SAS macros for estimation of direct adjusted cumulative incidence curves under proportional subdistribution hazards models

The cumulative incidence function is commonly reported in studies with competing risks. The aim of this paper is to compute the treatment-specific cumulative incidence functions, adjusting for potentially imbalanced prognostic factors among treatment groups. The underlying regression model considered in this study is the proportional hazards model for a subdistribution function [1]. We propose estimating the direct adjusted cumulative incidences for each treatment using the pooled samples as the reference population. We develop two SAS macros for estimating the direct adjusted cumulative incidence function for each treatment based on two regression models. One model assumes the constant subdistribution hazard ratios between the treatments and the alternative model allows each treatment to have its own baseline subdistribution hazard function. The macros compute the standard errors for the direct adjusted cumulative incidence estimates, as well as the standard errors for the differences of adjusted cumulative incidence functions between any two treatments. Based on the macros’ output, one can assess treatment effects at predetermined time points. A real bone marrow transplant data example illustrates the practical utility of the SAS macros.     

Dynamic risk score modeling for multiple longitudinal risk factors and survival

Modeling disease risk and survival using longitudinal risk factor trajectories is of interest in various clinical scenarios. The capacity to build a prognostic model using the trajectories of multiple longitudinal risk factors, in the presence of potential dependent censoring, would enable more informed, personalized decision making. A dynamic risk score modeling framework is proposed for multiple longitudinal risk factors and survival in the presence of dependent censoring, where both events depend on participants' post-baseline clinical progression and form a competing risks structure. The model requires relatively few random effects regardless of the number of longitudinal risk factors and can therefore accommodate multiple longitudinal risk factors in a parsimonious manner. The proposed method performed satisfactorily in extensive simulation studies. It is further applied to the motivating registry study on pediatric acute liver failure to model death using the trajectories of multiple clinical and biochemical markers. Once established, the model yields an easily calculable longitudinal risk score that can be used for disease monitoring among future patients.     

An R package for assessment of statistical downscaling methods for hydrological climate change impact studies

Due to inherent bias the climate model simulated precipitation and temperature cannot be used to drive a hydrological model without pre-processing – statistical downscaling. This often consists of reducing the bias in the climate model simulations (bias correction) and/or transformation of the observed data in order to match the projected changes (delta change). The validation of the statistical downscaling methods is typically limited to the scale for which the transformation was calibrated and the driving variables (precipitation and temperature) of the hydrological model. The paper introduces an R package ”musica” which provides ready to use tools for routine validation of statistical downscaling methods at multiple time scales as well as several advanced methods for statistical downscaling. The musica package is used to validate simulated runoff. It is shown that using conventional methods for downscaling of precipitation and temperature often leads to substantial biases in simulated runoff at all time scales.     

Fuzzy methods for case-based recommendation and decision support

The paper proposes two case-based methods for recommending decisions to users on the basis of information stored in a database. In both approaches, fuzzy sets and related (approximate) reasoning techniques are used for modeling user preferences and decision principles in a flexible manner. The first approach, case-based decision making, can principally be seen as a case-based counterpart to classical decision principles well-known from statistical decision theory. The second approach, called case-based elicitation, combines aspects from flexible querying of databases and case-based prediction. Roughly, imagine a user who aims at choosing an optimal alternative among a given set of options. The preferences with respect to these alternatives are formalized in terms of flexible constraints, the expression of which refers to cases stored in a database. As both types of decision support might provide useful tools for recommender systems, we also place the methods in a broader context and discuss the role of fuzzy set theory in some related fields.     

A comparison of multivariate statistical methods for estimating expected consequences for low‐probability and high‐consequence incidents

The catastrophic incidents involving hazardous materials (hazmats) have often been termed as low probability and high consequence (LPHC). The purpose of this article is to address some fundamental questions with regard to hazmats incidents: What is the expected consequence of a hazmats incident? How should the consequences of incidents involving hazmats be predicted? An exhaustive statistical analysis is performed on the hazmat incident data available from the U.S. Hazardous Materials Incident Reporting System (HMIRS). We present a sequence of logically deduced, linear statistical models to estimate the two major areas of impact of an incident: (1) population affected and (2) cost incurred due to an incident based on the outcomes of the incident. Our initial experiments indicated that linear models are not sufficient for predicting the consequences. Subsequently, we extended our work to evaluate the effectiveness of three multivariate statistical methods, namely (1) partial least squares, (2) spline regression, and (3) Box‐Cox transformations. Based on our experiments, Box‐Cox transformation showed significant improvement in estimating the consequences. Last, we summarize our findings and provide some general guidelines to entities interested in estimating events categorized as LPHC. © 2010 Wiley Periodicals, Inc.     

Mass flow estimation with model bias correction for a turbocharged Diesel engine

A systematic design method for mass flow estimation with correction for model bias is proposed. Based on an augmented observable Mean Value Engine Model (MVEM) of a turbocharged Diesel engine, the online estimation of states with additional biases is performed to compute the mass flows for different places. A correction method is applied, that utilizes estimated biases which are in a least-square sense redistributed between the correction terms to the uncertain mass flow maps and then added to the estimated mass flows. An Extended Kalman Filter (EKF) is tested off-line on production car engine data where the combination of an intake manifold pressure sensor, exhaust manifold pressure sensor and turbocharger speed sensor is compared and discussed in different sensor fusions. It is shown that the correction method improves the uncorrected estimated air mass flow which is validated against the airflow data measured in the intake duct.     

Computational Techniques for Spatial Logistic Regression with Large Datasets

In epidemiological research, outcomes are frequently non-normal, sample sizes may be large, and effect sizes are often small. To relate health outcomes to geographic risk factors, fast and powerful methods for fitting spatial models, particularly for non-normal data, are required. I focus on binary outcomes, with the risk surface a smooth function of space, but the development herein is relevant for non-normal data in general. I compare penalized likelihood (PL) models, including the penalized quasi-likelihood (PQL) approach, and Bayesian models based on fit, speed, and ease of implementation.A Bayesian model using a spectral basis (SB) representation of the spatial surface via the Fourier basis provides the best tradeoff of sensitivity and specificity in simulations, detecting real spatial features while limiting overfitting and being reasonably computationally efficient. One of the contributions of this work is further development of this underused representation. The SB model outperforms the PL methods, which are prone to overfitting, but is slower to fit and not as easily implemented. A Bayesian Markov random field model performs less well statistically than the SB model, but is very computationally efficient. We illustrate the methods on a real data set of cancer cases in Taiwan.The success of the SB with binary data and similar results with count data suggest that it may be generally useful in spatial models and more complicated hierarchical models.     

Comparison of fault detection and isolation methods for a small unmanned aircraft

This paper compares three model-based methods for detecting and isolating stuck control surface faults on a small unmanned aircraft. The first method is parity-space based and compares a sensor measurement against a model-based prediction of the same quantity. The second method is observer-based and involves robust estimation for linear parameter-varying systems. The third method is also observer-based and involves multiple model adaptive estimation. The performance of the three methods are compared using flight data. The comparison shows that the three methods have different detection performance and runtime. The selection of a particular method depends on the application requirements and implementation constraints.     

Maximum likelihood based identification methods for rational models

ABSTRACT

In a rational model, some terms of the information vector are correlated with the noise, which makes the traditional least squares based iterative algorithms biased. In order to overcome this shortcoming, this paper develops two recursive algorithms for estimating the rational model parameters. These two algorithms, based on the maximum likelihood principle, have three integrated key features: (1) to establish two unbiased maximum likelihood recursive algorithms, (2) to develop a maximum likelihood recursive least squares (ML-RLS) algorithm to decrease the computational efforts, (3) to update the parameter estimates by the ML-RLS based particle swarm optimisation (ML-RLS-PSO) algorithm when the noise-to-output ratio is large. Comparative studies demonstrate that (1) the ML-RLS algorithm is only valid for rational models when the noise-to-output ratio is small, (2) the ML-RLS-PSO algorithm is effective for rational models with random noise-to-output ratio, but at the cost of heavy computational efforts. Furthermore, the simulations provide cases for potential expansion and applications of the proposed algorithms.     

具有分片非线性输入的Wiener系统的随机梯度迭代(英文)

研究了一类具有分片非线性输入(又称为死区非线性输入)的Wiener系统的参数辨识,分片非线性输入是一个强非线性输入,其数学模型不能写成参数乘以输入的形式,首先引入开关函数,接着利用开关函数将原系统的不可辨识模型转换为可辨识模型,然后通过随机梯度迭代方法辨识出系统的参数,利用辨识出的参数可以计算出系统所有待辨识参数。仿真结果证明了本文方法的有效性。     

Auxiliary model multiinnovation stochastic gradient parameter estimation methods for nonlinear sandwich systems

This article studies the identification problem of the nonlinear sandwich systems. For the sandwich system, because there are inner variables which cannot be measured in the information vector of the identification models, it is difficult to identify the nonlinear sandwich systems. In order to overcome the difficulty, an auxiliary model is built to predict the estimates of inner variables by means of the output of the auxiliary model. For the purpose of employing the real‐time observed data, a cost function with dynamical data is constructed to capture on‐line information of the nonlinear sandwich system. On this basis, an auxiliary model stochastic gradient identification approach is proposed based on the gradient optimization. Moreover, an auxiliary model multiinnovation stochastic gradient estimation method is developed, which tends to enhance estimation accuracy by introducing more observed data dynamically. The numerical simulation is provided and the simulation results show that the proposed auxiliary model identification method is effective for the nonlinear sandwich systems.     

Parametric inference for progressive Type-I hybrid censored data on a simple step-stress accelerated life test model

This paper considers a simple step-stress accelerated life test model under progressive Type-I hybrid censoring scheme. The progressive Type-I hybrid censoring scheme and statistical method in synthetic accelerated stresses are provided so as to decrease the lifetime and reduce the test cost. An exponentially distributed life of test units and a cumulative exposure model are assumed. The maximum likelihood estimates of the model parameters are obtained using a pivotal quantity. Two useful lemmas and a theorem are given to construct the approximate confidence intervals for the model parameters. Finally, simulation results are provided to assess the method of inference developed in this article. The simulation results show that the method does improve for large sample size.     

基于辅助模型和数据滤波的伪线性回归系统参数估计方法

针对伪线性输出误差回归系统的辨识模型新息信息向量存在不可测变量的问题,首先通过构造一个辅助模型,用辅助模型的输出代替未知中间变量,推导得到的基于辅助模型的递推最小二乘参数估计算法计算量较大,但算法的辨识效果不佳。进一步采用估计的噪声模型对系统观测数据进行滤波,使用滤波后的数据进行参数估计,从而推导提出了基于数据滤波的递推最小二乘参数估计算法。仿真结果表明,所提算法能够有效估计伪线性回归线性输出误差系统的参数。     

Inference for a simple step-stress model with competing risks for failure from the exponential distribution under time constraint

In reliability analysis, accelerated life-testing allows for gradual increment of stress levels on test units during an experiment. In a special class of accelerated life tests known as step-stress tests, the stress levels increase discretely at pre-fixed time points, and this allows the experimenter to obtain information on the parameters of the lifetime distributions more quickly than under normal operating conditions. Moreover, when a test unit fails, there are often more than one fatal cause for the failure, such as mechanical or electrical. In this article, we consider the simple step-stress model under time constraint when the lifetime distributions of the different risk factors are independently exponentially distributed. Under this setup, we derive the maximum likelihood estimators (MLEs) of the unknown mean parameters of the different causes under the assumption of a cumulative exposure model. Since it is found that the MLEs do not exist when there is no failure by any particular risk factor within the specified time frame, the exact sampling distributions of the MLEs are derived through the use of conditional moment generating functions. Using these exact distributions as well as the asymptotic distributions, the parametric bootstrap method, and the Bayesian posterior distribution, we discuss the construction of confidence intervals and credible intervals for the parameters. Their performance is assessed through Monte Carlo simulations and finally, we illustrate the methods of inference discussed here with an example.     

Laplace random effects models for interlaboratory studies

A model is introduced for measurements obtained in collaborative interlaboratory studies, comprising measurement errors and random laboratory effects that have Laplace distributions, possibly with heterogeneous, laboratory-specific variances. Estimators are suggested for the common median and for its standard deviation. We provide predictors of the laboratory effects, and of their pairwise differences, along with the standard errors of these predictors. Explicit formulas are given for all estimators, whose sampling performance is assessed in a Monte Carlo simulation study.     

Recursive methods for estimating the radial basis function‐based state‐dependent autoregressive model

Identifying a nonlinear radial basis function‐based state‐dependent autoregressive (RBF‐AR) time series model is the basis for solving the corresponding prediction and control problems. This paper studies some recursive parameter estimation algorithms for the RBF‐AR model. Considering the difficulty of the nonlinear optimal problem arising in estimating the RBF‐AR model, an overall forgetting gradient algorithm is deduced based on the negative gradient search. A numerical method with a forgetting factor is provided to solve the problem of determining the optimal convergence factor. In order to improve the parameter estimation accuracy, the multi‐innovation identification theory is applied to develop an overall multi‐innovation forgetting gradient (O‐MIFG) algorithm. The simulation results indicate that the estimation model based on the O‐MIFG algorithm can capture the dynamics of the RBF‐AR model very well.     

有理模型辨识的两类新方法——混合迭代与柔性最小二乘法

针对有理模型提出两类辨识方法.首先提出基于递阶辨识思想的混合辨识方法,将模型分解为分子和分母两个子模型,分别用最小二乘法辨识分子参数,用粒子群算法和智能多步长梯度迭代算法辨识分母参数.由于降低了模型维数,且信息向量与噪声不相关,相对于传统的偏差补偿最小二乘算法,混合迭代法可以提高辨识精度并降低计算量.然后,为消除模型结构已知的假设,且充分利用最新数据更新系统参数,提出柔性递推最小二乘辨识方法,将有理模型转化为时变参数系统,进而辨识出时变系统的参数.仿真例子验证了所提出方法的有效性.     

Auxiliary model-based least-squares identification methods for Hammerstein output-error systems

The difficulty in identification of a Hammerstein (a linear dynamical block following a memoryless nonlinear block) nonlinear output-error model is that the information vector in the identification model contains unknown variables—the noise-free (true) outputs of the system. In this paper, an auxiliary model-based least-squares identification algorithm is developed. The basic idea is to replace the unknown variables by the output of an auxiliary model. Convergence analysis of the algorithm indicates that the parameter estimation error consistently converges to zero under a generalized persistent excitation condition. The simulation results show the effectiveness of the proposed algorithms.