Flexible regression modeling

The author proposes a new method for flexible regression modeling of multi‐dimensional data, where the regression function is approximated by a linear combination of logistic basis functions. The method is adaptive, selecting simple or more complex models as appropriate. The number, location, and (to some extent) shape of the basis functions are automatically determined from the data. The method is also affine invariant, so accuracy of the fit is not affected by rotation or scaling of the covariates. Squared error and absolute error criteria are both available for estimation. The latter provides a robust estimator of the conditional median function. Computation is relatively fast, particularly for large data sets, so the method is well suited for data mining applications.     

Nonparametric regression estimates with censored data based on block thresholding method

Here we consider wavelet-based identification and estimation of a censored nonparametric regression model via block thresholding methods and investigate their asymptotic convergence rates. We show that these estimators, based on block thresholding of empirical wavelet coefficients, achieve optimal convergence rates over a large range of Besov function classes, and in particular enjoy those rates without the extraneous logarithmic penalties that are usually suffered by term-by-term thresholding methods. This work is extension of results in Li et al. (2008). The performance of proposed estimator is investigated by a numerical study.     

Testing for a change in covariance operator

The paper considers a problem of equality of two covariance operators. Using functional principal component analysis, a method for testing equality of K largest eigenvalues and the corresponding eigenfunctions, together with its generalization to a corresponding change point problem is suggested. Asymptotic distributions of the test statistics are presented.     

Hypothesis test for paired samples in the presence of missing data

Missing data are present in almost all statistical analysis. In simple paired design tests, when some subject has one of the involved variables missing in the so-called partially overlapping samples scheme, it is usually discarded for the analysis. The lack of consistency between the information reported in the univariate and multivariate analysis is, perhaps, the main consequence. Although the randomness on the missing mechanism (missingness completely at random) is an usual and needed assumption for this particular situation, missing data presence could lead to serious inconsistencies on the reported conclusions. In this paper, the authors develop a simple and direct procedure which allows using the whole available information in order to perform paired tests. In particular, the proposed methodology is applied to check the equality among the means from two paired samples. In addition, the use of two different resampling techniques is also explored. Finally, real-world data are analysed.     

Parameter estimation of nonlinear mixed-effects models using first-order conditional linearization and the EM algorithm

Nonlinear mixed-effects (NLME) models are flexible enough to handle repeated-measures data from various disciplines. In this article, we propose both maximum-likelihood and restricted maximum-likelihood estimations of NLME models using first-order conditional expansion (FOCE) and the expectation–maximization (EM) algorithm. The FOCE-EM algorithm implemented in the ForStat procedure SNLME is compared with the Lindstrom and Bates (LB) algorithm implemented in both the SAS macro NLINMIX and the S-Plus/R function nlme in terms of computational efficiency and statistical properties. Two realworld data sets an orange tree data set and a Chinese fir (Cunninghamia lanceolata) data set, and a simulated data set were used for evaluation. FOCE-EM converged for all mixed models derived from the base model in the two realworld cases, while LB did not, especially for the models in which random effects are simultaneously considered in several parameters to account for between-subject variation. However, both algorithms had identical estimated parameters and fit statistics for the converged models. We therefore recommend using FOCE-EM in NLME models, particularly when convergence is a concern in model selection.     

Distance-based approach in univariate longitudinal data analysis

In this paper, we propose a methodology to analyze longitudinal data through distances between pairs of observations (or individuals) with regard to the explanatory variables used to fit continuous response variables. Restricted maximum-likelihood and generalized least squares are used to estimate the parameters in the model. We applied this new approach to study the effect of gender and exposure on the deviant behavior variable with respect to tolerance for a group of youths studied over a period of 5 years. Were performed simulations where we compared our distance-based method with classic longitudinal analysis with both AR(1) and compound symmetry correlation structures. We compared them under Akaike and Bayesian information criterions, and the relative efficiency of the generalized variance of the errors of each model. We found small gains in the proposed model fit with regard to the classical methodology, particularly in small samples, regardless of variance, correlation, autocorrelation structure and number of time measurements.     

Multivariate linear regression for heterogeneous data

The problem of multivariate regression modelling in the presence of heterogeneous data is dealt to address the relevant issue of the influence of such heterogeneity in assessing the linear relations between responses and explanatory variables. In spite of its popularity, clusterwise regression is not designed to identify the linear relationships within ‘homogeneous’ clusters exhibiting internal cohesion and external separation. A within-clusterwise regression is introduced to achieve this aim and, since the possible presence of a linear relation ‘between’ clusters should be also taken into account, a general regression model is introduced to account for both the between-cluster and the within-cluster regression variation. Some decompositions of the variance of the responses accounted for are also given, the least-squares estimation of the parameters is derived, together with an appropriate coordinate descent algorithms and the performance of the proposed methodology is evaluated in different datasets.     

Segmentation,alignment and statistical analysis of biosignals with application to disease classification

We present a novel methodology for a comprehensive statistical analysis of approximately periodic biosignal data. There are two main challenges in such analysis: (1) the automatic extraction (segmentation) of cycles from long, cyclostationary biosignals and (2) the subsequent statistical analysis, which in many cases involves the separation of temporal and amplitude variabilities. The proposed framework provides a principled approach for statistical analysis of such signals, which in turn allows for an efficient cycle segmentation algorithm. This is achieved using a convenient representation of functions called the square-root velocity function (SRVF). The segmented cycles, represented by SRVFs, are temporally aligned using the notion of the Karcher mean, which in turn allows for more efficient statistical summaries of signals. We show the strengths of this method through various disease classification experiments. In the case of myocardial infarction detection and localization, we show that our method compares favorably to methods described in the current literature.     

A longitudinal analysis of infant and senescent mortality using mixture models

We construct a mixture distribution including infant, exogenous and Gompertzian/non-Gompertzian senescent mortality. Using mortality data from Swedish females 1751–, we show that this outperforms models without these features, and compare its trends in cohort and period mortality over time. We find an almost complete disappearance of exogenous mortality within the last century of period mortality, with cohort mortality approaching the same limits. Both Gompertzian and non-Gompertzian senescent mortality are consistently present, with the estimated balance between them oscillating constantly. While the parameters of the latter appear to be trending over time, the parameters of the former do not.     

A structured framework for assessing sensitivity to missing data assumptions in longitudinal clinical trials

The objective of this research was to demonstrate a framework for drawing inference from sensitivity analyses of incomplete longitudinal clinical trial data via a re‐analysis of data from a confirmatory clinical trial in depression. A likelihood‐based approach that assumed missing at random (MAR) was the primary analysis. Robustness to departure from MAR was assessed by comparing the primary result to those from a series of analyses that employed varying missing not at random (MNAR) assumptions (selection models, pattern mixture models and shared parameter models) and to MAR methods that used inclusive models. The key sensitivity analysis used multiple imputation assuming that after dropout the trajectory of drug‐treated patients was that of placebo treated patients with a similar outcome history (placebo multiple imputation). This result was used as the worst reasonable case to define the lower limit of plausible values for the treatment contrast. The endpoint contrast from the primary analysis was ? 2.79 (p = .013). In placebo multiple imputation, the result was ? 2.17. Results from the other sensitivity analyses ranged from ? 2.21 to ? 3.87 and were symmetrically distributed around the primary result. Hence, no clear evidence of bias from missing not at random data was found. In the worst reasonable case scenario, the treatment effect was 80% of the magnitude of the primary result. Therefore, it was concluded that a treatment effect existed. The structured sensitivity framework of using a worst reasonable case result based on a controlled imputation approach with transparent and debatable assumptions supplemented a series of plausible alternative models under varying assumptions was useful in this specific situation and holds promise as a generally useful framework. Copyright © 2012 John Wiley & Sons, Ltd.