Analysis of clustered binary outcomes using within-cluster paired resampling

Conditional logistic regression (CLR) is useful for analyzing clustered binary outcome data when interest lies in estimating a cluster-specific exposure parameter while treating the dependency arising from random cluster effects as a nuisance. CLR aggregates unmeasured cluster-specific factors into a cluster-specific baseline risk and is invalid in the presence of unmodeled heterogeneous covariate effects or within-cluster dependency. We propose an alternative, resampling-based method for analyzing clustered binary outcome data, within-cluster paired resampling (WCPR), which allows for within-cluster dependency not solely due to baseline heterogeneity. For example, dependency may be in part caused by heterogeneity in response to an exposure across clusters due to unmeasured cofactors. When both CLR and WCPR are valid, our simulations suggest that the two methods perform comparably. When CLR is invalid, WCPR continues to have good operating characteristics. For illustration, we apply both WCPR and CLR to a periodontal data set where there is heterogeneity in response to exposure across clusters.     

Multivariate methods for clustered binary data with multiple subclasses, with application to binary longitudinal data.

Clustered binary data occur frequently in biostatistical work. Several approaches have been proposed for the analysis of clustered binary data. In Rosner (1984, Biometrics 40, 1025-1035), a polychotomous logistic regression model was proposed that is a generalization of the beta-binomial distribution and allows for unit- and subunit-specific covariates, while controlling for clustering effects. One assumption of this model is that all pairs of subunits within a cluster are equally correlated. This is appropriate for ophthalmologic work where clusters are generally of size 2, but may be inappropriate for larger cluster sizes. A beta-binomial mixture model is introduced to allow for multiple subclasses within a cluster and to estimate odds ratios relating outcomes for pairs of subunits within a subclass as well as in different subclasses. To include covariates, an extension of the polychotomous logistic regression model is proposed, which allows one to estimate effects of unit-, class-, and subunit-specific covariates, while controlling for clustering using the beta-binomial mixture model. This model is applied to the analysis of respiratory symptom data in children collected over a 14-year period in East Boston, Massachusetts, in relation to maternal and child smoking, where the unit is the child and symptom history is divided into early-adolescent and late-adolescent symptom experience.     

The nonparametric Behrens–Fisher problem in partially complete clustered data

In randomized trials or observational studies involving clustered units, the assumption of independence within clusters is not practical. Existing parametric or semiparametric methods assume specific dependence structures within a cluster. Furthermore, parametric model assumptions may not even be realistic when data are measured in a nonmetric scale as commonly happens, for example, in quality‐of‐life outcomes. In this paper, nonparametric effect‐size measures for clustered data that allow meaningful and interpretable probabilistic comparisons of treatments or intervention programs will be introduced. The dependence among observations within a cluster can be arbitrary. Point estimators along with their asymptotic properties for computing confidence intervals and performing hypothesis test will be discussed. Small sample approximations that retain some of the optimal asymptotic behaviors will be presented. In our setup, some clusters may involve observations coming from both intervention groups (referred to as complete clusters), while others may contain observations from one group only (referred to as incomplete clusters). In deriving the asymptotic theories, we do not impose any relation in the rate of divergence of the numbers of complete and incomplete clusters. Simulations show favorable performance of the methods for arbitrary combinations of complete and incomplete clusters. The developed nonparametric methods are illustrated using data from a randomized trial of indoor wood smoke reduction to improve asthma symptoms and a cluster‐randomized trial for smoking cessation.     

Binary data with two,non-nested sources of clustering: an analysis of physician recommendations for early prostate cancer treatment

A prospective cohort study of men with newly diagnosed early prostate cancer was undertaken Talcott et al. (1998) in order to evaluate both the patient-level and the physician-level determinants of physician recommendations for radical prostatectomy (surgery) versus radiation therapy. Each patient sought recommendations from as many as six physicians, and each physician provided recommendations for as many as 113 patients. Thus, the recommendations are clustered within physician and within patient. While methods have been developed for binary data with multiple-nested sources of clustering, they have not been fully explored for binary data with non-nested sources of clustering, such as the treatment recommendations. Here we propose reclustering the data to form binary data with one source of clustering. Because the reclustered data result in one very large cluster and several clusters of size one and two, marginal logistic regression models for the probability of a recommendation of surgery fit using a generalized estimating equation approach would produce unreliable estimates of uncertainty for the parameters. Thus, in addition to the mean model, we attempt to model the associations in as much detail as possible. We compare this model to a mixed-effects model that implicitly adjusts for both sources of clustering and to models based on the assumption of conditional independence with regard to one source of clustering.     

Bias correction of bounded location error in binary data

Binary regression models for spatial data are commonly used in disciplines such as epidemiology and ecology. Many spatially referenced binary data sets suffer from location error, which occurs when the recorded location of an observation differs from its true location. When location error occurs, values of the covariates associated with the true spatial locations of the observations cannot be obtained. We show how a change of support (COS) can be applied to regression models for binary data to provide coefficient estimates when the true values of the covariates are unavailable, but the unknown location of the observations are contained within nonoverlapping arbitrarily shaped polygons. The COS accommodates spatial and nonspatial covariates and preserves the convenient interpretation of methods such as logistic and probit regression. Using a simulation experiment, we compare binary regression models with a COS to naive approaches that ignore location error. We illustrate the flexibility of the COS by modeling individual-level disease risk in a population using a binary data set where the locations of the observations are unknown but contained within administrative units. Our simulation experiment and data illustration corroborate that conventional regression models for binary data that ignore location error are unreliable, but that the COS can be used to eliminate bias while preserving model choice.     

Logistic regression for clustered binary data in proband studies with application to familial aggregation of sleep disorders.

Estimation is considered for the class of conditional logistic regression models for clustered binary data proposed by Qu et al. (Communications in Statistics, Series A 16, 3447-3476, 1987) when clusters are sampled on the basis of the outcome for one or more cluster members. The problem is suggested by data from a study designed to investigate familial aggregation of sleep disorders. After appropriate consideration of the mode of ascertainment of "cases" and "controls," it is shown that the model is preserved under this form of sampling, and a method of estimation is presented. The inconsistency of two alternative methods is demonstrated, and an example is provided.     

Clustered microsatellite mutations in the pipefish Syngnathus typhle.

Clustered mutations are copies of a mutant allele that enter a population's gene pool together due to replication from a premeiotic germline mutation and distribution to multiple successful gametes of an individual. Although the phenomenon has been studied in Drosophila and noted in a few other species, the topic has received scant attention despite claims of being of major importance to population genetics theory. Here we capitalize upon the reproductive biology of male-pregnant pipefishes to document the occurrence of clustered microsatellite mutations and to estimate their rates and patterns from family data. Among a total of 3195 embryos genetically screened from 110 families, 40% of the 35 detected de novo mutant alleles resided in documented mutational clusters. Most of the microsatellite mutations appeared to involve small-integer changes in repeat copy number, and they arose in approximately equal frequency in paternal and maternal germlines. These findings extend observations on clustered mutations to another organismal group and motivate a broader critique of the mutation cluster phenomenon. They also carry implications for the evolution of microsatellites with respect to mutational models and homoplasy among alleles.     

Estimating marginal proportions and intraclass correlations with clustered binary data

A logistic regression with random effects model is commonly applied to analyze clustered binary data, and every cluster is assumed to have a different proportion of success. However, it could be of interest to obtain the proportion of success over clusters (i.e. the marginal proportion of success). Furthermore, the degree of correlation among data of the same cluster (intraclass correlation) is also a relevant concept to assess, but when using logistic regression with random effects it is not possible to get an analytical expression of the estimators for marginal proportion and intraclass correlation. In our paper, we assess and compare approaches using different kinds of approximations: based on the logistic‐normal mixed effects model (LN), linear mixed model (LMM), and generalized estimating equations (GEE). The comparisons are completed by using two real data examples and a simulation study. The results show the performance of the approaches strongly depends on the magnitude of the marginal proportion, the intraclass correlation, and the sample size. In general, the reliability of the approaches get worsen with low marginal proportion and large intraclass correlation. LMM and GEE approaches arises as reliable approaches when the sample size is large.     

Testing the correlation for clustered categorical and censored discrete time-to-event data when covariates are measured without/with errors

In the analysis of clustered categorical data, it is of common interest to test for the correlation within clusters, and the heterogeneity across different clusters. We address this problem by proposing a class of score tests for the null hypothesis that the variance components are zero in random effects models, for clustered nominal and ordinal categorical responses. We extend the results to accommodate clustered censored discrete time-to-event data. We next consider such tests in the situation where covariates are measured with errors. We propose using the SIMEX method to construct the score tests for the null hypothesis that the variance components are zero. Key advantages of the proposed score tests are that they can be easily implemented by fitting standard polytomous regression models and discrete failure time models, and that they are robust in the sense that no assumptions need to be made regarding the distributions of the random effects and the unobserved covariates. The asymptotic properties of the proposed tests are studied. We illustrate these tests by analyzing two data sets and evaluate their performance with simulations.     

Likelihood Methods for Binary Responses of Present Components in a Cluster

Summary In some biomedical studies involving clustered binary responses (say, disease status), the cluster sizes can vary because some components of the cluster can be absent. When both the presence of a cluster component as well as the binary disease status of a present component are treated as responses of interest, we propose a novel two‐stage random effects logistic regression framework. For the ease of interpretation of regression effects, both the marginal probability of presence/absence of a component as well as the conditional probability of disease status of a present component, preserve the approximate logistic regression forms. We present a maximum likelihood method of estimation implementable using standard statistical software. We compare our models and the physical interpretation of regression effects with competing methods from literature. We also present a simulation study to assess the robustness of our procedure to wrong specification of the random effects distribution and to compare finite‐sample performances of estimates with existing methods. The methodology is illustrated via analyzing a study of the periodontal health status in a diabetic Gullah population.     

Relative efficiency of unequal versus equal cluster sizes in cluster randomized trials using generalized estimating equation models

There is growing interest in conducting cluster randomized trials (CRTs). For simplicity in sample size calculation, the cluster sizes are assumed to be identical across all clusters. However, equal cluster sizes are not guaranteed in practice. Therefore, the relative efficiency (RE) of unequal versus equal cluster sizes has been investigated when testing the treatment effect. One of the most important approaches to analyze a set of correlated data is the generalized estimating equation (GEE) proposed by Liang and Zeger, in which the “working correlation structure” is introduced and the association pattern depends on a vector of association parameters denoted by ρ. In this paper, we utilize GEE models to test the treatment effect in a two‐group comparison for continuous, binary, or count data in CRTs. The variances of the estimator of the treatment effect are derived for the different types of outcome. RE is defined as the ratio of variance of the estimator of the treatment effect for equal to unequal cluster sizes. We discuss a commonly used structure in CRTs—exchangeable, and derive the simpler formula of RE with continuous, binary, and count outcomes. Finally, REs are investigated for several scenarios of cluster size distributions through simulation studies. We propose an adjusted sample size due to efficiency loss. Additionally, we also propose an optimal sample size estimation based on the GEE models under a fixed budget for known and unknown association parameter (ρ) in the working correlation structure within the cluster.     

Origin and distribution of epipolythiodioxopiperazine (ETP) gene clusters in filamentous ascomycetes

Background  

Genes responsible for biosynthesis of fungal secondary metabolites are usually tightly clustered in the genome and co-regulated with metabolite production. Epipolythiodioxopiperazines (ETPs) are a class of secondary metabolite toxins produced by disparate ascomycete fungi and implicated in several animal and plant diseases. Gene clusters responsible for their production have previously been defined in only two fungi. Fungal genome sequence data have been surveyed for the presence of putative ETP clusters and cluster data have been generated from several fungal taxa where genome sequences are not available. Phylogenetic analysis of cluster genes has been used to investigate the assembly and heredity of these gene clusters.     

Inference from clustering with application to gene-expression microarrays.

There are many algorithms to cluster sample data points based on nearness or a similarity measure. Often the implication is that points in different clusters come from different underlying classes, whereas those in the same cluster come from the same class. Stochastically, the underlying classes represent different random processes. The inference is that clusters represent a partition of the sample points according to which process they belong. This paper discusses a model-based clustering toolbox that evaluates cluster accuracy. Each random process is modeled as its mean plus independent noise, sample points are generated, the points are clustered, and the clustering error is the number of points clustered incorrectly according to the generating random processes. Various clustering algorithms are evaluated based on process variance and the key issue of the rate at which algorithmic performance improves with increasing numbers of experimental replications. The model means can be selected by hand to test the separability of expected types of biological expression patterns. Alternatively, the model can be seeded by real data to test the expected precision of that output or the extent of improvement in precision that replication could provide. In the latter case, a clustering algorithm is used to form clusters, and the model is seeded with the means and variances of these clusters. Other algorithms are then tested relative to the seeding algorithm. Results are averaged over various seeds. Output includes error tables and graphs, confusion matrices, principal-component plots, and validation measures. Five algorithms are studied in detail: K-means, fuzzy C-means, self-organizing maps, hierarchical Euclidean-distance-based and correlation-based clustering. The toolbox is applied to gene-expression clustering based on cDNA microarrays using real data. Expression profile graphics are generated and error analysis is displayed within the context of these profile graphics. A large amount of generated output is available over the web.     

Bootstrap confidence intervals for adaptive cluster sampling

Consider a collection of spatially clustered objects where the clusters are geographically rare. Of interest is estimation of the total number of objects on the site from a sample of plots of equal size. Under these spatial conditions, adaptive cluster sampling of plots is generally useful in improving efficiency in estimation over simple random sampling without replacement (SRSWOR). In adaptive cluster sampling, when a sampled plot meets some predefined condition, neighboring plots are added to the sample. When populations are rare and clustered, the usual unbiased estimators based on small samples are often highly skewed and discrete in distribution. Thus, confidence intervals based on asymptotic normal theory may not be appropriate. We investigated several nonparametric bootstrap methods for constructing confidence intervals under adaptive cluster sampling. To perform bootstrapping, we transformed the initial sample in order to include the information from the adaptive portion of the sample yet maintain a fixed sample size. In general, coverages of bootstrap percentile methods were closer to nominal coverage than the normal approximation.     

Evaluating Global Positioning System Telemetry Techniques for Estimating Cougar Predation Parameters

ABSTRACT Using clusters of locations obtained from Global Positioning System (GPS) telemetry collars to identify predation events may allow more efficient estimation of behavioral predation parameters for the study and management of large carnivore predator-prey systems. Applications of field- and model-based GPS telemetry cluster techniques, however, have met with mixed success. To further evaluate and refine these techniques for cougars (Puma concolor), we used data from visits to 1,735 GPS telemetry clusters, 637 of which were locations where cougars killed prey >8 kg in a multi-prey system in west-central Alberta. We tested 1) whether clusters were reliably created at kill locations, 2) the ability of logistic regression models to identify kill occurrence (prey >8 kg) and multinomial regression models to identify the prey species at a kill cluster, and 3) the duration of monitoring required to accurately estimate kill rate and prey composition. We found that GPS collars programmed to attempt location fixes every 3 hours consistently identified locations where prey >8 kg were handled, and cluster creation was robust to GPS location acquisition failures (poor collar fix success). The logistic regression model was capable of estimating cougar kill rate with a mean 5-fold cross validation error of <10%, provided the appropriate probability cutoff distinguishing kill clusters from non-kill clusters was selected. Logistic models also can be used to direct visits to clusters, reducing field efforts by as much as 25%, while still locating >95% of all kills. The multinomial model overpredicted occurrence of primary prey (deer) in the diet and underpredicted consumption of alternate prey (e.g., elk and moose) by as much as 100%. We conclude that a purely model-based approach should be used cautiously and that field visitation is required to obtain reliable information on species, sex, age, or condition of prey. Ultimately, we recommend a combined approach that involves using models to direct field visitation when estimating behavioral predation parameters. Regardless of the monitoring approach, long continuous monitoring periods (i.e., >100 days of a 180-day period) were necessary to reduce bias and imprecision in kill rate and prey composition estimates.     

Regression modeling of ordinal data with nonzero baselines

This paper develops regression models for ordinal data with nonzero control response probabilities. The models are especially useful in dose-response studies where the spontaneous or natural response rate is nonnegligible and the dosage is logarithmic. These models generalize Abbott's formula, which has been commonly used to model binary data with nonzero background observations. We describe a biologically plausible latent structure and develop an EM algorithm for fitting the models. The EM algorithm can be implemented using standard software for ordinal regression. A toxicology data set where the proposed model fits the data but a more conventional model fails is used to illustrate the methodology.     

Dealing with spatial autocorrelation when learning predictive clustering trees

Spatial autocorrelation is the correlation among data values which is strictly due to the relative spatial proximity of the objects that the data refer to. Inappropriate treatment of data with spatial dependencies, where spatial autocorrelation is ignored, can obfuscate important insights. In this paper, we propose a data mining method that explicitly considers spatial autocorrelation in the values of the response (target) variable when learning predictive clustering models. The method is based on the concept of predictive clustering trees (PCTs), according to which hierarchies of clusters of similar data are identified and a predictive model is associated to each cluster. In particular, our approach is able to learn predictive models for both a continuous response (regression task) and a discrete response (classification task). We evaluate our approach on several real world problems of spatial regression and spatial classification. The consideration of the autocorrelation in the models improves predictions that are consistently clustered in space and that clusters try to preserve the spatial arrangement of the data, at the same time providing a multi-level insight into the spatial autocorrelation phenomenon. The evaluation of SCLUS in several ecological domains (e.g. predicting outcrossing rates within a conventional field due to the surrounding genetically modified fields, as well as predicting pollen dispersal rates from two lines of plants) confirms its capability of building spatial aware models which capture the spatial distribution of the target variable. In general, the maps obtained by using SCLUS do not require further post-smoothing of the results if we want to use them in practice.     

MetaMirClust: Discovery of miRNA cluster patterns using a data-mining approach

Recent genome-wide surveys on ncRNA have revealed that a substantial fraction of miRNA genes is likely to form clusters. However, the evolutionary and biological function implications of clustered miRNAs are still elusive. After identifying clustered miRNA genes under different maximum inter-miRNA distances (MIDs), this study intended to reveal evolution conservation patterns among these clustered miRNA genes in metazoan species using a computation algorithm. As examples, a total of 15-35% of known and predicted miRNA genes in nine selected species constitute clusters under the MIDs ranging from 1kb to 50kb. Intriguingly, 33 out of 37 metazoan miRNA clusters in 56 metazoan genomes are co-conserved with their up/down-stream adjacent protein-coding genes. Meanwhile, a co-expression pattern of miR-1 and miR-133a in the mir-133-1 cluster has been experimentally demonstrated. Therefore, the MetaMirClust database provides a useful bioinformatic resource for biologists to facilitate the advanced interrogations on the composition of miRNA clusters and their evolution patterns.