods are very effective in finite samples.

In semivarying coefficient models for longitudinal/clustered data, usually of primary interest is usually the parametric component which involves unknown constant coefficients. First, we study semiparametric efficiency bound for estimation of the constant coefficients in a general setup. It can be achieved by spline regression provided that the within-cluster covariance matrices are all known, which is an unrealistic assumption in reality. Thus, we propose an adaptive estimator of the constant coefficients when the covariance matrices are unknown and depend only on the index random variable, such as time, and when the link function is the identity function. After preliminary estimation, based on working independence and both spline and local linear regression, we estimate the covariance matrices by applying local linear regression to the resulting residuals. Then we employ the covariance matrix estimates and spline regression to obtain our final estimators of the constant coefficients. The proposed estimator achieves the semiparametric efficiency bound under normality assumption, and it has the smallest covariance matrix among a class of estimators even when normality is violated. We also present results of numerical studies. The simulation results demonstrate that our estimator is superior to the one based on working independence. When applied to the CD4 count data, our method identifies an interesting structure that was not found by previous analyses.

Two popular variable screening methods under the ultra-high dimensional setting with the desirable sure screening property are the sure independence screening (SIS) and the forward regression (FR). Both are classical variable screening methods and recently have attracted greater attention under the new light of high-dimensional data analysis. We consider a new and simple screening method that incorporates multiple predictors in each step of forward regression, with decision on which variables to incorporate based on the same criterion. If only one step is carried out, it actually reduces to the SIS. Thus it can be regarded as a generalization and unification of the FR and the SIS. More importantly, it preserves the sure screening property and has similar computational complexity as FR in each step, yet it can discover the relevant covariates in fewer steps. Thus, it reduces the computational burden of FR drastically while retaining advantages of the latter over SIS. Furthermore, we show that it can find all the true variables if the number of steps taken is the same as the correct model size, even when using the original FR. An extensive simulation study and application to two real data examples demonstrate excellent performance of the proposed method.

In a range of practical problems the boundary of the support of a bivariate distribution is of interest, for example where it describes a limit to efficiency or performance, or where it determines the physical extremities of a spatially distributed population in forestry, marine science, medicine, meteorology or geology. We suggest a tracking-based method for estimating a support boundary when it is composed of a finite number of smooth curves, meeting together at corners. The smooth parts of the boundary are assumed to have continuously turning tangents and bounded curvature, and the corners are not allowed to be infinitely sharp; that is, the angle between the two tangents should not equal π. In other respects, however, the boundary may be quite general. In particular it need not be uniquely defined in Cartesian coordinates, its corners my be either concave or convex, and its smooth parts may be neither concave nor convex. Tracking methods are well suited to such generalities, and they also have the advantage of requiring relatively small amounts of computation. It is shown that they achieve optimal convergence rates, in the sense of uniform approximation.

SUMMARY We suggest a completely empirical approach to the construction of confidence bands for hazard functions, based on smoothing the Nelsen-Aalen estimator. In particular, we introduce a local bandwidth-choice method. Our approach uses empirical information about both the survival rate and the censoring rate, and employs undersmoothing to alleviate difficulties caused by bias. We use both Edgeworth expansion and numerical simulation, the former to develop a basic formula and the latter to modify it for general use.

We suggest a method for reducing variance in nonparametric surface estimation. The technique is applicable to a wide range of inferential problems, including both density estimation and regression, and to a wide variety of estimator types. It is based on estimating the contours of a surface by minimising deviations of elementary surface estimates along a quadratic curve. Once a contour estimate has been obtained, the final surface estimate is computed by averaging conventional surface estimates along a portion of the contour. Theoretical and numerical properties of the technique are discussed.

Ultra-high dimensional longitudinal data are increasingly common and the analysis is challenging both theoretically and methodologically. We offer a new automatic procedure for finding a sparse semivarying coefficient model, which is widely accepted for longitudinal data analysis. Our proposed method first reduces the number of covariates to a moderate order by employing a screening procedure, and then identifies both the varying and constant coefficients using a group SCAD estimator, which is subsequently refined by accounting for the within-subject correlation. The screening procedure is based on working independence and B-spline marginal models. Under weaker conditions than those in the literature, we show that with high probability only irrelevant variables will be screened out, and the number of selected variables can be bounded by a moderate order. This allows the desirable sparsity and oracle properties of the subsequent structure identification step. Note that existing methods require some kind of iterative screening in order to achieve this, thus they demand heavy computational effort and consistency is not guaranteed. The refined semivarying coefficient model employs profile least squares, local linear smoothing and nonparametric covariance estimation, and is semiparametric efficient. We also suggest ways to implement the proposed methods, and to select the tuning parameters. An extensive simulation study is summarized to demonstrate its finite sample performance and the yeast cell cycle data is analyzed., Comment: Published in at http://dx.doi.org/10.1214/14-AOS1236 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Varying coefficient models have numerous applications in a wide scope of scientific areas. While enjoying nice interpretability, they also allow flexibility in modeling dynamic impacts of the covariates. But, in the new era of big data, it is challenging to select the relevant variables when there are a large number of candidates. Recently several work are focused on this important problem based on sparsity assumptions; they are subject to some limitations, however. We introduce an appealing forward variable selection procedure. It selects important variables sequentially according to a sum of squares criterion, and it employs an EBIC- or BIC-based stopping rule. Clearly it is simple to implement and fast to compute, and it possesses many other desirable properties from both theoretical and numerical viewpoints. We establish rigorous selection consistency results when either EBIC or BIC is used as the stopping criterion, under some mild regularity conditions. Notably, unlike existing methods, an extra screening step is not required to ensure selection consistency. Even if the regularity conditions fail to hold, our procedure is still useful as an effective screening procedure in a less restrictive setup. We carried out simulation and empirical studies to show the efficacy and usefulness of our procedure., Comment: 33 pages, 5 figures and 4 tables

In the case of the random design nonparametric regression, to correct for the unbounded finite-sample variance of the local linear estimator (LLE), Seifert and Gasser (J. Amer. Statist. Assoc. 91 (1996) 267–275) apply the idea of ridge regression to the LLE, and propose the local linear ridge regression estimator (LLRRE). However, the finite sample and the asymptotic properties of the LLRRE are not discussed there. In this paper, upper bounds of the finite-sample variance and bias of the LLRRE are obtained. It is shown that if the ridge regression parameters are not properly selected, then the resulting LLRRE has some drawbacks. For example, it may have a nonzero constant asymptotic bias, may suffer from boundary effects, or may be unable to share the nice asymptotic bias quality of the LLE. On the other hand, if the ridge regression parameters are properly selected, then the resulting LLRRE does not suffer from the above problems, and has the same asymptotic mean-square error as the LLE. For this purpose, the ridge regression parameters are allowed to depend on the sample size, and converge to 0 as the sample size increases. In practice, to select both the bandwidth and the ridge regression parameters, the idea of cross-validation is applied. Simulation studies demonstrate that the LLRRE using the cross-validated bandwidth and ridge regression parameters could have smaller sample mean integrated square error than the LLE using the cross-validated bandwidth, in reasonable sample sizes.

We introduce a recursive method for estimating a probability density subject to constraints of unimodality or monotonicity. It uses an empirical estimate of the probability transform to construct a sequence of maps of a known template, which satisfies the constraints. The algorithm may be employed without a smoothing step, in which case it produces step-function approximations to the sampling density. More satisfactorily, a certain amount of smoothing may be interleaved between each recursion, in which case the estimate is smooth. The amount of smoothing may be chosen using a standard cross-validation algorithm. Unlike other methods for density estimation, however, the recursive approach is robust against variation of the amount of smoothing, and so choice of bandwidth is not critical.

Summary Nonparametric tests of modality are a distribution-free way of assessing evidence about inhomogeneity in a population, provided that the potential sub populations are sufficiently well separated. They include the excess mass and dip tests, which are equivalent in univariate settings and are alternatives to the bandwidth test. Only very conservative forms of the excess mass and dip tests are available at presently, however, and for that reason they are generally not competitive with the bandwidth test. In the present paper we develop a practical approach to calibrating the excess mass and dip tests to improve their level accuracy and power substantially. Our method exploits the fact that the limiting distribution of the excess mass statistic under the null hypothesis depends on unknowns only through a constant, which may be estimated. Our calibrated test exploits this fact and is shown to have greater power and level accuracy than the bandwidth test has. The latter tends to be quite conservative, even in an asymptotic sense. Moreover, the calibrated test avoids difficulties that the bandwidth test has with spurious modes in the tails, which often must be discounted through subjective intervention of the experimenter.

There are close connections between the theory of statistical inference under order restrictions and the theory of tests for unimodality. In particular, a result of Kiefer and Wolfowitz, on the error of convex approximations to empirical distribution functions, is basic to limit theory for the dip test for unimodality. We develop a version of Kiefer and Wolfowitz' result in the context of distributions that are strongly unimodal, and apply it and related limit theory to compare the powers, against local alternatives, of three different tests of unimodality. In this context it is shown that the dip, excess mass and bandwidth tests are all able to detect departures of size n −3 5 (measured in terms of the distribution function) from the null hypothesis, where n denotes sample size; but are not able to detect departures of smaller order. Thus, they have similar powers.

Local linear curve estimators are typically constructed using a compactly supported kernel, which minimizes edge effects and (in the case of the Epanechnikov kernel) optimizes asymptotic performance in a mean square sense. The use of compactly supported kernels can produce numerical problems, however. A common remedy is ‘ridging’, which may be viewed as shrinkage of the local linear estimator towards the origin. In this paper we propose a general form of shrinkage, and suggest that, in practice, shrinkage be towards a proper curve estimator. For the latter we propose a local linear estimator based on an infinitely supported kernel. This approach is resistant against selection of too large a shrinkage parameter, which can impair performance when shrinkage is towards the origin. It also removes problems of numerical instability resulting from using a compactly supported kernel, and enjoys very good mean squared error properties.

High-dimensional data analysis has been an active area, and the main focuses have been variable selection and dimension reduction. In practice, it occurs often that the variables are located on an unknown, lower-dimensional nonlinear manifold. Under this manifold assumption, one purpose of this paper is regression and gradient estimation on the manifold, and another is developing a new tool for manifold learning. To the first aim, we suggest directly reducing the dimensionality to the intrinsic dimension $d$ of the manifold, and performing the popular local linear regression (LLR) on a tangent plane estimate. An immediate consequence is a dramatic reduction in the computation time when the ambient space dimension $p\gg d$. We provide rigorous theoretical justification of the convergence of the proposed regression and gradient estimators by carefully analyzing the curvature, boundary, and non-uniform sampling effects. A bandwidth selector that can handle heteroscedastic errors is proposed. To the second aim, we analyze carefully the behavior of our regression estimator both in the interior and near the boundary of the manifold, and make explicit its relationship with manifold learning, in particular estimating the Laplace-Beltrami operator of the manifold. In this context, we also make clear that it is important to use a smaller bandwidth in the tangent plane estimation than in the LLR. Simulation studies and the Isomap face data example are used to illustrate the computational speed and estimation accuracy of our methods., Comment: 58 pages, 5 figures

Hsin-I Chang1, Ming-Kung Yeh21Department of Biochemical Science and Technology, National Chia Yi University, Chiayi City, 2Institute of Preventive Medicine, National Defence Medical Center, Sanhsia, Taipei, TaiwanAbstract: Research on liposome formulations has progressed from that on conventional vesicles to new generation liposomes, such as cationic liposomes, temperature sensitive liposomes, and virosomes, by modulating the formulation techniques and lipid composition. Many research papers focus on the correlation of blood circulation time and drug accumulation in target tissues with physicochemical properties of liposomal formulations, including particle size, membrane lamellarity, surface charge, permeability, encapsulation volume, shelf time, and release rate. This review is mainly to compare the therapeutic effect of current clinically approved liposome-based drugs with free drugs, and to also determine the clinical effect via liposomal variations in lipid composition. Furthermore, the major preclinical and clinical data related to the principal liposomal formulations are also summarized.Keywords: PEGlated liposomes, temperature sensitive liposomes, therapeutic efficiency, virosomes, cationic liposomes

Research on liposome formulations has progressed from that on conventional vesicles to new generation liposomes, such as cationic liposomes, temperature sensitive liposomes, and virosomes, by modulating the formulation techniques and lipid composition. Many research papers focus on the correlation of blood circulation time and drug accumulation in target tissues with physicochemical properties of liposomal formulations, including particle size, membrane lamellarity, surface charge, permeability, encapsulation volume, shelf time, and release rate. This review is mainly to compare the therapeutic effect of current clinically approved liposome-based drugs with free drugs, and to also determine the clinical effect via liposomal variations in lipid composition. Furthermore, the major preclinical and clinical data related to the principal liposomal formulations are also summarized.

The phenomenon of crossing hazard rates is common in clinical trials with time to event endpoints. Many methods have been proposed for testing equality of hazard functions against a crossing hazards alternative. However, there has been relatively few approaches available in the literature for point or interval estimation of the crossing time point. The problem of constructing confidence intervals for the first crossing time point of two hazard functions is considered in this paper. After reviewing a recent procedure based on Cox proportional hazard modeling with Box-Cox transformation of the time to event, a nonparametric procedure using the kernel smoothing estimate of the hazard ratio is proposed. The proposed procedure and the one based on Cox proportional hazard modeling with Box-Cox transformation of the time to event are both evaluated by Monte–Carlo simulations and applied to two clinical trial datasets.

A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias remains unchanged. The nearby points are chosen to maximize the variance reduction. We study in detail the case of univariate local linear regression. While the new estimator retains many advantages of the local linear estimator, it has appealing asymptotic relative efficiencies. Bandwidth selection rules are available by a simple constant factor adjustment of those for local linear estimation. A simulation study indicates that the finite sample relative efficiency often matches the asymptotic relative efficiency for moderate sample sizes. This technique is very general and has a wide range of applications., Comment: Published at http://dx.doi.org/10.1214/009053606000001398 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

With applications to cluster analysis in mind, we suggest new approaches to constructing tree diagrams that describe associations among points in a scatterplot. Our most basic tree diagram results in two data points being associated with one another if and only if their respective curves of steepest ascent up the density or intensity surface lead toward the same mode. The representation, in the sample space, of the set of steepest ascent curves corresponding to the data, is called the gradient tree. It has a regular, octopuslike structure, and is consistently estimated by its analogue computed from a nonparametric estimator which gives consistent estimation of both the density surface and its derivatives. We also suggest ‘forests’, in which data are linked by line segments which represent good approximations to portions of the population gradient tree. A forest is closely related to a minimum spanning tree, or MST, defined as the graph of minimum total length connecting all sample points. However, forests use a larger bandwidth for constructing the density-surface estimate than is implicit in the MST, with the result that they are substantially more orderly and are more readily interpreted. The effective bandwidth for the MST is so small that even the corresponding density-surface estimate, let alone its derivatives, is inconsistent. As a result, relationships that are suggested by the MST can change considerably if relatively small quantities of data are added or removed. Our trees and forests do not suffer from this problem. They are related to the concept of gradient traces, introduced by Wegman, Carr and Luo (1993) and Wegman and Carr (1993) for purposes quite different from our own.

Usually, when testing the null hypothesis that a distribution has one mode against the alternative that it has two, the null hypothesis is interpreted as entailing that the density of the sampling distribution has a unique point of zero slope, which is a local maximum. In this paper we argue that a more appropriate null hypothesis is that the density has two points of zero slope, of which one is a local maximum and the other is a shoulder. We show that when a test for a mode-with-shoulder is properly calibrated, so that it has asymptotically correct level, it is generally conservative when applied to the case of a mode without a shoulder. We suggest methods for calibrating both the bandwidth and dip-excess mass tests in the setting of a mode with a shoulder. We also provide evidence in support of the converse: a test calibrated for a single mode without a shoulder tends to be anticonservative when applied to a mode with a shoulder. The calibration method involves resampling from a ‘‘template’’ density with exactly one mode and one shoulder. It exploits the following asymptotic factorization property for both the sample and resample forms of the test statistic: all dependence of these quantities on the sampling distribution cancels asymptotically from their ratio. In contrast to other approaches, the method has very good adaptivity properties.

Many popular curve estimators based on smoothing have difficulties caused by boundary effects. These effects are visually disturbing in practice and can play a dominant role in theoretical analysis. Local polynomial regression smoothers are known to correct boundary effects automatically. Some analogs are implemented for density estimation and the resulting estimators also achieve automatic boundary corrections. In both settings of density and regression estimation, we investigate best weight functions for local polynomial fitting at the endpoints and find a simple solution. The solution is universal for general degree of local polynomial fitting and general order of estimated derivative. Furthermore, such local polynomial estimators are best among all linear estimators in a weak minimax sense, and they are highly efficient even in the usual linear minimax sense.

A `skewing' method is shown to effectively reduce the order of bias of locally parametric estimators, and at the same time retain positivity properties. The technique involves first calculating the usual locally parametric approximation in the neighbourhood of a point x' that is a short distance from the place x where the we wish to estimate the density, and then evaluating this approximation at x. By way of comparison, the usual locally parametric approach takes x'=x. In our construction, x'-x depends in a very simple way on the bandwidth and the kernel, and not at all on the unknown density. Using skewing in this simple form reduces the order of bias from the square to the cube of bandwidth; and taking the average of two estimators computed in this way further reduces bias, to the fourth power of bandwidth. On the other hand, variance increases only by at most a moderate constant factor.

The integral of the mean squared error of an estimator of a regression function is used as a criterion for defining an optimal design measure in the context of local linear regression, when the bandwidth is chosen in a locally optimal manner. An algorithm is proposed that constructs a sequence of piecewise uniform designs with the help of current estimates of the integral of the mean squared error. These estimates do not require direct estimation of the second derivative of the regression function. Asymptotic properties of the algorithm are established and numerical results illustrate the gains that can be made, relative to a uniform design, by using the optimal design or sub-optimal, piecewise uniform designs. The behaviour of the algorithm in practice is also illustrated.