Pearson Residuals Research Articles

On the specificity of different methods for neutral detergent fiber and related problems

We compared alternative methods for analyzing Neutral Detergent Fiber with the reference AOAC 2002.04 method for specificity. We reported the chemical composition of major nutrients for the matrixes of 19 feeds and one non-feed (sawdust). Two independent matrixes were from animal origin: meat and bone meal, and milk powder. All fiber residues were ash and blank-corrected to yield values comparable to the reference aNDFom obtained with the reflux in crucibles (Fibertec, method 1) or in Berzelius beakers without spouts (method 2). The alternative fiber methods were as follow: reflux in Berzelius beakers with spouts (method 3), the ANKOM pressurized filter bag system (method 4), a non-pressurized filter bags (nonwoven tissue) immersion system (TECNAL, method 5), and micro-NDF digestion in crimp-sealed penicillin flasks deposited in an autoclave (method 6). The major nutrients were fractional mass proportions described as Beta-distributed variables. Assuming aNDFom as normally distributed because of negative fiber values recorded, an information-theoretic approach identified the relevance of the random effects of analyst (three analysts of the same laboratory) and their interactions with matrix, method, and matrix-method interaction as fixed effects. We also challenged the traditional homoscedastic assumption. The GLIMMIX procedure of SAS was used to fit the models. In sequence, we chose the model without all random effects except for the analyst-method-matrix interaction defined as the subject and a complete heteroscedastic structure with one variance estimate for each method-matrix group. We removed milk powder from the dataset to fit the same model by assuming that aNDFom/1000 was Beta-distributed, and Pearson residuals demonstrated a comparable fit to the normal assumption. Within the limits of the experimental error, the ADFom was entirely formed by Lignin (sa) for meat and bone meal and for powdered milk. We observed a significant method-matrix interaction for aNDFom. Therefore, effect slices for methods within matrix and vice-versa revealed several significant contrasts between reference and alternative methods for aNDFom. Methods 1 and 2 were not different. With powdered milk removed from the analysis, the fit under Beta-distributed aNDFom resulted in an increased number of significant contrasts; however, contrasts between methods 1 and 2 remained non-significant, regardless of the matrix analyzed. Significant contrasts demonstrated the lack of specificity of the alternative methods used to measure insoluble fiber compared with the reference methods. In terms of variability, within-laboratory variance for aNDFom corresponded to the method-matrix-analyst component, and the variation introduced by different analysts in the same laboratory was negligible.

Producing Distribution Maps for a Spatially-Explicit Ecosystem Model Using Large Monitoring and Environmental Databases and a Combination of Interpolation and Extrapolation

To be able to simulate spatial patterns of predator-prey interactions, many spatially-explicit ecosystem modeling platforms, including Atlantis, need to be provided with distribution maps defining the annual or seasonal spatial distributions of functional groups and life stages. We developed a methodology combining extrapolation and interpolation of the predictions made by statistical habitat models to produce distribution maps for the fish and invertebrates represented in the Atlantis model of the Gulf of Mexico (GOM) Large Marine Ecosystem (LME) (“Atlantis-GOM”). This methodology consists of: (1) compiling a large monitoring database, gathering all the fisheries-independent and fisheries-dependent data collected in the northern (U.S.) GOM since 2000; (2) compiling a large environmental database, storing all the environmental parameters known to influence the spatial distribution patterns of fish and invertebrates of the GOM; (3) fitting binomial generalized additive models (GAMs) to the large monitoring and environmental databases, and geostatistical binomial generalized linear mixed models (GLMMs) to the large monitoring database; and (4) employing GAM predictions to infer spatial distributions in the southern GOM, and GLMM predictions to infer spatial distributions in the U.S. GOM. Thus, our methodology allows for reasonable extrapolation in the southern GOM based on a large amount of monitoring and environmental data, and for interpolation in the U.S. GOM accurately reflecting the probability of encountering fish and invertebrates in that region. We used an iterative cross-validation procedure to validate GAMs. When a GAM did not pass the validation test, we employed a GAM for a related functional group/life stage to generate distribution maps for the southern GOM. In addition, no geostatistical GLMMs were fit for the functional groups and life stages whose depth, longitudinal and latitudinal ranges within the U.S. GOM are not entirely covered by the data from the large monitoring database; for those, only GAM predictions were employed to obtain distribution maps for Atlantis-GOM. Pearson residuals were computed to validate geostatistical binomial GLMMs. Ultimately, 53 annual maps and 64 seasonal maps (for 32 different functional groups/life stages) were produced for Atlantis-GOM. Our methodology could serve other world’s regions characterized by a large surface area, particularly LMEs bordered by several countries.

Cochrane systematic reviews of interventions for risk factors correlate weakly with global risk factor burden: a cross-sectional study

Background and ObjectivesSystematic reviews (SRs) are important for health-care decision-makers requiring evidence for interventions that target modifiable risk factors to prevent disease. We investigated whether Cochrane SR output correlated with risk factor burden as assessed by the Global Burden of Disease Study 2015. MethodsWe screened and extracted data from Cochrane reviews and protocols published since January 2011 investigating modifiable risk factors as outcomes. We calculated Spearman's rank correlation between number of occasions a risk factor was an SR outcome and that risk factor's global disease burden in disability-adjusted life years (DALYs). We also calculated standardized Pearson residuals (SPRs) of the variance between the observed and expected frequency of a risk factor featuring as an outcome. ResultsWe obtained 400 unique SRs and 174 unique protocols from 6,392 Cochrane publications. Risk factors were an outcome a total of 965 times. The number of SR outcomes and DALYs per risk factor shared a weak-positive correlation (r = 0.45) for all risk factors, but was high (r = 0.83) for metabolic risks, similar for behavioral risks (r = 0.46), and weak negative for occupational and environmental risks (r = −0.40). SPRs for “high total cholesterol”, “low bone mineral density”, “alcohol and drug use” , and “child and maternal malnutrition” inferred a higher than expected frequency of outcomes, and for “air pollution”, “dietary risk”, and “unsafe water, sanitation, and hand-washing”, fewer than expected. ConclusionOur study investigated whether Cochrane risk factor SRs align with global risk factor burden, demonstrating a weak-positive correlation. Interventions modifying air pollution and dietary risks were sparsely studied, given disease burden.

Robust Adaptive Lasso method for parameter's estimation and variable selection in high-dimensional sparse models.

High dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. To address this issue different penalized regression procedures have been introduced in the litrature, but these methods cannot cope with the problem of outliers and leverage points in the heavy tailed high dimensional data. For this purppose, a new Robust Adaptive Lasso (RAL) method is proposed which is based on pearson residuals weighting scheme. The weight function determines the compatibility of each observations and downweight it if they are inconsistent with the assumed model. It is observed that RAL estimator can correctly select the covariates with non-zero coefficients and can estimate parameters, simultaneously, not only in the presence of influential observations, but also in the presence of high multicolliearity. We also discuss the model selection oracle property and the asymptotic normality of the RAL. Simulations findings and real data examples also demonstrate the better performance of the proposed penalized regression approach.

Producing distribution maps for informing ecosystem-based fisheries management using a comprehensive survey database and spatio-temporal models

Abstract Ecosystem-based fisheries-management (EBFM) is increasingly used in the United States (U.S.), including in the Gulf of Mexico (GOM). Producing distribution maps for marine organisms is a critical step in the implementation of EBFM. In particular, distribution maps are important inputs for many spatially-explicit ecosystem models, such as OSMOSE models, as well as for biophysical models used to predict annual recruitment anomalies due to oceanographic factors. In this study, we applied a recently proposed statistical modelling framework to produce distribution maps for: (i) younger juveniles (ages 0–1) of red snapper (Lutjanus campechanus), red grouper (Epinephelus morio), and gag (Mycteroperca microlepis), so as to be able to define the potential larval settlement areas of the three species in a biophysical model; and (ii) the functional groups and life stages represented in the OSMOSE model of the West Florida Shelf (“OSMOSE-WFS”). This statistical modelling framework consists of: (i) compiling a large database blending all of the encounter/non-encounter data of the GOM collected by the fisheries-independent and fisheries-dependent surveys using random sampling schemes, referred to as the “comprehensive survey database;” (ii) employing the comprehensive survey database to fit spatio-temporal binomial generalized linear mixed models (GLMMs) that integrate the confounding effects of survey and year; and (iii) using the predictions of the fitted spatio-temporal binomial GLMMs to generate distribution maps. This large endeavour allowed us to produce distribution maps for younger juveniles of red snapper, red grouper and gag and nearly all of the other functional groups and life stages represented in OSMOSE-WFS, at different seasons. Using Pearson residuals, the probabilities of encounter predicted by all spatio-temporal binomial GLMMs were demonstrated to be reasonable. Moreover, the results obtained for younger juvenile fish concur with the literature, provide additional insights into the spatial distribution patterns of these life stages, and highlight important future research avenues.

Antibiotic Resistances in Livestock: A Comparative Approach to Identify an Appropriate Regression Model for Count Data.

Antimicrobial resistance in livestock is a matter of general concern. To develop hygiene measures and methods for resistance prevention and control, epidemiological studies on a population level are needed to detect factors associated with antimicrobial resistance in livestock holdings. In general, regression models are used to describe these relationships between environmental factors and resistance outcome. Besides the study design, the correlation structures of the different outcomes of antibiotic resistance and structural zero measurements on the resistance outcome as well as on the exposure side are challenges for the epidemiological model building process. The use of appropriate regression models that acknowledge these complexities is essential to assure valid epidemiological interpretations. The aims of this paper are (i) to explain the model building process comparing several competing models for count data (negative binomial model, quasi-Poisson model, zero-inflated model, and hurdle model) and (ii) to compare these models using data from a cross-sectional study on antibiotic resistance in animal husbandry. These goals are essential to evaluate which model is most suitable to identify potential prevention measures. The dataset used as an example in our analyses was generated initially to study the prevalence and associated factors for the appearance of cefotaxime-resistant Escherichia coli in 48 German fattening pig farms. For each farm, the outcome was the count of samples with resistant bacteria. There was almost no overdispersion and only moderate evidence of excess zeros in the data. Our analyses show that it is essential to evaluate regression models in studies analyzing the relationship between environmental factors and antibiotic resistances in livestock. After model comparison based on evaluation of model predictions, Akaike information criterion, and Pearson residuals, here the hurdle model was judged to be the most appropriate model.

Validation of ecological state space models using the Laplace approximation

Many statistical models in ecology follow the state space paradigm. For such models, the important step of model validation rarely receives as much attention as estimation or hypothesis testing, perhaps due to lack of available algorithms and software. Model validation is often based on a naive adaptation of Pearson residuals, i.e. the difference between observations and posterior means, even if this approach is flawed. Here, we consider validation of state space models through one-step prediction errors, and discuss principles and practicalities arising when the model has been fitted with a tool for estimation in general mixed effects models. Implementing one-step predictions in the R package Template Model Builder, we demonstrate that it is possible to perform model validation with little effort, even if the ecological model is multivariate, has non-linear dynamics, and whether observations are continuous or discrete. With both simulated data, and a real data set related to geolocation of seals, we demonstrate both the potential and the limitations of the techniques. Our results fill a need for convenient methods for validating a state space model, or alternatively, rejecting it while indicating useful directions in which the model could be improved.

Object selection in credit scoring using covariance matrix of parameters estimations

We address the problem of outlier detection for more reliable credit scoring. Scoring models are used to estimate the probability of loan default based on the customer’s application. To get an unbiased estimation of the model parameters one must select a set of informative objects (customers). We propose an object selection algorithm based on analysis of the covariance matrix for the estimated parameters of the model. To detect outliers we introduce a new quality function called specificity measure. For common practical case of ill-conditioned covariance matrix we suggest an empirical approximation of specificity. We illustrate the algorithm with eight benchmark datasets from the UCI machine learning repository and several artificial datasets. Computational experiments show statistical significance of the classification quality improvement for all considered datasets. The method is compared with four other widely used methods of outlier detection: deviance, Pearson and Bayesian residuals and gamma plots. Suggested method performs generally better for both clustered and non-clustered outliers. The method shows acceptable outlier discrimination for datasets that contain up to 30–40% of outliers.

Asymptotic adjustments of Pearson residuals in exponential family nonlinear models

ABSTRACTIn this work we define a set of corrected Pearson residuals for continuous exponential family nonlinear models that have the same distribution as the true Pearson residuals up to order , where n is the sample size. Furthermore, we also introduce a new modification of the Pearson residuals, which we call PCA Pearson residuals, that are approximately uncorrelated. These PCA residuals are new even for the generalized linear models. The numerical results show that the PCA residuals are approximately normally distributed, thus improving previous results by Simas and Cordeiro [Adjusted Pearson residuals in exponential family nonlinear models. J Stat Comput Simul. 2009;79:411–425]. These numerical results also show that the corrected Pearson residuals approximately follow the same distribution as the true residuals, which is a considerable improvement with respect to the Pearson residuals and also extends the previous work by Cordeiro and Simas [The distribution of Pearson residuals in generalized linear models. Comput Stat Data Anal. 2009;53:3397–3411].

On Comparison of Stochastic Reserving Methods with Bootstrapping

We consider the well-known stochastic reserve estimation methods on the basis of generalized linear models, such as the (over-dispersed) Poisson model, the gamma model and the log-normal model. For the likely variability of the claims reserve, bootstrap method is considered. In the bootstrapping framework, we discuss the choice of residuals, namely the Pearson residuals, the deviance residuals and the Anscombe residuals. In addition, several possible residual adjustments are discussed and compared in a case study. We carry out a practical implementation and comparison of methods using real-life insurance data to estimate reserves and their prediction errors. We propose to consider proper scoring rules for model validation, and the assessments will be drawn from an extensive case study.

Modeling Longitudinal Obesity Data with Intermittent Missingness Using a New Latent Variable Model

We propose a latent variable model for informative missingness in longitudinal studies which is an extension of latent dropout class model. In our model, the value of the latent variable is affected by the missingness pattern and it is also used as a covariate in modeling the longitudinal response. So the latent variable links the longitudinal response and the missingness process. In our model, the latent variable is continuous instead of categorical and we assume that it is from a normal distribution. The EM algorithm is used to obtain the estimates of the parameter we are interested in and Gauss–Hermite quadrature is used to approximate the integration of the latent variable. The standard errors of the parameter estimates can be obtained from the bootstrap method or from the inverse of the Fisher information matrix of the final marginal likelihood. Comparisons are made to the mixed model and complete-case analysis in terms of a clinical trial dataset, which is Weight Gain Prevention among Women (WGPW) study. We use the generalized Pearson residuals to assess the fit of the proposed latent variable model.

On a dispersion model with Pearson residual responses

Dispersion regression is often used to predict the expected deviance in a generalised linear model. Using the individual deviance residual as the response variable in that model is considered the standard approach in dispersion modelling. In this paper, we investigate an alternative approach by fitting the dispersion model on the individual Pearson residual responses, which is more straightforward than and has superior interpretability to the deviance approach because no transformation on the observed and expected responses via the likelihood function is required. However, the mean and dispersion parameters are non-orthogonal if the model parameter estimates are obtained by maximising the pseudo-likelihood function. Consequently, the mean and dispersion regression parameters must be estimated simultaneously, and the estimation algorithm is multidimensional and hence more complex. As the asymptotic behaviour of both the deviance and Pearson residuals suggests that they should converge, we expect Pearson residual dispersion models to perform in the same way as or even better than deviance residual models.

Predicting return of erectile function following external beam radiotherapy or brachytherapy for prostate cancer using EPIC-CP.

87 Background: EPIC-CP (Expanded Prostate Cancer Index Composite for Clinical Practice) is a one page, 16-item questionnaire designed and validated to measure patient-reported health related quality of life in prostate cancer (PC) patients at the point of care in the clinical setting. We previously developed and externally validated models predictive of intact sexual function (i.e. achieving an erection firm enough for intercourse) at two years following external beam radiation (EBRT) or brachytherapy (BT) using EPIC-26, the parent tool from which EPIC-CP was derived. We aimed to enable the use of these models in clinical practice by recalibrating them for use with EPIC-CP. Methods: Using a previously described multicenter longitudinal cohort (PROST-QA), we identified 217 men treated with EBRT and 230 with BT with complete sexual domain and model covariate information. We used the established covariates predictive of functional erections in the EPIC-26-based models (baseline sexual score, neoadjuvant hormonal therapy, and baseline PSA for EBRT, and baseline sexual score, age, race, and BMI for BT) to recalibrate the multivariable logistic regression models for use with EPIC-CP. We examined Pearson residuals to determine goodness of fit and compared the individual predictions based on the revised models with those generated by the EPIC-26-based models. Results: The recalibrated EPIC-CP-based models demonstrated excellent discrimination (AUC 0.81 for EBRT, AUC 0.87 for BT). Odds ratio estimates for the EPIC-CP models changed by no more than 0.2 from their EPIC-26 counterparts, and remained statistically significant. EPIC-CP and EPIC-26-based predictions had good concordance: the mean ± SD difference in predicted probability between EPIC-26 and EPIC-CP models was 0.0 ± 0.08 in each treatment group. Predicted probabilities were within 15.4% and 15.8% for 95% of the subjects treated with EBRT and BT, respectively. Conclusions: EPIC-CP-based nomograms predicting erectile function two years after EBRT or BT are in good agreement with established EPIC-26-based tools and offer an easily applied and accurate prediction regarding a common and impactful side effect of PC treatment.

PP12.1 – 2938: Comparison of Burke-Fahn-Marsden dystonia severity, Gross Motor, Manual Abilities and Communication Function classification scales in childhood hyperkinetic movement disorders including cerebral palsy: a Rosetta Stone study

Objective The Burke-Fahn-Marsden Dystonia Rating Scale-Movement (BFM-M) evaluates dystonia impairment, but may not reflect functional ability in paediatric movement disorders (PMD). The Gross Motor Classification System (GMFCS), Manual Ability Classification System (MACS) and Communication Function Classification System (CFCS) are widely used in the cerebral palsy (CP) literature to classify functional ability. This study explores the concordance of the three functional scales in a large sample of PMD and the impact of dystonia severity on these functional scales. Methods Children with PMD (n=161, median age 10y3mo SD 4y) were assessed using the BFM-M, and classified using the 3 scales. Data analysis was performed using the R language and environment for statistical computing, version 3.01 RDev. Overall relationships between BFM-M and categorical variables were evaluated with the Kruskal-Wallis Rank Sum Test and the proportion variation explained (R b ). Relationships between two categorical variables were assessed using Pearson's chi-squared test and Pearson residuals. Spearman correlations (rs) were also provided as an estimate of the strength of the association between variables. The information provided by these scales is compared. Results Of the 161 children included, secondary dystonias (n=125, 78%) included those of both static (n=99, 61%), including dystonic/dyskinetic CP (n=75, 47%), and progressive (n=26, 16%) dystonia. All four scales were strongly associated (all rS>0.72, p Conclusion The BFM-M is strongly linked with the GMFCS, MACS and CFCS, irrespective of aetiology. PMD other than CP could be effectively evaluated using these scales. The ability of the BFM-M scale to discriminate between GMFCS levels in this sample offers the possibility to compare samples across different studies. However, the similarity between MACS I-III in terms of BFM-M scores indicates that non-motor components such as process skills and planning are required for functional activities and cannot be explained by dystonia alone.

Abstract P4-14-10: Breast cancer histolological subtypes by race/ethnicity

Abstract BACKGROUND It is generally accepted that Asian/Pacific Islanders with breast cancer have the same or better survival than whites. Infiltrating duct carcinoma (IDC) is the most common histologic subtype of breast cancer but little is known about whether this subtype varies by race/ethnicity. The purpose of this study was to determine if there was a difference in incidence of IDC among different race/ethnicities. METHODS We identified 197,570 cases of AJCC stages 1-4 first primary female invasive breast cancer from the California Cancer registry 2000-2011. The race/ethnicity distribution was as follows: Whites n=130,634; Blacks n=11,927; Hispanics n=32,291; Asian/Pacific Islanders (API) n=22,027; and American Indians n= 691. Histology was classified using ICDO-3. The distribution of infiltrating ductal, infiltrating lobular, mixed ductal/lobular, mucinous, tubular, and medullary cancer was examined using contingency tables and Pearson Residuals. Odds ratios were computed for infiltrating ductal versus all other histologies for each race/ethnicity using whites as the comparator with logistic regression analysis adjusting for age, stage, socioeconomic status, grade, and ER/PR/HER2. The stage X race interaction was tested. RESULTS Whites had fewer than expected cases of IDC (z = -8.5) and APIs had more than expected (z = 9.2). Blacks (z = 5.6) and Hispanics (z = 6.1) had a higher number of IDC cases than expected and also had a higher than expected number of cases of medullary (black: z=12.8; Hispanic: z =10.7). The proportion of American Indians with each of the subtypes was similar to what would be expected. The stage X race interaction was statistically significant so analyses were conducted separately for each stage. APIs had an increased risk of IDC in all stages except for stage 4. Hispanics had an increased risk in stage 3 but a decreased risk in stage 4. American Indians had the same risk as whites for all stages. Blacks had decreased odds of IDC in stage 1 but increased odds in stage 3. (Table 1) Table 1. Odds ratios and 95% confidence intervals of infiltrating duct carcinoma from the California Cancer Registry 2000-2011. WhiteBlackHispanicAsian/Pacific IslanderAmerican Indian OR (95% CI)OR (95% CI)OR (95% CI)OR (95% CI)OR (95% CI)Stage 11.000.90 (0.81, 0.99)0.98 (0.92, 1.05)1.20 (1.12,1.29)1.31 (0.89, 1.92)Stage 21.000.99 (0.90, 1.09)1.06 (1.00, 1.14)1.39 (1.29, 1.50)0.73 (.051, 1.02)Stage 31.001.27 (1.10, 1.48)1.24 (1.12, 1.37)1.74 (1.52, 1.99)1.02 (0.59, 1.76)Stage 41.001.02 (0.79, 1.31)0.78 (0.64, 0.94)1.21 (0.94, 1.56)0.48 (0.19, 1.19)Confidence intervals that include 1.00 indicate that the odds of IDC were no different than the reference category CONCLUSION The incidence of IDC is not the same for all race/ethnicities and depends on the stage of disease. APIs are at an increased risk for IDC in all except for the highest stage of disease. Citation Format: Carol Parise, Vincent Caggiano. Breast cancer histolological subtypes by race/ethnicity [abstract]. In: Proceedings of the Thirty-Seventh Annual CTRC-AACR San Antonio Breast Cancer Symposium: 2014 Dec 9-13; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2015;75(9 Suppl):Abstract nr P4-14-10.

Detection of influenza-like illness aberrations by directly monitoring Pearson residuals of fitted negative binomial regression models.

BackgroundEmerging novel influenza outbreaks have increasingly been a threat to the public and a major concern of public health departments. Real-time data in seamless surveillance systems such as health insurance claims data for influenza-like illnesses (ILI) are ready for analysis, making it highly desirable to develop practical techniques to analyze such readymade data for outbreak detection so that the public can receive timely influenza epidemic warnings. This study proposes a simple and effective approach to analyze area-based health insurance claims data including outpatient and emergency department (ED) visits for early detection of any aberrations of ILI.MethodsThe health insurance claims data during 2004–2009 from a national health insurance research database were used for developing early detection methods. The proposed approach fitted the daily new ILI visits and monitored the Pearson residuals directly for aberration detection. First, negative binomial regression was used for both outpatient and ED visits to adjust for potentially influential factors such as holidays, weekends, seasons, temporal dependence and temperature. Second, if the Pearson residuals exceeded 1.96, aberration signals were issued. The empirical validation of the model was done in 2008 and 2009. In addition, we designed a simulation study to compare the time of outbreak detection, non-detection probability and false alarm rate between the proposed method and modified CUSUM.ResultsThe model successfully detected the aberrations of 2009 pandemic (H1N1) influenza virus in northern, central and southern Taiwan. The proposed approach was more sensitive in identifying aberrations in ED visits than those in outpatient visits. Simulation studies demonstrated that the proposed approach could detect the aberrations earlier, and with lower non-detection probability and mean false alarm rate in detecting aberrations compared to modified CUSUM methods.ConclusionsThe proposed simple approach was able to filter out temporal trends, adjust for temperature, and issue warning signals for the first wave of the influenza epidemic in a timely and accurate manner.Electronic supplementary materialThe online version of this article (doi:10.1186/s12889-015-1500-4) contains supplementary material, which is available to authorized users.

Robust inference in the negative binomial regression model with an application to falls data.

A popular way to model overdispersed count data, such as the number of falls reported during intervention studies, is by means of the negative binomial (NB) distribution. Classical estimating methods are well-known to be sensitive to model misspecifications, taking the form of patients falling much more than expected in such intervention studies where the NB regression model is used. We extend in this article two approaches for building robust M-estimators of the regression parameters in the class of generalized linear models to the NB distribution. The first approach achieves robustness in the response by applying a bounded function on the Pearson residuals arising in the maximum likelihood estimating equations, while the second approach achieves robustness by bounding the unscaled deviance components. For both approaches, we explore different choices for the bounding functions. Through a unified notation, we show how close these approaches may actually be as long as the bounding functions are chosen and tuned appropriately, and provide the asymptotic distributions of the resulting estimators. Moreover, we introduce a robust weighted maximum likelihood estimator for the overdispersion parameter, specific to the NB distribution. Simulations under various settings show that redescending bounding functions yield estimates with smaller biases under contamination while keeping high efficiency at the assumed model, and this for both approaches. We present an application to a recent randomized controlled trial measuring the effectiveness of an exercise program at reducing the number of falls among people suffering from Parkinsons disease to illustrate the diagnostic use of such robust procedures and their need for reliable inference.

The influence of environmental factors on abundance and prevalence of a commensal ostracod hosted by an invasive crayfish: are ‘parasite rules’ relevant to non‐parasitic symbionts?

Summary Symbiosis represents a widespread and successful lifestyle, but research on symbiotic associations has been mainly focused on parasites. Three general patterns in parasite ecology have been proposed: (i) aggregation, (ii) positive and tight correlation between mean symbiont abundance and its variance and (iii) positive correlation between abundance and prevalence of symbionts. The factors affecting abundance and prevalence within symbiont species can be grouped into host features and environmental conditions. According to research in parasite ecology, environmental conditions seem to play a minor role. We investigated whether the three most recognised parasite patterns were also evident in a non‐parasitic freshwater ectosymbiont and analysed the effects of host features (sex, body size, density and ecdysis) and environmental conditions (climate and water chemistry) on abundance and prevalence of the symbiont. Our species model was an exotic ectocommensal ostracod, Ankylocythere sinuosa, inhabiting the invasive crayfish Procambarus clarkii in Europe. We sampled 373 crayfish from 26 Spanish localities. We modelled both abundance per occupied host (i.e. intensity) and prevalence using zero‐altered models and a backward model selection of host and environmental variables, and assessed model performance through graphical analyses of Pearson residuals and the relationship between observed and fitted values of the finally selected model. We observed all three parasite patterns in A. sinuosa. Abundance of A. sinuosa was most strongly related to conductivity (negative effect), followed by host density (positive) and ecdysis (negative), with moderate relationships to variables related to water chemistry ( concentration, alkalinity/(Cl− + ) and Cl−/ ratios). Prevalence was related mainly to crayfish density (positive effect) and also to climatic conditions (maximum temperature of warmest month, annual precipitation and precipitation seasonality). Our results suggest that some ‘parasite rules’ may actually be general ‘symbiont rules’. Moreover, our symbiont model was markedly affected by climatic conditions at a regional scale acting on prevalence, and water chemistry at a local level acting on symbiont abundance. This supports the hypothesis of a prominent role of environmental conditions influencing population parameters of non‐parasitic freshwater ectosymbionts. Physiological tolerances to highly unstable environmental factors, together with dependence on highly variable external food sources, probably underlie the high sensitivity to environmental conditions of this category of symbiont.

Jackknife-After-Bootstrap as Logistic Regression Diagnostic Tool

In this study, we propose using Jackknife-after-Bootstrap (JaB) method to detect influential observations in binary logistic regression model. Performance of the proposed method has been compared with the traditional method for standardized Pearson residuals, Cook's distance, change in the Pearson chi-square and change in the deviance statistics by both real world examples and simulation studies. The results reveal that under the various scenarios considered in this article, JaB performs better than the traditional method and is more robust to masking effect especially for Cook's distance.

Elevated dry-season malaria prevalence associated with fine-scale spatial patterns of environmental risk: a case–control study of children in rural Malawi

BackgroundUnderstanding the role of local environmental risk factors for malaria in holo-endemic, poverty-stricken settings will be critical to more effectively implement- interventions aimed at eventual elimination. Household-level environmental drivers of malaria risk during the dry season were investigated in rural southern Malawi among children < five years old in two neighbouring rural Traditional Authority (TA) regions dominated by small-scale agriculture.MethodsTen villages were randomly selected from TA Sitola (n = 6) and Nsamala (n = 4). Within each village, during June to August 2011, a census was conducted of all households with children under-five and recorded their locations with a geographic position system (GPS) device. At each participating house, a nurse administered a malaria rapid diagnostic test (RDT) to children under five years of age, and a questionnaire to parents. Environmental data were collected for each house, including land cover within 50-m radius. Variables found to be significantly associated with P. falciparum infection status in bivariate analysis were included in generalized linear models, including multivariate logistic regression (MLR) and multi-level multivariate logistic regression (MLLR). Spatial clustering of RDT status, environmental factors, and Pearson residuals from MLR and MLLR were analysed using the Getis-Ord Gi* statistic.ResultsOf 390 children enrolled from six villages in Sitola (n = 162) and four villages in Nsamala (n = 228), 45.6% tested positive (n = 178) for Plasmodium infection by RDT. The MLLR modelled the statistical relationship of Plasmodium positives and household proximity to agriculture (<25-m radius), controlling for the child sex and age (in months), bed net ownership, elevation, and random effects intercepts for village and TA-level unmeasured factors. After controlling for area affects in MLLR, proximity to active agriculture remained a significant predictor of positive RDT result (OR 2.80, 95% CI 1.41-5.55). Mapping of Pearson residuals from MLR showed significant clustering (Gi* z > 2.58, p < 0.01) predominantly within TA Sitola, while residuals from MLLR showed no such clustering.ConclusionThis study provides evidence for significant, dry-season heterogeneity of malaria prevalence strongly linked to peridomestic land use, and particularly of elevated risk associated with nearby crop production.