Joint frailty modeling of time-to-event data to elicit the evolution pathway of events: a generalized linear mixed model approach.

Multimorbidity constitutes a serious challenge on the healthcare systems in the world, due to its association with poorer health-related outcomes, more complex clinical management, increases in health service utilization and costs, but a decrease in productivity. However, to date, most evidence on multimorbidity is derived from cross-sectional studies that have limited capacity to understand the pathway of multimorbid conditions. In this article, we present an innovative perspective on analyzing longitudinal data within a statistical framework of survival analysis of time-to-event recurrent data. The proposed methodology is based on a joint frailty modeling approach with multivariate random effects to account for the heterogeneous risk of failure and the presence of informative censoring due to a terminal event. We develop a generalized linear mixed model method for the efficient estimation of parameters. We demonstrate the capacity of our approach using a real cancer registry data set on the multimorbidity of melanoma patients and document the relative performance of the proposed joint frailty model to the natural competitor of a standard frailty model via extensive simulation studies. Our new approach is timely to advance evidence-based knowledge to address increasingly complex needs related to multimorbidity and develop interventions that are most effective and viable to better help a large number of individuals with multiple conditions.

Mixture cure models with time-varying and multilevel frailties for recurrent event data.

Many medical studies yield data on recurrent clinical events from populations which consist of a proportion of cured patients in the presence of those who experience the event at several times (uncured). A frailty mixture cure model has recently been postulated for such data, with an assumption that the random subject effect (frailty) of each uncured patient is constant across successive gap times between recurrent events. We propose two new models in a more general setting, assuming a multivariate time-varying frailty with an AR(1) correlation structure for each uncured patient and addressing multilevel recurrent event data originated from multi-institutional (multi-centre) clinical trials, using extra random effect terms to adjust for institution effect and treatment-by-institution interaction. To solve the difficulties in parameter estimation due to these highly complex correlation structures, we develop an efficient estimation procedure via an EM-type algorithm based on residual maximum likelihood (REML) through the generalised linear mixed model (GLMM) methodology. Simulation studies are presented to assess the performances of the models. Data sets from a colorectal cancer study and rhDNase multi-institutional clinical trial were analyzed to exemplify the proposed models. The results demonstrate a large positive AR(1) correlation among frailties across successive gap times, indicating a constant frailty may not be realistic in some situations. Comparisons of findings with existing frailty models are discussed.

A bivariate joint frailty model with mixture framework for survival analysis of recurrent events with dependent censoring and cure fraction.

In the study of multiple failure time data with recurrent clinical endpoints, the classical independent censoring assumption in survival analysis can be violated when the evolution of the recurrent events is correlated with a censoring mechanism such as death. Moreover, in some situations, a cure fraction appears in the data because a tangible proportion of the study population benefits from treatment and becomes recurrence free and insusceptible to death related to the disease. A bivariate joint frailty mixture cure model is proposed to allow for dependent censoring and cure fraction in recurrent event data. The latency part of the model consists of two intensity functions for the hazard rates of recurrent events and death, wherein a bivariate frailty is introduced by means of the generalized linear mixed model methodology to adjust for dependent censoring. The model allows covariates and frailties in both the incidence and the latency parts, and it further accounts for the possibility of cure after each recurrence. It includes the joint frailty model and other related models as special cases. An expectation-maximization (EM)-type algorithm is developed to provide residual maximum likelihood estimation of model parameters. Through simulation studies, the performance of the model is investigated under different magnitudes of dependent censoring and cure rate. The model is applied to data sets from two colorectal cancer studies to illustrate its practical value.

Multilevel model with random effects for clustered survival data with multiple failure outcomes.

We present a multilevel frailty model for handling serial dependence and simultaneous heterogeneity in survival data with a multilevel structure attributed to clustering of subjects and the presence of multiple failure outcomes. One commonly observes such data, for example, in multi-institutional, randomized placebo-controlled trials in which patients suffer repeated episodes (eg, recurrent migraines) of the disease outcome being measured. The model extends the proportional hazards model by incorporating a random covariate and unobservable random institution effect to respectively account for treatment-by-institution interaction and institutional variation in the baseline risk. Moreover, a random effect term with correlation structure driven by a first-order autoregressive process is attached to the model to facilitate estimation of between patient heterogeneity and serial dependence. By means of the generalized linear mixed model methodology, the random effects distribution is assumed normal and the residual maximum likelihood and the maximum likelihood methods are extended for estimation of model parameters. Simulation studies are carried out to evaluate the performance of the residual maximum likelihood and the maximum likelihood estimators and to assess the impact of misspecifying random effects distribution on the proposed inference. We demonstrate the practical feasibility of the modeling methodology by analyzing real data from a double-blind randomized multi-institutional clinical trial, designed to examine the effect of rhDNase on the occurrence of respiratory exacerbations among patients with cystic fibrosis.

Modeling of inter-sample variation in flow cytometric data with the joint clustering and matching procedure.

We present an algorithm for modeling flow cytometry data in the presence of large inter-sample variation. Large-scale cytometry datasets often exhibit some within-class variation due to technical effects such as instrumental differences and variations in data acquisition, as well as subtle biological heterogeneity within the class of samples. Failure to account for such variations in the model may lead to inaccurate matching of populations across a batch of samples and poor performance in classification of unlabeled samples. In this paper, we describe the Joint Clustering and Matching (JCM) procedure for simultaneous segmentation and alignment of cell populations across multiple samples. Under the JCM framework, a multivariate mixture distribution is used to model the distribution of the expressions of a fixed set of markers for each cell in a sample such that the components in the mixture model may correspond to the various populations of cells, which have similar expressions of markers (that is, clusters), in the composition of the sample. For each class of samples, an overall class template is formed by the adoption of random-effects terms to model the inter-sample variation within a class. The construction of a parametric template for each class allows for direct quantification of the differences between the template and each sample, and also between each pair of samples, both within or between classes. The classification of a new unclassified sample is then undertaken by assigning the unclassified sample to the class that minimizes the distance between its fitted mixture density and each class density as provided by the class templates. For illustration, we use a symmetric form of the Kullback-Leibler divergence as a distance measure between two densities, but other distance measures can also be applied. We show and demonstrate on four real datasets how the JCM procedure can be used to carry out the tasks of automated clustering and alignment of cell populations, and supervised classification of samples.

Inference on differences between classes using cluster-specific contrasts of mixed effects.

The detection of differentially expressed (DE) genes, that is, genes whose expression levels vary between two or more classes representing different experimental conditions (say, diseases), is one of the most commonly studied problems in bioinformatics. For example, the identification of DE genes between distinct disease phenotypes is an important first step in understanding and developing treatment drugs for the disease. We present a novel approach to the problem of detecting DE genes that is based on a test statistic formed as a weighted (normalized) cluster-specific contrast in the mixed effects of the mixture model used in the first instance to cluster the gene profiles into a manageable number of clusters. The key factor in the formation of our test statistic is the use of gene-specific mixed effects in the cluster-specific contrast. It thus means that the (soft) assignment of a given gene to a cluster is not crucial. This is because in addition to class differences between the (estimated) fixed effects terms for a cluster, gene-specific class differences also contribute to the cluster-specific contributions to the final form of the test statistic. The proposed test statistic can be used where the primary aim is to rank the genes in order of evidence against the null hypothesis of no DE. We also show how a P-value can be calculated for each gene for use in multiple hypothesis testing where the intent is to control the false discovery rate (FDR) at some desired level. With the use of publicly available and simulated datasets, we show that the proposed contrast-based approach outperforms other methods commonly used for the detection of DE genes both in a ranking context with lower proportion of false discoveries and in a multiple hypothesis testing context with higher power for a specified level of the FDR.

On the classification of microarray gene-expression data.

We consider the classification of microarray gene-expression data. First, attention is given to the supervised case, where the tissue samples are classified with respect to a number of predefined classes and the intent is to assign a new unclassified tissue to one of these classes. The problems of forming a classifier and estimating its error rate are addressed in the context of there being a relatively small number of observations (tissue samples) compared to the number of variables (that is, the genes, which can number in the tens of thousands). We then proceed to the unsupervised case and consider the clustering of the tissue samples and also the clustering of the gene profiles. Both problems can be viewed as being non-standard ones in statistics and we address some of the key issues involved. The focus is on the use of mixture models to effect the clustering for both problems.

Conservation and divergence in Toll-like receptor 4-regulated gene expression in primary human versus mouse macrophages.

Evolutionary change in gene expression is generally considered to be a major driver of phenotypic differences between species. We investigated innate immune diversification by analyzing interspecies differences in the transcriptional responses of primary human and mouse macrophages to the Toll-like receptor (TLR)-4 agonist lipopolysaccharide (LPS). By using a custom platform permitting cross-species interrogation coupled with deep sequencing of mRNA 5' ends, we identified extensive divergence in LPS-regulated orthologous gene expression between humans and mice (24% of orthologues were identified as "divergently regulated"). We further demonstrate concordant regulation of human-specific LPS target genes in primary pig macrophages. Divergently regulated orthologues were enriched for genes encoding cellular "inputs" such as cell surface receptors (e.g., TLR6, IL-7Rα) and functional "outputs" such as inflammatory cytokines/chemokines (e.g., CCL20, CXCL13). Conversely, intracellular signaling components linking inputs to outputs were typically concordantly regulated. Functional consequences of divergent gene regulation were confirmed by showing LPS pretreatment boosts subsequent TLR6 responses in mouse but not human macrophages, in keeping with mouse-specific TLR6 induction. Divergently regulated genes were associated with a large dynamic range of gene expression, and specific promoter architectural features (TATA box enrichment, CpG island depletion). Surprisingly, regulatory divergence was also associated with enhanced interspecies promoter conservation. Thus, the genes controlled by complex, highly conserved promoters that facilitate dynamic regulation are also the most susceptible to evolutionary change.

Mixtures of common t-factor analyzers for clustering high-dimensional microarray data.

MOTIVATION: Mixtures of factor analyzers enable model-based clustering to be undertaken for high-dimensional microarray data, where the number of observations n is small relative to the number of genes p. Moreover, when the number of clusters is not small, for example, where there are several different types of cancer, there may be the need to reduce further the number of parameters in the specification of the component-covariance matrices. A further reduction can be achieved by using mixtures of factor analyzers with common component-factor loadings (MCFA), which is a more parsimonious model. However, this approach is sensitive to both non-normality and outliers, which are commonly observed in microarray experiments. This sensitivity of the MCFA approach is due to its being based on a mixture model in which the multivariate normal family of distributions is assumed for the component-error and factor distributions. RESULTS: An extension to mixtures of t-factor analyzers with common component-factor loadings is considered, whereby the multivariate t-family is adopted for the component-error and factor distributions. An EM algorithm is developed for the fitting of mixtures of common t-factor analyzers. The model can handle data with tails longer than that of the normal distribution, is robust against outliers and allows the data to be displayed in low-dimensional plots. It is applied here to both synthetic data and some microarray gene expression data for clustering and shows its better performance over several existing methods. AVAILABILITY: The algorithms were implemented in Matlab. The Matlab code is available at http://blog.naver.com/aggie100.

Integrative mixture of experts to combine clinical factors and gene markers.

MOTIVATION: Microarrays are being increasingly used in cancer research to better characterize and classify tumors by selecting marker genes. However, as very few of these genes have been validated as predictive biomarkers so far, it is mostly conventional clinical and pathological factors that are being used as prognostic indicators of clinical course. Combining clinical data with gene expression data may add valuable information, but it is a challenging task due to their categorical versus continuous characteristics. We have further developed the mixture of experts (ME) methodology, a promising approach to tackle complex non-linear problems. Several variants are proposed in integrative ME as well as the inclusion of various gene selection methods to select a hybrid signature. RESULTS: We show on three cancer studies that prediction accuracy can be improved when combining both types of variables. Furthermore, the selected genes were found to be of high relevance and can be considered as potential biomarkers for the prognostic selection of cancer therapy. AVAILABILITY: Integrative ME is implemented in the R package integrativeME (http://cran.r-project.org/).

Autoantibody profiling to identify biomarkers of key pathogenic pathways in mucinous ovarian cancer.

Mucinous epithelial ovarian cancers are clinically and morphologically distinct from the other histopathologic subtypes of ovarian cancer. Unlike other ovarian subtypes, epidemiologic studies have indicated that tobacco exposure is a significant risk factor for developing mucinous ovarian cancer. Detection of autoantibody reactivity is useful in biomarker discovery and for explaining the role of important pathophysiologic pathways in disease. In order to study if there are specific antibody biomarkers in the plasma samples of mucinous ovarian cancer patients, we have initiated a screen by employing a 'reverse capture antibody microarray' platform that uses native host antigens derived from mucinous ovarian tissues as 'baits' for the capture of differentially labelled patient and control autoantibodies. Thirty-five autoantibodies that were significantly elevated in the cancer plasma samples compared with healthy controls, and six autoantibodies that segregated smoking and non-smoking patients were identified. Functional annotation of the antibody targets has identified nine target antigens involved in integrin and Wnt signalling pathways. Immunohistochemistry of archived ovarian specimens showed significant overexpression of eight of the nine target antigens in mucinous ovarian tumour tissues, suggesting that plasma autoantibodies from mucinous ovarian cancer patients might have heightened reactivities with epitopes presented by these overexpressed antigens. Autoantibody profiling may have an unexpected utility in uncovering key signalling pathways that are dysregulated in the system of interest.

A score test for assessing the cured proportion in the long-term survivor mixture model.

The long-term survivor mixture model is commonly applied to analyse survival data when some individuals may never experience the failure event of interest. A score test is presented to assess whether the cured proportion is significant to justify the long-term survivor mixture model. Sampling distribution and power of the test statistic are evaluated by simulation studies. The results confirm that the proposed test statistic performs well in finite sample situations. The test procedure is illustrated using a breast cancer survival data set and the clustered multivariate failure times from a multi-centre clinical trial of carcinoma.

Bivariate mixture modeling of transferrin saturation and serum ferritin concentration in Asians, African Americans, Hispanics, and whites in the Hemochromatosis and Iron Overload Screening (HEIRS) Study.

Bivariate mixture modeling was used to analyze joint population distributions of transferrin saturation (TS) and serum ferritin concentration (SF) measured in the Hemochromatosis and Iron Overload Screening (HEIRS) Study. Four components (C1, C2, C3, and C4) with successively age-adjusted increasing means for TS and SF were identified in data from 26,832 African Americans, 12,620 Asians, 12,264 Hispanics, and 43,254 whites. The largest component, C2, had normal mean TS (21% to 26% for women, 29% to 30% for men) and SF (43-82 microg/L for women, 165-242 microg/L for men), which consisted of component proportions greater than 0.59 for women and greater than 0.68 for men. C3 and C4 had progressively greater mean values for TS and SF with progressively lesser component proportions. C1 had mean TS values less than 16% for women (<20% for men) and SF values less than 28 microg/L for women (<47 microg/L for men). Compared with C2, adjusted odds of iron deficiency were significantly greater in C1 (14.9-47.5 for women, 60.6-3530 for men), adjusted odds of liver disease were significantly greater in C3 and C4 for African-American women and all men, and adjusted odds of any HFE mutation were increased in C3 (1.4-1.8 for women, 1.2-1.9 for men) and in C4 for Hispanic and white women (1.5 and 5.2, respectively) and men (2.8 and 4.7, respectively). Joint mixture modeling identifies a component with lesser SF and TS at risk for iron deficiency and 2 components with greater SF and TS at risk for liver disease or HFE mutations. This approach can identify populations in which hereditary or acquired factors influence metabolism measurement.

Mixture models for detecting differentially expressed genes in microarrays.

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local FDR (false discovery rate) is provided for each gene. An attractive feature of the mixture model approach is that it provides a framework for the estimation of the prior probability that a gene is not differentially expressed, and this probability can subsequently be used in forming a decision rule. The rule can also be formed to take the false negative rate into account. We apply this approach to a well-known publicly available data set on breast cancer, and discuss our findings with reference to other approaches.

Selection bias in gene extraction on the basis of microarray gene-expression data.

In the context of cancer diagnosis and treatment, we consider the problem of constructing an accurate prediction rule on the basis of a relatively small number of tumor tissue samples of known type containing the expression data on very many (possibly thousands) genes. Recently, results have been presented in the literature suggesting that it is possible to construct a prediction rule from only a few genes such that it has a negligible prediction error rate. However, in these results the test error or the leave-one-out cross-validated error is calculated without allowance for the selection bias. There is no allowance because the rule is either tested on tissue samples that were used in the first instance to select the genes being used in the rule or because the cross-validation of the rule is not external to the selection process; that is, gene selection is not performed in training the rule at each stage of the cross-validation process. We describe how in practice the selection bias can be assessed and corrected for by either performing a cross-validation or applying the bootstrap external to the selection process. We recommend using 10-fold rather than leave-one-out cross-validation, and concerning the bootstrap, we suggest using the so-called .632+ bootstrap error estimate designed to handle overfitted prediction rules. Using two published data sets, we demonstrate that when correction is made for the selection bias, the cross-validated error is no longer zero for a subset of only a few genes.

Influence of patient age and implantation technique on the probability of re-replacement of the homograft aortic valve.

BACKGROUND AND AIM OF THE STUDY: Results of valve rereplacement (reoperation) in 898 patients undergoing aortic valve replacement with cryopreserved homograft valves between 1975 and 1998 are reported. The study aim was to provide estimates of unconditional probability of valve reoperation and cumulative incidence function (actual risk) of reoperation. METHODS: Valves were implanted by subcoronary insertion (n = 500), inclusion cylinder (n = 46), and aortic root replacement (n = 352). Probability of reoperation was estimated by adopting a mixture model framework within which estimates were adjusted for two risk factors: patient age at initial replacement, and implantation technique. RESULTS: For a patient aged 50 years, the probability of reoperation in his/her lifetime was estimated as 44% and 56% for non-root and root replacement techniques, respectively. For a patient aged 70 years, estimated probability of reoperation was 16% and 25%, respectively. Given that a reoperation is required, patients with non-root replacement have a higher hazard rate than those with root replacement (hazards ratio = 1.4), indicating that non-root replacement patients tend to undergo reoperation earlier before death than root replacement patients. CONCLUSION: Younger patient age and root versus nonroot replacement are risk factors for reoperation. Valve durability is much less in younger patients, while root replacement patients appear more likely to live longer and hence are more likely to require reoperation.