Flexible semi-parametric regression of state occupational probabilities in a multistate model with right-censored data

Inference for the state occupation probabilities, given a set of baseline covariates, is an important problem in survival analysis and time to event multistate data. We introduce an inverse censoring probability re-weighted semi-parametric single index model based approach to estimate conditional state occupation probabilities of a given individual in a multistate model under right-censoring. Besides obtaining a temporal regression function, we also test the potential time varying effect of a baseline covariate on future state occupation. We show that the proposed technique has desirable finite sample performances and its performance is competitive when compared with three other existing approaches. We illustrate the proposed methodology using two different data sets. First, we re-examine a well-known data set dealing with leukemia patients undergoing bone marrow transplant with various state transitions. Our second illustration is based on data from a study involving functional status of a set of spinal cord injured patients undergoing a rehabilitation program.     

A wavelet approach to shape analysis for spinal curves

We present a new method to describe shape change and shape differences in curves, by constructing a deformation function in terms of a wavelet decomposition. Wavelets form an orthonormal basis which allows representations at multiple resolutions. The deformation function is estimated, in a fully Bayesian framework, using a Markov chain Monte Carlo algorithm. This Bayesian formulation incorporates prior information about the wavelets and the deformation function. The flexibility of the MCMC approach allows estimation of complex but clinically important summary statistics, such as curvature in our case, as well as estimates of deformation functions with variance estimates, and allows thorough investigation of the posterior distribution. This work is motivated by multi-disciplinary research involving a large-scale longitudinal study of idiopathic scoliosis in UK children. This paper provides novel statistical tools to study this spinal deformity, from which 5% of UK children suffer. Using the data we consider statistical inference for shape differences between normals, scoliotics and developers of scoliosis, in particular for spinal curvature, and look at longitudinal deformations to describe shape changes with time.     

A study of three-dimensional curves

In certain abnormalities of spinal shape, the long axis of the spine moves out of the median sagittal plane, producing both an axial torsion and a lateral deviation out of the usual front-back plane. Clinicians need to be able to assess rapidly and accurately whether or not an individual has such an abnormality. In this paper, we examine several case studies. These are analyzed using some simple summary statistics, and the use of these methods to infer abnormality is demonstrated. Using a simple fitted model for the data, an angular estimate of abnormality is obtained. Empirical measures of abnormality based on the eigenvalues of the covariance matrix are also determined. These methods are applied to a number of individuals for whom the surface spinal profiles have been recorded and who have been assessed as normal or abnormal by clinicians.     

Familial spinal shape

It has been proposed that there is a familial relationship in the shape of the spine. This paper describes a pilot study investigating familial shape in the sagittal plane (side view), using three data sets of normal Leeds schoolchildren. The study is exploratory in nature, because only small samples were available. Data acquisition was by means of the Quantec system, which obtains surface shape measurements and extracts a line representing the spinal curve. The coordinates of the spine line in the sagittal plane are then used to investigate familial correlations of spinal shape. The spine lines first undergo some preprocessing, including Procrustes rotations to remove location, rotation and size effects. Smoothed principal component analysis of the curves provides suitable shape variables, and familial correlations between curves are then investigated. The covariates of sex and height are also investigated in the analysis. It does appear that there could be some evidence for familial correlations in sagittal spinal shape, although a further large-scale study is required. Finally, a discussion of the approach and other alternatives is considered.     

A technique for generating Gray codes

It is often desirable to use Gray codes with properties different from those of the standard binary reflected code. Previously, only short codes (32- to 256-element) could be systematically generated or found with a given set of properties. This paper describes a technique where long codes (65000-element or longer) as well as short codes can systematically be generated with desired properties. The technique is described and demostrated by generating codes of various lenght with the desired property of equal column change counts. Several examples of the use of the technique for generating codes with other desired properties are outlined.     

Following a moving target—Monte Carlo inference for dynamic Bayesian models

Markov chain Monte Carlo (MCMC) sampling is a numerically intensive simulation technique which has greatly improved the practicality of Bayesian inference and prediction. However, MCMC sampling is too slow to be of practical use in problems involving a large number of posterior (target) distributions, as in dynamic modelling and predictive model selection. Alternative simulation techniques for tracking moving target distributions, known as particle filters, which combine importance sampling, importance resampling and MCMC sampling, tend to suffer from a progressive degeneration as the target sequence evolves. We propose a new technique, based on these same simulation methodologies, which does not suffer from this progressive degeneration.     

Forecasting before,during, and after recession with singular spectrum analysis

The aim of this research is to apply the singular spectrum analysis (SSA) technique, which is a relatively new and powerful technique in time series analysis and forecasting, to forecast the 2008 UK recession, using eight economic time series. These time series were selected as they represent the most important economic indicators in the UK. The ability to understand the underlying structure of these series and to quickly identify turning points such as the on-set of the recent recession is of key interest to users. In recent years, the SSA technique has been further developed and applied to many practical problems. Hence, these series will provide an ideal practical test of the potential benefits from SSA during one of the most challenging periods for econometric analyses of recent years. The results are compared with those obtained using the ARIMA and Holt–Winters models as these methods are currently used as standard forecasting methods in the Office for National Statistics in the UK.     

Model-based classification using latent Gaussian mixture models

A novel model-based classification technique is introduced based on parsimonious Gaussian mixture models (PGMMs). PGMMs, which were introduced recently as a model-based clustering technique, arise from a generalization of the mixtures of factor analyzers model and are based on a latent Gaussian mixture model. In this paper, this mixture modelling structure is used for model-based classification and the particular area of application is food authenticity. Model-based classification is performed by jointly modelling data with known and unknown group memberships within a likelihood framework and then estimating parameters, including the unknown group memberships, within an alternating expectation-conditional maximization framework. Model selection is carried out using the Bayesian information criteria and the quality of the maximum a posteriori classifications is summarized using the misclassification rate and the adjusted Rand index. This new model-based classification technique gives excellent classification performance when applied to real food authenticity data on the chemical properties of olive oils from nine areas of Italy.     

Generalized geometric distribution of order k: A flexible choice to randomize the response

This article focuses on the improvement of a well-celebrated randomized response technique of Kuk. A generalized randomized response technique is suggested. In particular, the generalized geometric distribution of order k is introduced as a randomization device for estimating the population proportion of a rare sensitive attribute. The proposed randomized response technique includes Singh and Grewal and Hussain et al. techniques as its special cases. Through numerical illustrations, it is established that the suggested technique is superior to the Kuk, Singh and Grewal, and Hussain et al. techniques. Flexibility of the proposed technique is also discussed.     

Adaptive Elastic Net for Generalized Methods of Moments

Model selection and estimation are crucial parts of econometrics. This article introduces a new technique that can simultaneously estimate and select the model in generalized method of moments (GMM) context. The GMM is particularly powerful for analyzing complex datasets such as longitudinal and panel data, and it has wide applications in econometrics. This article extends the least squares based adaptive elastic net estimator by Zou and Zhang to nonlinear equation systems with endogenous variables. The extension is not trivial and involves a new proof technique due to estimators’ lack of closed-form solutions. Compared to Bridge-GMM by Caner, we allow for the number of parameters to diverge to infinity as well as collinearity among a large number of variables; also, the redundant parameters are set to zero via a data-dependent technique. This method has the oracle property, meaning that we can estimate nonzero parameters with their standard limit and the redundant parameters are dropped from the equations simultaneously. Numerical examples are used to illustrate the performance of the new method.     

Analyzing center specific outcomes in hematopoietic cell transplantation

Reporting transplant center-specific survival rates after hematopoietic cell transplantation is required in the United States. We describe a method to report 1-year survival outcomes by center, as well as to quantify center performance relative to the transplant center network average, which can be reliably used with censored data and for small center sizes. Each center's observed 1-year survival outcome is compared to a predicted survival outcome adjusted for patient characteristics using a pseudovalue regression technique. A 95% prediction interval for 1-year survival assuming no center effect is computed for each center by bootstrapping the scaled residuals from the regression model, and the observed 1-year survival is compared to this prediction interval to determine center performance. We illustrate the technique using a recent center specific analysis performed by the Center for International Blood and Marrow Transplant Research, and study the performance of this method using simulation.     

A non linear analysis of the preference for preservation of the teeth

Data resulting from behavioral dental research, usually categorical or discretized and having unknown measurement and distributional characteristics, often cannot be analyzed with classical multivariate techniques. A non linear principal components technique called multiple correspondence analysis is presented with its corresponding computer program that can handle this kind of data. The model is described as a form of multidimensional scaling. The technique Is applied in order to establish which factors are associated with an Individual's preference for preservation of the teeth.     

Model-averaged ℓ1 regularization using Markov chain Monte Carlo model composition

Bayesian model averaging (BMA) is an effective technique for addressing model uncertainty in variable selection problems. However, current BMA approaches have computational difficulty dealing with data in which there are many more measurements (variables) than samples. This paper presents a method for combining ?₁ regularization and Markov chain Monte Carlo model composition techniques for BMA. By treating the ?₁ regularization path as a model space, we propose a method to resolve the model uncertainty issues arising in model averaging from solution path point selection. We show that this method is computationally and empirically effective for regression and classification in high-dimensional data sets. We apply our technique in simulations, as well as to some applications that arise in genomics.     

Bayesian variable selection in logistic regression: predicting company earnings direction

This paper presents a Bayesian technique for the estimation of a logistic regression model including variable selection. As in Ou & Penman (1989), the model is used to predict the direction of company earnings, one year ahead, from a large set of accounting variables from financial statements. To estimate the model, the paper presents a Markov chain Monte Carlo sampling scheme that includes the variable selection technique of Smith & Kohn (1996) and the non-Gaussian estimation method of Mira & Tierney (2001). The technique is applied to data for companies in the United States and Australia. The results obtained compare favourably to the technique used by Ou & Penman (1989) for both regions.     

Difference-based estimation and model identification for panel data semiparametric models with cross-section dependence

Abstract

In this article, we consider a panel data partially linear regression model with fixed effect and non parametric time trend function. The data can be dependent cross individuals through linear regressor and error components. Unlike the methods using non parametric smoothing technique, a difference-based method is proposed to estimate linear regression coefficients of the model to avoid bandwidth selection. Here the difference technique is employed to eliminate the non parametric function effect, not the fixed effects, on linear regressor coefficient estimation totally. Therefore, a more efficient estimator for parametric part is anticipated, which is shown to be true by the simulation results. For the non parametric component, the polynomial spline technique is implemented. The asymptotic properties of estimators for parametric and non parametric parts are presented. We also show how to select informative ones from a number of covariates in the linear part by using smoothly clipped absolute deviation-penalized estimators on a difference-based least-squares objective function, and the resulting estimators perform asymptotically as well as the oracle procedure in terms of selecting the correct model.     

Bootstrap techniques for proportional hazards models with censored observations

We propose a bootstrap technique for generating pseudo-samples from survival data containing censored observations. This simulation selects a survival time with replacement from the data and then assigns a covariate according to the model of proportional hazards. We also develop a constrained bootstrap technique in which every pseudo-sample has the same distribution of covariate values as does the original, observed data. We use these simulation techniques to estimate the bias and variance of regression coefficients and to approximate the significance levels of goodness-of-fit statistics for testing the assumption of the proportional hazards model.     

Local Linear Estimation for Time-Dependent Coefficients in Cox's Regression Models

This article develops a local partial likelihood technique to estimate the time-dependent coefficients in Cox's regression model. The basic idea is a simple extension of the local linear fitting technique used in the scatterplot smoothing. The coefficients are estimated locally based on the partial likelihood in a window around each time point. Multiple time-dependent covariates are incorporated in the local partial likelihood procedure. The procedure is useful as a diagnostic tool and can be used in uncovering time-dependencies or departure from the proportional hazards model. The programming involved in the local partial likelihood estimation is relatively simple and it can be modified with few efforts from the existing programs for the proportional hazards model. The asymptotic properties of the resulting estimator are established and compared with those from the local constant fitting. A consistent estimator of the asymptotic variance is also proposed. The approach is illustrated by a real data set from the study of gastric cancer patients and a simulation study is also presented.     

Categorical variable selection based on entropy reduction

This paper presents the derivation of a categorical variable selection technique which utilizes the entropy function as a measure of variability for nominally scaled variables. The selection criterion uses likelihood ratio statistics which, for the hypotheses under consideration, are identical to minimum discrimination information statistics. Thus, the paper provides an alternative motivation for a selection technique based on discriminatory power, and it provides an extension of that technique to the multipopulation discrimination problem. The selection technique is illustrated for a study in which we discriminate among three populations: cervical cancer patients, population-based controls, and hospital-based controls.     

On the Use of Semi-folding in Regular Blocked Two-level Factorial Designs

In this article, we consider experimental situations where a blocked regular two-level fractional factorial initial design is used. We investigate the use of the semi-fold technique as a follow-up strategy for de-aliasing effects that are confounded in the initial design as well as an alternative method for constructing blocked fractional factorial designs. A construction method is suggested based on the full foldover technique and sufficient conditions are obtained when the semi-fold yields as many estimable effects as the full foldover.