Bayesian influence measures for joint models for longitudinal and survival data

Summary This article develops a variety of influence measures for carrying out perturbation (or sensitivity) analysis to joint models of longitudinal and survival data (JMLS) in Bayesian analysis. A perturbation model is introduced to characterize individual and global perturbations to the three components of a Bayesian model, including the data points, the prior distribution, and the sampling distribution. Local influence measures are proposed to quantify the degree of these perturbations to the JMLS. The proposed methods allow the detection of outliers or influential observations and the assessment of the sensitivity of inferences to various unverifiable assumptions on the Bayesian analysis of JMLS. Simulation studies and a real data set are used to highlight the broad spectrum of applications for our Bayesian influence methods.     

Assessment of local influence for the analysis of agreement

The concordance correlation coefficient (CCC) and the probability of agreement (PA) are two frequently used measures for evaluating the degree of agreement between measurements generated by two different methods. In this paper, we consider the CCC and the PA using the bivariate normal distribution for modeling the observations obtained by two measurement methods. The main aim of this paper is to develop diagnostic tools for the detection of those observations that are influential on the maximum likelihood estimators of the CCC and the PA using the local influence methodology but not based on the likelihood displacement. Thus, we derive first‐ and second‐order measures considering the case‐weight perturbation scheme. The proposed methodology is illustrated through a Monte Carlo simulation study and using a dataset from a clinical study on transient sleep disorder. Empirical results suggest that under certain circumstances first‐order local influence measures may be more powerful than second‐order measures for the detection of influential observations.     

Model choice and influential cases for survival studies

Deletion diagnostics are developed for identifying observations that influence the estimates of regression parameters and the mixture parameter in the families of relative risk functions for failure time data. The diagnostic for the regression parameters is a generalization of Cain and Lange's (1984, Biometrics 40, 493-499) measure of individual influence. The generalizations of martingale residuals, Schoenfeld's partial residuals (1982, Biometrika 69, 239-241), and score residuals by Therneau, Grambsch, and Fleming (1990, Biometrika 77, 147-160) are also obtained. The influence of some observations on regression parameters can be drastically modified as the mixture parameter changes, even for a very small change. In addition, adding or deleting some observations might result in choosing different models. The diagnostics are applied to a family proposed by Guerrero and Johnson (1982, Biometrika 69, 309-314). One illustrative example is presented.     

Masking unmasked in the proportional hazards model

Influence measures based on the pairwise deletion approach and the differentiation approach are developed for unmasking observations masked by other observations in the proportional hazards model. These influential observations might have substantial impact on statistical inference and might provide important information for model adequacy. One numerical example based on real data is presented and discussed.     

Assessing Local Influence in Measurement Error Models

We consider the assessment of local influence for generalized linear models when the covariates are measured with errors. We show how to evaluate the effect that perturbations to the data, case weights, and model assumptions may have on the parameter estimates. Based on the likelihood displacement functions, some useful influence diagnostics are derived. Two examples illustrate application of the proposed diagnostics and assessment of the measurement error assumptions.     

Procedure for Detecting Outliers in a Circular Regression Model

A number of circular regression models have been proposed in the literature. In recent years, there is a strong interest shown on the subject of outlier detection in circular regression. An outlier detection procedure can be developed by defining a new statistic in terms of the circular residuals. In this paper, we propose a new measure which transforms the circular residuals into linear measures using a trigonometric function. We then employ the row deletion approach to identify observations that affect the measure the most, a candidate of outlier. The corresponding cut-off points and the performance of the detection procedure when applied on Down and Mardia’s model are studied via simulations. For illustration, we apply the procedure on circadian data.     

Local influence diagnostics for hierarchical count data models with overdispersion and excess zeros

We consider models for hierarchical count data, subject to overdispersion and/or excess zeros. Molenberghs et al. ( 2007 ) and Molenberghs et al. ( 2010 ) extend the Poisson‐normal generalized linear‐mixed model by including gamma random effects to accommodate overdispersion. Excess zeros are handled using either a zero‐inflation or a hurdle component. These models were studied by Kassahun et al. ( 2014 ). While flexible, they are quite elaborate in parametric specification and therefore model assessment is imperative. We derive local influence measures to detect and examine influential subjects, that is subjects who have undue influence on either the fit of the model as a whole, or on specific important sub‐vectors of the parameter vector. The latter include the fixed effects for the Poisson and for the excess‐zeros components, the variance components for the normal random effects, and the parameters describing gamma random effects, included to accommodate overdispersion. Interpretable influence components are derived. The method is applied to data from a longitudinal clinical trial involving patients with epileptic seizures. Even though the data were extensively analyzed in earlier work, the insight gained from the proposed diagnostics, statistically and clinically, is considerable. Possibly, a small but important subgroup of patients has been identified.     

Multi-Objective Community Detection Based on Memetic Algorithm

Community detection has drawn a lot of attention as it can provide invaluable help in understanding the function and visualizing the structure of networks. Since single objective optimization methods have intrinsic drawbacks to identifying multiple significant community structures, some methods formulate the community detection as multi-objective problems and adopt population-based evolutionary algorithms to obtain multiple community structures. Evolutionary algorithms have strong global search ability, but have difficulty in locating local optima efficiently. In this study, in order to identify multiple significant community structures more effectively, a multi-objective memetic algorithm for community detection is proposed by combining multi-objective evolutionary algorithm with a local search procedure. The local search procedure is designed by addressing three issues. Firstly, nondominated solutions generated by evolutionary operations and solutions in dominant population are set as initial individuals for local search procedure. Then, a new direction vector named as pseudonormal vector is proposed to integrate two objective functions together to form a fitness function. Finally, a network specific local search strategy based on label propagation rule is expanded to search the local optimal solutions efficiently. The extensive experiments on both artificial and real-world networks evaluate the proposed method from three aspects. Firstly, experiments on influence of local search procedure demonstrate that the local search procedure can speed up the convergence to better partitions and make the algorithm more stable. Secondly, comparisons with a set of classic community detection methods illustrate the proposed method can find single partitions effectively. Finally, the method is applied to identify hierarchical structures of networks which are beneficial for analyzing networks in multi-resolution levels.     

Local Influence for Generalized Linear Models with Missing Covariates

Summary In the analysis of missing data, sensitivity analyses are commonly used to check the sensitivity of the parameters of interest with respect to the missing data mechanism and other distributional and modeling assumptions. In this article, we formally develop a general local influence method to carry out sensitivity analyses of minor perturbations to generalized linear models in the presence of missing covariate data. We examine two types of perturbation schemes (the single‐case and global perturbation schemes) for perturbing various assumptions in this setting. We show that the metric tensor of a perturbation manifold provides useful information for selecting an appropriate perturbation. We also develop several local influence measures to identify influential points and test model misspecification. Simulation studies are conducted to evaluate our methods, and real datasets are analyzed to illustrate the use of our local influence measures.     

A systematic survey of centrality measures for protein-protein interaction networks

Background

Numerous centrality measures have been introduced to identify “central” nodes in large networks. The availability of a wide range of measures for ranking influential nodes leaves the user to decide which measure may best suit the analysis of a given network. The choice of a suitable measure is furthermore complicated by the impact of the network topology on ranking influential nodes by centrality measures. To approach this problem systematically, we examined the centrality profile of nodes of yeast protein-protein interaction networks (PPINs) in order to detect which centrality measure is succeeding in predicting influential proteins. We studied how different topological network features are reflected in a large set of commonly used centrality measures.

Results

We used yeast PPINs to compare 27 common of centrality measures. The measures characterize and assort influential nodes of the networks. We applied principal component analysis (PCA) and hierarchical clustering and found that the most informative measures depend on the network’s topology. Interestingly, some measures had a high level of contribution in comparison to others in all PPINs, namely Latora closeness, Decay, Lin, Freeman closeness, Diffusion, Residual closeness and Average distance centralities.

Conclusions

The choice of a suitable set of centrality measures is crucial for inferring important functional properties of a network. We concluded that undertaking data reduction using unsupervised machine learning methods helps to choose appropriate variables (centrality measures). Hence, we proposed identifying the contribution proportions of the centrality measures with PCA as a prerequisite step of network analysis before inferring functional consequences, e.g., essentiality of a node.

     

Birnbaum–Saunders frailty regression models: Diagnostics and application to medical data

In survival models, some covariates affecting the lifetime could not be observed or measured. These covariates may correspond to environmental or genetic factors and be considered as a random effect related to a frailty of the individuals explaining their survival times. We propose a methodology based on a Birnbaum–Saunders frailty regression model, which can be applied to censored or uncensored data. Maximum‐likelihood methods are used to estimate the model parameters and to derive local influence techniques. Diagnostic tools are important in regression to detect anomalies, as departures from error assumptions and presence of outliers and influential cases. Normal curvatures for local influence under different perturbations are computed and two types of residuals are introduced. Two examples with uncensored and censored real‐world data illustrate the proposed methodology. Comparison with classical frailty models is carried out in these examples, which shows the superiority of the proposed model.     

Suprathreshold Heat Pain Response Predicts Activity-Related Pain,but Not Rest-Related Pain,in an Exercise-Induced Injury Model

Exercise-induced injury models are advantageous for studying pain since the onset of pain is controlled and both pre-injury and post-injury factors can be utilized as explanatory variables or predictors. In these studies, rest-related pain is often considered the primary dependent variable or outcome, as opposed to a measure of activity-related pain. Additionally, few studies include pain sensitivity measures as predictors. In this study, we examined the influence of pre-injury and post-injury factors, including pain sensitivity, for induced rest and activity-related pain following exercise induced muscle injury. The overall goal of this investigation was to determine if there were convergent or divergent predictors of rest and activity-related pain. One hundred forty-three participants provided demographic, psychological, and pain sensitivity information and underwent a standard fatigue trial of resistance exercise to induce injury of the dominant shoulder. Pain at rest and during active and resisted shoulder motion were measured at 48- and 96-hours post-injury. Separate hierarchical models were generated for assessing the influence of pre-injury and post-injury factors on 48- and 96-hour rest-related and activity-related pain. Overall, we did not find a universal predictor of pain across all models. However, pre-injury and post-injury suprathreshold heat pain response (SHPR), a pain sensitivity measure, was a consistent predictor of activity-related pain, even after controlling for known psychological factors. These results suggest there is differential prediction of pain. A measure of pain sensitivity such as SHPR appears more influential for activity-related pain, but not rest-related pain, and may reflect different underlying processes involved during pain appraisal.     

Automated assembly of protein blocks for database searching.

A system is described for finding and assembling the most highly conserved regions of related proteins for database searching. First, an automated version of Smith's algorithm for finding motifs is used for sensitive detection of multiple local alignments. Next, the local alignments are converted to blocks and the best set of non-overlapping blocks is determined. When the automated system was applied successively to all 437 groups of related proteins in the PROSITE catalog, 1764 blocks resulted; these could be used for very sensitive searches of sequence databases. Each block was calibrated by searching the SWISS-PROT database to obtain a measure of the chance distribution of matches, and the calibrated blocks were concatenated into a database that could itself be searched. Examples are provided in which distant relationships are detected either using a set of blocks to search a sequence database or using sequences to search the database of blocks. The practical use of the blocks database is demonstrated by detecting previously unknown relationships between oxidoreductases and by evaluating a proposed relationship between HIV Vif protein and thiol proteases.     

THE MEASUREMENT THEORY OF FITNESS

In this article, an approach to measure fitness is proposed that considers fitness as a measure of competitive ability among phenotypes or genotypes. This approach is based on pairwise competition tests and is related to measures of “utility” in mathematical economics. Extending the results from utility theory it is possible to recover the classical Wrightian fitness measure without reference to models of population growth. A condition, quasi‐BTL, similar to the Bradley–Terry–Luce condition of classical utility theory is shown to be necessary for the existence of frequency and context‐independent fitness measures. Testing for violations of this quasi‐BTL condition can be used to the detect genotype‐by‐genotype interactions and frequency‐dependent fitness. A method for the detection of genotype by environment interactions is proposed that avoids potential scaling artifacts. Furthermore the measurement theoretical approach allows one to derive Wright's selection equation. This shows that classical selection equations are entirely general and exact. It is concluded that measurement theory is able to give definite answers to a number theoretical and practical questions. For instance, this theory identifies the correct scale for measuring gene interaction with respect to fitness and shows that different scales may lead to wrong conclusions.     

Bayesian Local Influence in Growth Curve Model with Unstructured Covariance

From the Bayesian point of view, a local influence approach is developed to diagnose the adequacy of the growth curve model with an unstructured covariance. Based on the Kullback-Leibler divergence, the Bayesian Hessian matrices of the parameters in the model are studied under an abstract perturbation scheme and the eigenvector associated with the largest eigenvalue of the Hessian matrix is used to identify influential observations. For illustration, the covariance-weighted perturbation, a commonly encountered perturbation, is considered particularly and used to analyze a practical data set. Comparisons with the likelihood-based local influence are also made.     

Linear and nonlinear mixed-effects models for censored HIV viral loads using normal/independent distributions

HIV RNA viral load measures are often subjected to some upper and lower detection limits depending on the quantification assays. Hence, the responses are either left or right censored. Linear (and nonlinear) mixed-effects models (with modifications to accommodate censoring) are routinely used to analyze this type of data and are based on normality assumptions for the random terms. However, those analyses might not provide robust inference when the normality assumptions are questionable. In this article, we develop a Bayesian framework for censored linear (and nonlinear) models replacing the Gaussian assumptions for the random terms with normal/independent (NI) distributions. The NI is an attractive class of symmetric heavy-tailed densities that includes the normal, Student's-t, slash, and the contaminated normal distributions as special cases. The marginal likelihood is tractable (using approximations for nonlinear models) and can be used to develop Bayesian case-deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated with two HIV AIDS studies on viral loads that were initially analyzed using normal (censored) mixed-effects models, as well as simulations.     

Automatic food intake detection based on swallowing sounds

This paper presents a novel fully automatic food intake detection methodology, an important step toward objective monitoring of ingestive behavior. The aim of such monitoring is to improve our understanding of eating behaviors associated with obesity and eating disorders. The proposed methodology consists of two stages. First, acoustic detection of swallowing instances based on mel-scale Fourier spectrum features and classification using support vector machines is performed. Principal component analysis and a smoothing algorithm are used to improve swallowing detection accuracy. Second, the frequency of swallowing is used as a predictor for detection of food intake episodes. The proposed methodology was tested on data collected from 12 subjects with various degrees of adiposity. Average accuracies of >80% and >75% were obtained for intra-subject and inter-subject models correspondingly with a temporal resolution of 30 s. Results obtained on 44.1 h of data with a total of 7305 swallows show that detection accuracies are comparable for obese and lean subjects. They also suggest feasibility of food intake detection based on swallowing sounds and potential of the proposed methodology for automatic monitoring of ingestive behavior. Based on a wearable non-invasive acoustic sensor the proposed methodology may potentially be used in free-living conditions.     

Zero‐modified Poisson model: Bayesian approach,influence diagnostics,and an application to a Brazilian leptospirosis notification data

In this paper, a Bayesian method for inference is developed for the zero‐modified Poisson (ZMP) regression model. This model is very flexible for analyzing count data without requiring any information about inflation or deflation of zeros in the sample. A general class of prior densities based on an information matrix is considered for the model parameters. A sensitivity study to detect influential cases that can change the results is performed based on the Kullback–Leibler divergence. Simulation studies are presented in order to illustrate the performance of the developed methodology. Two real datasets on leptospirosis notification in Bahia State (Brazil) are analyzed using the proposed methodology for the ZMP model.