Spatial Cluster Detection for Weighted Outcomes Using Cumulative Geographic Residuals

Summary Spatial cluster detection is an important methodology for identifying regions with excessive numbers of adverse health events without making strong model assumptions on the underlying spatial dependence structure. Previous work has focused on point or individual‐level outcome data and few advances have been made when the outcome data are reported at an aggregated level, for example, at the county‐ or census‐tract level. This article proposes a new class of spatial cluster detection methods for point or aggregate data, comprising of continuous, binary, and count data. Compared with the existing spatial cluster detection methods it has the following advantages. First, it readily incorporates region‐specific weights, for example, based on a region's population or a region's outcome variance, which is the key for aggregate data. Second, the established general framework allows for area‐level and individual‐level covariate adjustment. A simulation study is conducted to evaluate the performance of the method. The proposed method is then applied to assess spatial clustering of high Body Mass Index in a health maintenance organization population in the Seattle, Washington, USA area.     

Clustering in linear‐mixed models with a group fused lasso penalty

A method is proposed that aims at identifying clusters of individuals that show similar patterns when observed repeatedly. We consider linear‐mixed models that are widely used for the modeling of longitudinal data. In contrast to the classical assumption of a normal distribution for the random effects a finite mixture of normal distributions is assumed. Typically, the number of mixture components is unknown and has to be chosen, ideally by data driven tools. For this purpose, an EM algorithm‐based approach is considered that uses a penalized normal mixture as random effects distribution. The penalty term shrinks the pairwise distances of cluster centers based on the group lasso and the fused lasso method. The effect is that individuals with similar time trends are merged into the same cluster. The strength of regularization is determined by one penalization parameter. For finding the optimal penalization parameter a new model choice criterion is proposed.     

Incorporating Correlation for Multivariate Failure Time Data When Cluster Size Is Large

Summary We propose a new estimation method for multivariate failure time data using the quadratic inference function (QIF) approach. The proposed method efficiently incorporates within‐cluster correlations. Therefore, it is more efficient than those that ignore within‐cluster correlation. Furthermore, the proposed method is easy to implement. Unlike the weighted estimating equations in Cai and Prentice (1995, Biometrika 82 , 151–164), it is not necessary to explicitly estimate the correlation parameters. This simplification is particularly useful in analyzing data with large cluster size where it is difficult to estimate intracluster correlation. Under certain regularity conditions, we show the consistency and asymptotic normality of the proposed QIF estimators. A chi‐squared test is also developed for hypothesis testing. We conduct extensive Monte Carlo simulation studies to assess the finite sample performance of the proposed methods. We also illustrate the proposed methods by analyzing primary biliary cirrhosis (PBC) data.     

Optimizing performance of nonparametric species richness estimators under constrained sampling

Understanding the functional relationship between the sample size and the performance of species richness estimators is necessary to optimize limited sampling resources against estimation error. Nonparametric estimators such as Chao and Jackknife demonstrate strong performances, but consensus is lacking as to which estimator performs better under constrained sampling. We explore a method to improve the estimators under such scenario. The method we propose involves randomly splitting species‐abundance data from a single sample into two equally sized samples, and using an appropriate incidence‐based estimator to estimate richness. To test this method, we assume a lognormal species‐abundance distribution (SAD) with varying coefficients of variation (CV), generate samples using MCMC simulations, and use the expected mean‐squared error as the performance criterion of the estimators. We test this method for Chao, Jackknife, ICE, and ACE estimators. Between abundance‐based estimators with the single sample, and incidence‐based estimators with the split‐in‐two samples, Chao2 performed the best when CV < 0.65, and incidence‐based Jackknife performed the best when CV > 0.65, given that the ratio of sample size to observed species richness is greater than a critical value given by a power function of CV with respect to abundance of the sampled population. The proposed method increases the performance of the estimators substantially and is more effective when more rare species are in an assemblage. We also show that the splitting method works qualitatively similarly well when the SADs are log series, geometric series, and negative binomial. We demonstrate an application of the proposed method by estimating richness of zooplankton communities in samples of ballast water. The proposed splitting method is an alternative to sampling a large number of individuals to increase the accuracy of richness estimations; therefore, it is appropriate for a wide range of resource‐limited sampling scenarios in ecology.     

Estimated quadratic inference function for correlated failure time data

An estimated quadratic inference function method is proposed for correlated failure time data with auxiliary covariates. The proposed method makes efficient use of the auxiliary information for the incomplete exposure covariates and preserves the property of the quadratic inference function method that requires the covariates to be completely observed. It can improve the estimation efficiency and easily deal with the situation when the cluster size is large. The proposed estimator which minimizes the estimated quadratic inference function is shown to be consistent and asymptotically normal. A chi-squared test based on the estimated quadratic inference function is proposed to test hypotheses about the regression parameters. The small-sample performance of the proposed method is investigated through extensive simulation studies. The proposed method is then applied to analyze the Study of Left Ventricular Dysfunction (SOLVD) data as an illustration.     

Marginal Models for Clustered Time‐to‐Event Data with Competing Risks Using Pseudovalues

Summary Many time‐to‐event studies are complicated by the presence of competing risks and by nesting of individuals within a cluster, such as patients in the same center in a multicenter study. Several methods have been proposed for modeling the cumulative incidence function with independent observations. However, when subjects are clustered, one needs to account for the presence of a cluster effect either through frailty modeling of the hazard or subdistribution hazard, or by adjusting for the within‐cluster correlation in a marginal model. We propose a method for modeling the marginal cumulative incidence function directly. We compute leave‐one‐out pseudo‐observations from the cumulative incidence function at several time points. These are used in a generalized estimating equation to model the marginal cumulative incidence curve, and obtain consistent estimates of the model parameters. A sandwich variance estimator is derived to adjust for the within‐cluster correlation. The method is easy to implement using standard software once the pseudovalues are obtained, and is a generalization of several existing models. Simulation studies show that the method works well to adjust the SE for the within‐cluster correlation. We illustrate the method on a dataset looking at outcomes after bone marrow transplantation.     

Modeling continuous auxiliary covariate data in generalized linear mixed models using the kernel smoother

Auxiliary covariate data are often collected in biomedical studies when the primary exposure variable is only assessed on a subset of the study subjects. In this study, we investigate a semiparametric‐estimated likelihood estimation for the generalized linear mixed models (GLMM) in the presence of a continuous auxiliary variable. We use a kernel smoother to handle continuous auxiliary data. The method can be used to deal with missing or mismeasured covariate data problems in a variety of applications when an auxiliary variable is available and cluster sizes are not too small. Simulation study results show that the proposed method performs better than that which ignores the random effects in GLMM and that which only uses data in the validation data set. We illustrate the proposed method with a real data set from a recent environmental epidemiology study on the maternal serum 1,1‐dichloro‐2,2‐bis(p‐chlorophenyl) ethylene level in relationship to preterm births.     

DNABind: A hybrid algorithm for structure‐based prediction of DNA‐binding residues by combining machine learning‐ and template‐based approaches

Accurate prediction of DNA‐binding residues has become a problem of increasing importance in structural bioinformatics. Here, we presented DNABind, a novel hybrid algorithm for identifying these crucial residues by exploiting the complementarity between machine learning‐ and template‐based methods. Our machine learning‐based method was based on the probabilistic combination of a structure‐based and a sequence‐based predictor, both of which were implemented using support vector machines algorithms. The former included our well‐designed structural features, such as solvent accessibility, local geometry, topological features, and relative positions, which can effectively quantify the difference between DNA‐binding and nonbinding residues. The latter combined evolutionary conservation features with three other sequence attributes. Our template‐based method depended on structural alignment and utilized the template structure from known protein–DNA complexes to infer DNA‐binding residues. We showed that the template method had excellent performance when reliable templates were found for the query proteins but tended to be strongly influenced by the template quality as well as the conformational changes upon DNA binding. In contrast, the machine learning approach yielded better performance when high‐quality templates were not available (about 1/3 cases in our dataset) or the query protein was subject to intensive transformation changes upon DNA binding. Our extensive experiments indicated that the hybrid approach can distinctly improve the performance of the individual methods for both bound and unbound structures. DNABind also significantly outperformed the state‐of‐art algorithms by around 10% in terms of Matthews's correlation coefficient. The proposed methodology could also have wide application in various protein functional site annotations. DNABind is freely available at http://mleg.cse.sc.edu/DNABind/ . Proteins 2013; 81:1885–1899. © 2013 Wiley Periodicals, Inc.     

Inferential Clustering Approach for Microarray Experiments with Replicated Measurements

Cluster analysis has proven to be a useful tool for investigating the association structure among genes in a microarray data set. There is a rich literature on cluster analysis and various techniques have been developed. Such analyses heavily depend on an appropriate (dis)similarity measure. In this paper, we introduce a general clustering approach based on the confidence interval inferential methodology, which is applied to gene expression data of microarray experiments. Emphasis is placed on data with low replication (three or five replicates). The proposed method makes more efficient use of the measured data and avoids the subjective choice of a dissimilarity measure. This new methodology, when applied to real data, provides an easy-to-use bioinformatics solution for the cluster analysis of microarray experiments with replicates (see the Appendix). Even though the method is presented under the framework of microarray experiments, it is a general algorithm that can be used to identify clusters in any situation. The method's performance is evaluated using simulated and publicly available data set. Our results also clearly show that our method is not an extension of the conventional clustering method based on correlation or euclidean distance.     

A Semiparametric Missing‐Data‐Induced Intensity Method for Missing Covariate Data in Individually Matched Case–Control Studies

Summary In individually matched case–control studies, when some covariates are incomplete, an analysis based on the complete data may result in a large loss of information both in the missing and completely observed variables. This usually results in a bias and loss of efficiency. In this article, we propose a new method for handling the problem of missing covariate data based on a missing‐data‐induced intensity approach when the missingness mechanism does not depend on case–control status and show that this leads to a generalization of the missing indicator method. We derive the asymptotic properties of the estimates from the proposed method and, using an extensive simulation study, assess the finite sample performance in terms of bias, efficiency, and 95% confidence coverage under several missing data scenarios. We also make comparisons with complete‐case analysis (CCA) and some missing data methods that have been proposed previously. Our results indicate that, under the assumption of predictable missingness, the suggested method provides valid estimation of parameters, is more efficient than CCA, and is competitive with other, more complex methods of analysis. A case–control study of multiple myeloma risk and a polymorphism in the receptor Inter‐Leukin‐6 (IL‐6‐α) is used to illustrate our findings.     

A new unsupervised feature ranking method for gene expression data based on consensus affinity

Feature selection is widely established as one of the fundamental computational techniques in mining microarray data. Due to the lack of categorized information in practice, unsupervised feature selection is more practically important but correspondingly more difficult. Motivated by the cluster ensemble techniques, which combine multiple clustering solutions into a consensus solution of higher accuracy and stability, recent efforts in unsupervised feature selection proposed to use these consensus solutions as oracles. However,these methods are dependent on both the particular cluster ensemble algorithm used and the knowledge of the true cluster number. These methods will be unsuitable when the true cluster number is not available, which is common in practice. In view of the above problems, a new unsupervised feature ranking method is proposed to evaluate the importance of the features based on consensus affinity. Different from previous works, our method compares the corresponding affinity of each feature between a pair of instances based on the consensus matrix of clustering solutions. As a result, our method alleviates the need to know the true number of clusters and the dependence on particular cluster ensemble approaches as in previous works. Experiments on real gene expression data sets demonstrate significant improvement of the feature ranking results when compared to several state-of-the-art techniques.     

A hybrid genetic algorithm and expectation maximization method for global gene trajectory clustering

Clustering time-course gene expression data (gene trajectories) is an important step towards solving the complex problem of gene regulatory network modeling and discovery as it significantly reduces the dimensionality of the gene space required for analysis. Traditional clustering methods that perform hill-climbing from randomly initialized cluster centers are prone to produce inconsistent and sub-optimal cluster solutions over different runs. This paper introduces a novel method that hybridizes genetic algorithm (GA) and expectation maximization algorithms (EM) for clustering gene trajectories with the mixtures of multiple linear regression models (MLRs), with the objective of improving the global optimality and consistency of the clustering performance. The proposed method is applied to cluster the human fibroblasts and the yeast time-course gene expression data based on their trajectory similarities. It outperforms the standard EM method significantly in terms of both clustering accuracy and consistency. The biological implications of the improved clustering performance are demonstrated.     

Optimal design of longitudinal data analysis using generalized estimating equation models

Longitudinal studies are often applied in biomedical research and clinical trials to evaluate the treatment effect. The association pattern within the subject must be considered in both sample size calculation and the analysis. One of the most important approaches to analyze such a study is the generalized estimating equation (GEE) proposed by Liang and Zeger, in which “working correlation structure” is introduced and the association pattern within the subject depends on a vector of association parameters denoted by ρ. The explicit sample size formulas for two‐group comparison in linear and logistic regression models are obtained based on the GEE method by Liu and Liang. For cluster randomized trials (CRTs), researchers proposed the optimal sample sizes at both the cluster and individual level as a function of sampling costs and the intracluster correlation coefficient (ICC). In these approaches, the optimal sample sizes depend strongly on the ICC. However, the ICC is usually unknown for CRTs and multicenter trials. To overcome this shortcoming, Van Breukelen et al. consider a range of possible ICC values identified from literature reviews and present Maximin designs (MMDs) based on relative efficiency (RE) and efficiency under budget and cost constraints. In this paper, the optimal sample size and number of repeated measurements using GEE models with an exchangeable working correlation matrix is proposed under the considerations of fixed budget, where “optimal” refers to maximum power for a given sampling budget. The equations of sample size and number of repeated measurements for a known parameter value ρ are derived and a straightforward algorithm for unknown ρ is developed. Applications in practice are discussed. We also discuss the existence of the optimal design when an AR(1) working correlation matrix is assumed. Our proposed method can be extended under the scenarios when the true and working correlation matrix are different.     

Ensemble survival trees for identifying subpopulations in personalized medicine

Recently, personalized medicine has received great attention to improve safety and effectiveness in drug development. Personalized medicine aims to provide medical treatment that is tailored to the patient's characteristics such as genomic biomarkers, disease history, etc., so that the benefit of treatment can be optimized. Subpopulations identification is to divide patients into several different subgroups where each subgroup corresponds to an optimal treatment. For two subgroups, traditionally the multivariate Cox proportional hazards model is fitted and used to calculate the risk score when outcome is survival time endpoint. Median is commonly chosen as the cutoff value to separate patients. However, using median as the cutoff value is quite subjective and sometimes may be inappropriate in situations where data are imbalanced. Here, we propose a novel tree‐based method that adopts the algorithm of relative risk trees to identify subgroup patients. After growing a relative risk tree, we apply k‐means clustering to group the terminal nodes based on the averaged covariates. We adopt an ensemble Bagging method to improve the performance of a single tree since it is well known that the performance of a single tree is quite unstable. A simulation study is conducted to compare the performance between our proposed method and the multivariate Cox model. The applications of our proposed method to two public cancer data sets are also conducted for illustration.     

On computation of semiparametric maximum likelihood estimators with shape constraints

Large sample theory of semiparametric models based on maximum likelihood estimation (MLE) with shape constraint on the nonparametric component is well studied. Relatively less attention has been paid to the computational aspect of semiparametric MLE. The computation of semiparametric MLE based on existing approaches such as the expectation‐maximization (EM) algorithm can be computationally prohibitive when the missing rate is high. In this paper, we propose a computational framework for semiparametric MLE based on an inexact block coordinate ascent (BCA) algorithm. We show theoretically that the proposed algorithm converges. This computational framework can be applied to a wide range of data with different structures, such as panel count data, interval‐censored data, and degradation data, among others. Simulation studies demonstrate favorable performance compared with existing algorithms in terms of accuracy and speed. Two data sets are used to illustrate the proposed computational method. We further implement the proposed computational method in R package BCA1SG , available at CRAN.     

Detecting Genomic Aberrations Using Products in a Multiscale Analysis

Summary Genomic instability, such as copy‐number losses and gains, occurs in many genetic diseases. Recent technology developments enable researchers to measure copy numbers at tens of thousands of markers simultaneously. In this article, we propose a nonparametric approach for detecting the locations of copy‐number changes and provide a measure of significance for each change point. The proposed test is based on seeking scale‐based changes in the sequence of copy numbers, which is ordered by the marker locations along the chromosome. The method leads to a natural way to estimate the null distribution for the test of a change point and adjusted p‐values for the significance of a change point using a step‐down maxT permutation algorithm to control the family‐wise error rate. A simulation study investigates the finite sample performance of the proposed method and compares it with a more standard sequential testing method. The method is illustrated using two real data sets.     

Testing Markovianity in the three‐state progressive model via future‐past association

The three‐state progressive model is a special multi‐state model with important applications in Survival Analysis. It provides a suitable representation of the individual’s history when an intermediate event (with a possible influence on the survival prognosis) is experienced before the main event of interest. Estimation of transition probabilities in this and other multi‐state models is usually performed through the Aalen–Johansen estimator. However, Aalen–Johansen may be biased when the underlying process is not Markov. In this paper, we provide a new approach for testing Markovianity in the three‐state progressive model. The new method is based on measuring the future‐past association along time. This results in a deep inspection of the process that often reveals a non‐Markovian behaviour with different trends in the association measure. A test of significance for zero future‐past association at each time point is introduced, and a significance trace is proposed accordingly. The finite sample performance of the test is investigated through simulations. We illustrate the new method through real data analysis.     

A spatial scan statistic for multiple clusters

Spatial scan statistics are commonly used for geographical disease surveillance and cluster detection. While there are multiple clusters coexisting in the study area, they become difficult to detect because of clusters’ shadowing effect to each other. The recently proposed sequential method showed its better power for detecting the second weaker cluster, but did not improve the ability of detecting the first stronger cluster which is more important than the second one. We propose a new extension of the spatial scan statistic which could be used to detect multiple clusters. Through constructing two or more clusters in the alternative hypothesis, our proposed method accounts for other coexisting clusters in the detecting and evaluating process. The performance of the proposed method is compared to the sequential method through an intensive simulation study, in which our proposed method shows better power in terms of both rejecting the null hypothesis and accurately detecting the coexisting clusters. In the real study of hand-foot-mouth disease data in Pingdu city, a true cluster town is successfully detected by our proposed method, which cannot be evaluated to be statistically significant by the standard method due to another cluster’s shadowing effect.     

On small‐sample inference in group randomized trials with binary outcomes and cluster‐level covariates

Group randomized trials (GRTs) randomize groups, or clusters, of people to intervention or control arms. To test for the effectiveness of the intervention when subject‐level outcomes are binary, and while fitting a marginal model that adjusts for cluster‐level covariates and utilizes a logistic link, we develop a pseudo‐Wald statistic to improve inference. Alternative Wald statistics could employ bias‐corrected empirical sandwich standard error estimates, which have received limited attention in the GRT literature despite their broad utility and applicability in our settings of interest. The test could also be carried out using popular approaches based upon cluster‐level summary outcomes. A simulation study covering a variety of realistic GRT settings is used to compare the accuracy of these methods in terms of producing nominal test sizes. Tests based upon the pseudo‐Wald statistic and a cluster‐level summary approach utilizing the natural log of observed cluster‐level odds worked best. Due to weighting, some popular cluster‐level summary approaches were found to lead to invalid inference in many settings. Finally, although use of bias‐corrected empirical sandwich standard error estimates did not consistently result in nominal sizes, they did work well, thus supporting the applicability of marginal models in GRT settings.     

Selection of the Maximum Spatial Cluster Size of the Spatial Scan Statistic by Using the Maximum Clustering Set-Proportion Statistic

Spatial scan statistics are widely used in various fields. The performance of these statistics is influenced by parameters, such as maximum spatial cluster size, and can be improved by parameter selection using performance measures. Current performance measures are based on the presence of clusters and are thus inapplicable to data sets without known clusters. In this work, we propose a novel overall performance measure called maximum clustering set–proportion (MCS-P), which is based on the likelihood of the union of detected clusters and the applied dataset. MCS-P was compared with existing performance measures in a simulation study to select the maximum spatial cluster size. Results of other performance measures, such as sensitivity and misclassification, suggest that the spatial scan statistic achieves accurate results in most scenarios with the maximum spatial cluster sizes selected using MCS-P. Given that previously known clusters are not required in the proposed strategy, selection of the optimal maximum cluster size with MCS-P can improve the performance of the scan statistic in applications without identified clusters.