Log-modified Weibull regression models with censored data: Sensitivity and residual analysis

This paper proposes a regression model considering the modified Weibull distribution. This distribution can be used to model bathtub-shaped failure rate functions. Assuming censored data, we consider maximum likelihood and Jackknife estimators for the parameters of the model. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and we also present some ways to perform global influence. Besides, for different parameter settings, sample sizes and censoring percentages, various simulations are performed and the empirical distribution of the modified deviance residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for a martingale-type residual in log-modified Weibull regression models with censored data. Finally, we analyze a real data set under log-modified Weibull regression models. A diagnostic analysis and a model checking based on the modified deviance residual are performed to select appropriate models. (c) 2008 Elsevier B.V. All rights reserved.

Regression models for grouped survival data: Estimation and sensitivity analysis

In this study, regression models are evaluated for grouped survival data when the effect of censoring time is considered in the model and the regression structure is modeled through four link functions. The methodology for grouped survival data is based on life tables, and the times are grouped in k intervals so that ties are eliminated. Thus, the data modeling is performed by considering the discrete models of lifetime regression. The model parameters are estimated by using the maximum likelihood and jackknife methods. To detect influential observations in the proposed models, diagnostic measures based on case deletion, which are denominated global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to those measures, the local influence and the total influential estimate are also employed. Various simulation studies are performed and compared to the performance of the four link functions of the regression models for grouped survival data for different parameter settings, sample sizes and numbers of intervals. Finally, a data set is analyzed by using the proposed regression models. (C) 2010 Elsevier B.V. All rights reserved.

The exponentiated generalized gamma distribution with application to lifetime data

A four-parameter extension of the generalized gamma distribution capable of modelling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma and generalized Rayleigh, among others. We derive two infinite sum representations for its moments. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is obtained. Finally, a real data set from the medical area is analysed.

Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.

Evaluation of FAO Penman-Monteith and alternative methods for estimating reference evapotranspiration with missing data in Southern Ontario, Canada

Grass reference evapotranspiration (ETo) is an important agrometeorological parameter for climatological and hydrological studies, as well as for irrigation planning and management. There are several methods to estimate ETo, but their performance in different environments is diverse, since all of them have some empirical background. The FAO Penman-Monteith (FAD PM) method has been considered as a universal standard to estimate ETo for more than a decade. This method considers many parameters related to the evapotranspiration process: net radiation (Rn), air temperature (7), vapor pressure deficit (Delta e), and wind speed (U); and has presented very good results when compared to data from lysimeters Populated with short grass or alfalfa. In some conditions, the use of the FAO PM method is restricted by the lack of input variables. In these cases, when data are missing, the option is to calculate ETo by the FAD PM method using estimated input variables, as recommended by FAD Irrigation and Drainage Paper 56. Based on that, the objective of this study was to evaluate the performance of the FAO PM method to estimate ETo when Rn, Delta e, and U data are missing, in Southern Ontario, Canada. Other alternative methods were also tested for the region: Priestley-Taylor, Hargreaves, and Thornthwaite. Data from 12 locations across Southern Ontario, Canada, were used to compare ETo estimated by the FAD PM method with a complete data set and with missing data. The alternative ETo equations were also tested and calibrated for each location. When relative humidity (RH) and U data were missing, the FAD PM method was still a very good option for estimating ETo for Southern Ontario, with RMSE smaller than 0.53 mm day(-1). For these cases, U data were replaced by the normal values for the region and Delta e was estimated from temperature data. The Priestley-Taylor method was also a good option for estimating ETo when U and Delta e data were missing, mainly when calibrated locally (RMSE = 0.40 mm day(-1)). When Rn was missing, the FAD PM method was not good enough for estimating ETo, with RMSE increasing to 0.79 mm day(-1). When only T data were available, adjusted Hargreaves and modified Thornthwaite methods were better options to estimate ETo than the FAO) PM method, since RMSEs from these methods, respectively 0.79 and 0.83 mm day(-1), were significantly smaller than that obtained by FAO PM (RMSE = 1.12 mm day(-1). (C) 2009 Elsevier B.V. All rights reserved.

Spatio-temporal modeling of agricultural yield data with an application to pricing crop insurance contracts

This article presents a statistical model of agricultural yield data based on a set of hierarchical Bayesian models that allows joint modeling of temporal and spatial autocorrelation. This method captures a comprehensive range of the various uncertainties involved in predicting crop insurance premium rates as opposed to the more traditional ad hoc, two-stage methods that are typically based on independent estimation and prediction. A panel data set of county-average yield data was analyzed for 290 counties in the State of Parana (Brazil) for the period of 1990 through 2002. Posterior predictive criteria are used to evaluate different model specifications. This article provides substantial improvements in the statistical and actuarial methods often applied to the calculation of insurance premium rates. These improvements are especially relevant to situations where data are limited.

Development and evaluation of neural network freeway incident detection models using field data

This paper discusses a multi-layer feedforward (MLF) neural network incident detection model that was developed and evaluated using field data. In contrast to published neural network incident detection models which relied on simulated or limited field data for model development and testing, the model described in this paper was trained and tested on a real-world data set of 100 incidents. The model uses speed, flow and occupancy data measured at dual stations, averaged across all lanes and only from time interval t. The off-line performance of the model is reported under both incident and non-incident conditions. The incident detection performance of the model is reported based on a validation-test data set of 40 incidents that were independent of the 60 incidents used for training. The false alarm rates of the model are evaluated based on non-incident data that were collected from a freeway section which was video-taped for a period of 33 days. A comparative evaluation between the neural network model and the incident detection model in operation on Melbourne's freeways is also presented. The results of the comparative performance evaluation clearly demonstrate the substantial improvement in incident detection performance obtained by the neural network model. The paper also presents additional results that demonstrate how improvements in model performance can be achieved using variable decision thresholds. Finally, the model's fault-tolerance under conditions of corrupt or missing data is investigated and the impact of loop detector failure/malfunction on the performance of the trained model is evaluated and discussed. The results presented in this paper provide a comprehensive evaluation of the developed model and confirm that neural network models can provide fast and reliable incident detection on freeways. (C) 1997 Elsevier Science Ltd. All rights reserved.

Mitochondrial genome data alone are not enough to unambiguously resolve the relationships of Entognatha, Insecta and Crustacea sensu lato (Arthropoda)

An analysis of the relationships of the major arthropod groups Was undertaken using mitochondrial genome data to examine the hypotheses that Hexapoda is polyphyletic and that Collembola is more closely related to branchiopod crustaceans than insects. We sought to examine the sensitivity of this relationship to outgroup choice, data treatment. gene choice and optimality criteria used in the phylogenetic analysis of mitochondrial genome data. Additionally we sequenced the mitochondrial genome of ail archaeognathan, Nesomachilis australica. to improve taxon selection in the apterygote insects, a group poorly represented in previous mitochondrial phylogenies. The sister group of the Collembola was rarely resolved in our analyses with a significant level of support. The use of different outgroups (myriapods, nematodes, or annelids + mollusks) resulted in many different placements of Collembola. The way in which the dataset was coded for analysis (DNA, DNA with the exclusion of third codon position and as amino acids) also had marked affects on tree topology. We found that nodal Support was spread evenly throughout the 13 mitochondrial genes and the exclusion of genes resulted in significantly less resolution in the inferred trees. Optimality criteria had a much lesser effect on topology than the preceding factors; parsimony and Bayesian trees for a given data set and treatment were quite similar. We therefore conclude that the relationships of the extant arthropod groups as inferred by mitochondrial genomes are highly vulnerable to outgroup choice, data treatment and gene choice, and no consistent alternative hypothesis of Collembola's relationships is supported. Pending the resolution of these identified problems with the application of mitogenomic data to basal arthropod relationships, it is difficult to justify the rejection of hexapod monophyly, which is well supported on morphological grounds. (c) The Willi Hennig Society 2004.

Analyzing the connectivity between regions of interest: An approach based on cluster Granger causality for NRI data analysis

The identification, modeling, and analysis of interactions between nodes of neural systems in the human brain have become the aim of interest of many studies in neuroscience. The complex neural network structure and its correlations with brain functions have played a role in all areas of neuroscience, including the comprehension of cognitive and emotional processing. Indeed, understanding how information is stored, retrieved, processed, and transmitted is one of the ultimate challenges in brain research. In this context, in functional neuroimaging, connectivity analysis is a major tool for the exploration and characterization of the information flow between specialized brain regions. In most functional magnetic resonance imaging (fMRI) studies, connectivity analysis is carried out by first selecting regions of interest (ROI) and then calculating an average BOLD time series (across the voxels in each cluster). Some studies have shown that the average may not be a good choice and have suggested, as an alternative, the use of principal component analysis (PCA) to extract the principal eigen-time series from the ROI(s). In this paper, we introduce a novel approach called cluster Granger analysis (CGA) to study connectivity between ROIs. The main aim of this method was to employ multiple eigen-time series in each ROI to avoid temporal information loss during identification of Granger causality. Such information loss is inherent in averaging (e.g., to yield a single ""representative"" time series per ROI). This, in turn, may lead to a lack of power in detecting connections. The proposed approach is based on multivariate statistical analysis and integrates PCA and partial canonical correlation in a framework of Granger causality for clusters (sets) of time series. We also describe an algorithm for statistical significance testing based on bootstrapping. By using Monte Carlo simulations, we show that the proposed approach outperforms conventional Granger causality analysis (i.e., using representative time series extracted by signal averaging or first principal components estimation from ROIs). The usefulness of the CGA approach in real fMRI data is illustrated in an experiment using human faces expressing emotions. With this data set, the proposed approach suggested the presence of significantly more connections between the ROIs than were detected using a single representative time series in each ROI. (c) 2010 Elsevier Inc. All rights reserved.

A general hazard model for lifetime data in the presence of cure rate

Historically, the cure rate model has been used for modeling time-to-event data within which a significant proportion of patients are assumed to be cured of illnesses, including breast cancer, non-Hodgkin lymphoma, leukemia, prostate cancer, melanoma, and head and neck cancer. Perhaps the most popular type of cure rate model is the mixture model introduced by Berkson and Gage [1]. In this model, it is assumed that a certain proportion of the patients are cured, in the sense that they do not present the event of interest during a long period of time and can found to be immune to the cause of failure under study. In this paper, we propose a general hazard model which accommodates comprehensive families of cure rate models as particular cases, including the model proposed by Berkson and Gage. The maximum-likelihood-estimation procedure is discussed. A simulation study analyzes the coverage probabilities of the asymptotic confidence intervals for the parameters. A real data set on children exposed to HIV by vertical transmission illustrates the methodology.

Integrating high and moderate spatial resolution image data to estimate forest age structure

The collection of spatial information to quantify changes to the state and condition of the environment is a fundamental component of conservation or sustainable utilization of tropical and subtropical forests, Age is an important structural attribute of old-growth forests influencing biological diversity in Australia eucalypt forests. Aerial photograph interpretation has traditionally been used for mapping the age and structure of forest stands. However this method is subjective and is not able to accurately capture fine to landscape scale variation necessary for ecological studies. Identification and mapping of fine to landscape scale vegetative structural attributes will allow the compilation of information associated with Montreal Process indicators lb and ld, which seek to determine linkages between age structure and the diversity and abundance of forest fauna populations. This project integrated measurements of structural attributes derived from a canopy-height elevation model with results from a geometrical-optical/spectral mixture analysis model to map forest age structure at a landscape scale. The availability of multiple-scale data allows the transfer of high-resolution attributes to landscape scale monitoring. Multispectral image data were obtained from a DMSV (Digital Multi-Spectral Video) sensor over St Mary's State Forest in Southeast Queensland, Australia. Local scene variance levels for different forest tapes calculated from the DMSV data were used to optimize the tree density and canopy size output in a geometric-optical model applied to a Landsat Thematic Mapper (TU) data set. Airborne laser scanner data obtained over the project area were used to calibrate a digital filter to extract tree heights from a digital elevation model that was derived from scanned colour stereopairs. The modelled estimates of tree height, crown size, and tree density were used to produce a decision-tree classification of forest successional stage at a landscape scale. The results obtained (72% accuracy), were limited in validation, but demonstrate potential for using the multi-scale methodology to provide spatial information for forestry policy objectives (ie., monitoring forest age structure).

Fitting a mixture model to three-mode three-way data with missing information

When the data consist of certain attributes measured on the same set of items in different situations, they would be described as a three-mode three-way array. A mixture likelihood approach can be implemented to cluster the items (i.e., one of the modes) on the basis of both of the other modes simultaneously (i.e,, the attributes measured in different situations). In this paper, it is shown that this approach can be extended to handle three-mode three-way arrays where some of the data values are missing at random in the sense of Little and Rubin (1987). The methodology is illustrated by clustering the genotypes in a three-way soybean data set where various attributes were measured on genotypes grown in several environments.

An EM-based Semi-Parametric Mixture Model Approach to the Regression Analysis of Competing-Risks Data

We consider a mixture model approach to the regression analysis of competing-risks data. Attention is focused on inference concerning the effects of factors on both the probability of occurrence and the hazard rate conditional on each of the failure types. These two quantities are specified in the mixture model using the logistic model and the proportional hazards model, respectively. We propose a semi-parametric mixture method to estimate the logistic and regression coefficients jointly, whereby the component-baseline hazard functions are completely unspecified. Estimation is based on maximum likelihood on the basis of the full likelihood, implemented via an expectation-conditional maximization (ECM) algorithm. Simulation studies are performed to compare the performance of the proposed semi-parametric method with a fully parametric mixture approach. The results show that when the component-baseline hazard is monotonic increasing, the semi-parametric and fully parametric mixture approaches are comparable for mildly and moderately censored samples. When the component-baseline hazard is not monotonic increasing, the semi-parametric method consistently provides less biased estimates than a fully parametric approach and is comparable in efficiency in the estimation of the parameters for all levels of censoring. The methods are illustrated using a real data set of prostate cancer patients treated with different dosages of the drug diethylstilbestrol. Copyright (C) 2003 John Wiley Sons, Ltd.

Effect of changing data collection parameters on statistical motor unit number estimates

The effect of number of samples and selection of data for analysis on the calculation of surface motor unit potential (SMUP) size in the statistical method of motor unit number estimates (MUNE) was determined in 10 normal subjects and 10 with amyotrophic lateral sclerosis (ALS). We recorded 500 sequential compound muscle action potentials (CMAPs) at three different stable stimulus intensities (10–50% of maximal CMAP). Estimated mean SMUP sizes were calculated using Poisson statistical assumptions from the variance of 500 sequential CMAP obtained at each stimulus intensity. The results with the 500 data points were compared with smaller subsets from the same data set. The results using a range of 50–80% of the 500 data points were compared with the full 500. The effect of restricting analysis to data between 5–20% of the CMAP and to standard deviation limits was also assessed. No differences in mean SMUP size were found with stimulus intensity or use of different ranges of data. Consistency was improved with a greater sample number. Data within 5% of CMAP size gave both increased consistency and reduced mean SMUP size in many subjects, but excluded valid responses present at that stimulus intensity. These changes were more prominent in ALS patients in whom the presence of isolated SMUP responses was a striking difference from normal subjects. Noise, spurious data, and large SMUP limited the Poisson assumptions. When these factors are considered, consistent statistical MUNE can be calculated from a continuous sequence of data points. A 2 to 2.5 SD or 10% window are reasonable methods of limiting data for analysis. Muscle Nerve 27: 320–331, 2003

Geostatistical Mapping of Outfall Plume Dispersion Data gathered with an autonomous underwater vehicle

The main purpose of this study was to examine the applicability of geostatistical modeling to obtain valuable information for assessing the environmental impact of sewage outfall discharges. The data set used was obtained in a monitoring campaign to S. Jacinto outfall, located off the Portuguese west coast near Aveiro region, using an AUV. The Matheron’s classical estimator was used the compute the experimental semivariogram which was fitted to three theoretical models: spherical, exponential and gaussian. The cross-validation procedure suggested the best semivariogram model and ordinary kriging was used to obtain the predictions of salinity at unknown locations. The generated map shows clearly the plume dispersion in the studied area, indicating that the effluent does not reach the near by beaches. Our study suggests that an optimal design for the AUV sampling trajectory from a geostatistical prediction point of view, can help to compute more precise predictions and hence to quantify more accurately dilution. Moreover, since accurate measurements of plume’s dilution are rare, these studies might be very helpful in the future for validation of dispersion models.