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In many cluster-correlated data analyses, informative cluster size poses a challenge that can potentially introduce bias in statistical analyses. Different methodologies have been introduced in statistical literature to address this bias. In this study, we consider a complex form of informativeness where the number of observations corresponding to latent levels of a unit-level continuous covariate within a cluster is associated with the response variable. This type of informativeness has not been explored in prior research. We present a novel test statistic designed to evaluate the effect of the continuous covariate while accounting for the presence of informativeness. The covariate induces a continuum of latent subgroups within the clusters, and our test statistic is formulated by aggregating values from an established statistic that accounts for informative subgroup sizes when comparing group-specific marginal distributions. Through carefully designed simulations, we compare our test with four traditional methods commonly employed in the analysis of cluster-correlated data. Only our test maintains the size across all data-generating scenarios with informativeness. We illustrate the proposed method to test for marginal associations in periodontal data with this distinctive form of informativeness., Competing Interests: Declaration of conflicting interestsThe authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

We present a nonparametric method for estimating the conditional future state entry probabilities and distributions of state entry time conditional on a past state visit when data are subject to dependent censorings in a progressive multistate model where Markovianity of the system is not assumed. These estimators are constructed using the competing risk techniques with risk sets consisting of fractional observations and inverse probability of censoring weights. The fractional observations correspond to estimates of the number of persons who ultimately enter a state from which the future state in question can be reached in one step. We then address the corresponding regression problem by combining these marginal estimators with the pseudo-value approach. The performance of our regression scheme is studied using a comprehensive simulation study. An analysis of existing data on graft-versus-host disease for bone marrow transplant individuals is presented using our novel methodology. A second analysis of another well-known data set on burn patients is also included., Competing Interests: Declaration of conflicting interestsThe authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Multistate current status data presents a more severe form of censoring due to the single observation of study participants transitioning through a sequence of well-defined disease states at random inspection times. Moreover, these data may be clustered within specified groups, and informativeness of the cluster sizes may arise due to the existing latent relationship between the transition outcomes and the cluster sizes. Failure to adjust for this informativeness may lead to a biased inference. Motivated by a clinical study of periodontal disease, we propose an extension of the pseudo-value approach to estimate covariate effects on the state occupation probabilities for these clustered multistate current status data with informative cluster or intra-cluster group sizes. In our approach, the proposed pseudo-value technique initially computes marginal estimators of the state occupation probabilities utilizing nonparametric regression. Next, the estimating equations based on the corresponding pseudo-values are reweighted by functions of the cluster sizes to adjust for informativeness. We perform a variety of simulation studies to study the properties of our pseudo-value regression based on the nonparametric marginal estimators under different scenarios of informativeness. For illustration, the method is applied to the motivating periodontal disease dataset, which encapsulates the complex data-generation mechanism.

Informative cluster size (ICS) arises in situations with clustered data where a latent relationship exists between the number of participants in a cluster and the outcome measures. Although this phenomenon has been sporadically reported in the statistical literature for nearly two decades now, further exploration is needed in certain statistical methodologies to avoid potentially misleading inferences. For inference about population quantities without covariates, inverse cluster size reweightings are often employed to adjust for ICS. Further, to study the effect of covariates on disease progression described by a multistate model, the pseudo-value regression technique has gained popularity in time-to-event data analysis. We seek to answer the question: "How to apply pseudo-value regression to clustered time-to-event data when cluster size is informative?" ICS adjustment by the reweighting method can be performed in two steps; estimation of marginal functions of the multistate model and fitting the estimating equations based on pseudo-value responses, leading to four possible strategies. We present theoretical arguments and thorough simulation experiments to ascertain the correct strategy for adjusting for ICS. A further extension of our methodology is implemented to include informativeness induced by the intracluster group size. We demonstrate the methods in two real-world applications: (i) to determine predictors of tooth survival in a periodontal study and (ii) to identify indicators of ambulatory recovery in spinal cord injury patients who participated in locomotor-training rehabilitation., (© 2023 John Wiley & Sons Ltd.)

We propose a Bayesian hurdle mixed-effects model to analyze longitudinal ordinal data under a complex multilevel structure. This research was motivated by the dataset gathered from the Iowa Fluoride Study (IFS) in order to establish the relationships between fluorosis status and potential risk/protective factors. Dental fluorosis is characterized by spots on tooth enamel and is due to ingestion of excessive fluoride intake during enamel formation. Observations are collected from multiple surface zones on each tooth and on all available teeth of children from the studied cohort, which are longitudinally observed at ages 9, 13, and 17. The data not only exhibit a complex hierarchical structure, but also have a large proportion of zero values that are likely to follow different statistical patterns from non-zero categories. Therefore, we develop a hurdle model to consider the zero category separately, while a proportional odds model is used for the positive categories. The estimated parameters are obtained from a Gibbs sampler implemented by the OpenBUGS software. Our model is compared with two popular methods for ordinal data: the proportional odds model and the partial proportional odds model. We perform a comprehensive analysis of the IFS data and evaluate the accuracy and effectiveness of our methodology through simulation studies. Our discoveries provide novel insights to statisticians and dental practitioners about the associations between patient and clinical characteristics and dental fluorosis., (© 2022 John Wiley & Sons Ltd.)

Repeated measures are often collected in longitudinal follow-up from clinical trials and observational studies. In many situations, these measures are adherent to some specific event and are only available when it occurs; an example is serum creatinine from laboratory tests for hospitalized acute kidney injuries. The frequency of event recurrences is potentially correlated with overall health condition and hence may influence the distribution of the outcome measure of interest, leading to informative cluster size. In particular, there may be a large portion of subjects without any events, thus no longitudinal measures are available, which may be due to insusceptibility to such events or censoring before any events, and this zero-inflation nature of the data needs to be taken into account. On the other hand, there often exists a terminal event that may be correlated with the recurrent events. Previous work in this area suffered from the limitation that not all these issues were handled simultaneously. To address this deficiency, we propose a novel joint modeling approach for longitudinal data adjusting for zero-inflated and informative cluster size as well as a terminal event. A three-stage semiparametric likelihood-based approach is applied for parameter estimation and inference. Extensive simulations are conducted to evaluate the performance of our proposal. Finally, we utilize the Assessment, Serial Evaluation, and Subsequent Sequelae of Acute Kidney Injury (ASSESS-AKI) study for illustration., (© 2021 John Wiley & Sons Ltd.)

Biological and medical researchers often collect count data in clusters at multiple time points. The data can exhibit excessive zeros and a wide range of dispersion levels. In particular, our research was motivated by a dental dataset with such complex data features: the Iowa Fluoride Study (IFS). The study was designed to investigate the effects of various dietary and nondietary factors on the caries development of a cohort of Iowa school children at the ages of 5, 9, and 13. To analyze the multiyear IFS data, we propose a novel longitudinal method of a generalized estimating equations based marginal regression model. We use a zero-inflated model with a Conway-Maxwell-Poisson (CMP) distribution, which has the flexibility to account for all levels of dispersion. The parameters of interest are estimated through a modified expectation-solution algorithm to account for the clustered and temporal correlation structure. We fit the proposed zero-inflated CMP model and perform a comprehensive secondary analysis of the IFS dataset. It resulted in a number of notable conclusions that also make clinical sense. Additionally, we demonstrated the superiority of this modeling approach over two other popular competing models: the zero-inflated Poisson and negative binomial models. In the simulation studies, we further evaluate the performance of our point estimators, the variance estimators, and that of the large sample confidence intervals for the parameters of interest. It is also demonstrated that our longitudinal CMP model can correctly identify the time-varying dispersion patterns., (© 2021 Wiley-VCH GmbH.)

In this work, we propose a semiparametric method for estimating the optimal treatment for a given patient based on individual covariate information for that patient when data from a crossover design are available. Here, we assume there are carry-over effects for patients switching from one treatment to another. For the K treatment (K ≥ 2) scenario, we show that nonparametric estimation of carry-over effects can have the undesirable property that comparison of treatment means can only be done using independent outcome measurements from different groups of patients rather than using available joint measurements for each patient. To overcome this barrier, we compare probabilities of outcome variable of each treatment dominating outcome variables for all other treatments conditional on patient-specific scores constructed from patient covariates. We suggest single-index models as appropriate models connecting outcome variables to covariates and our empirical investigations show that frequencies of correct treatment assignments are highly accurate. The proposed method is also rather robust against departures from a single-index model structure. We also conduct a real data analysis to show the applicability of the proposed procedure., (© 2019 John Wiley & Sons, Ltd.)

In this work we propose a method for optimal treatment assignment based on individual covariate information for a patient. For the K treatment ( K ≥ 2 ) scenario, we compare quantities that are suitable surrogates to true conditional probabilities of outcome variable of each treatment dominating outcome variables for all other treatments conditional on patient specific scores constructed from patient-specific covariates. As opposed to methods based on conditional means, our method can be applied for a broad set of models and error structures. Furthermore, the proposed method has very desirable large sample properties. We suggest Single Index Models as appropriate models connecting outcome variables to covariates and our empirical investigations show that correct treatment assignments are highly accurate. The proposed method is also rather robust against departures from a Single Index Model structure. Furthermore, selection of a treatment using the proposed metric appears to incur no losses in terms of the average reward for cases when two treatments are close in terms of this metric. We also conduct a real data analysis to show the applicability of the proposed procedure. This analysis highlights possible gains both in terms of average response and survival time if one were to use the proposed method.

Disease severity is a latent concept which should be observed using a measurement tool; it can be useful in assessing disease status both cross-sectionally and longitudinally. Medsger scale is a valid instrument for assessing the systemic sclerosis severity in which the items are categorized from 0 (normal) to 4 (endstage) for each organ system. We simultaneously analyzed two of the Medsger scale items, namely, general system and skin system as two correlated ordinal responses using an overdispersed marginalized random-effects model for longitudinal ordinal data exhibiting an overdispersion pattern. In general, a random-effects approach is implemented to account for the correlation between these two stochastic processes and to make simultaneous inference; our model also accounts for temporal correlations amongst observations taken on the same subject. Another important aspect of our model is its capacity to handle data overdispersion in order to make reliable inference. Last but not least, it is proved that certain parameters in our joint model have marginal interpretations. We investigate the statistical properties of our estimators through extensive simulation study. Finally, the methodology is applied to a data of systemic sclerosis patients.

Multisample U-statistics encompass a wide class of test statistics that allow the comparison of 2 or more distributions. U-statistics are especially powerful because they can be applied to both numeric and nonnumeric data, eg, ordinal and categorical data where a pairwise similarity or distance-like measure between categories is available. However, when comparing the distribution of a variable across 2 or more groups, observed differences may be due to confounding covariates. For example, in a case-control study, the distribution of exposure in cases may differ from that in controls entirely because of variables that are related to both exposure and case status and are distributed differently among case and control participants. We propose to use individually reweighted data (ie, using the stratification score for retrospective data or the propensity score for prospective data) to construct adjusted U-statistics that can test the equality of distributions across 2 (or more) groups in the presence of confounding covariates. Asymptotic normality of our adjusted U-statistics is established and a closed form expression of their asymptotic variance is presented. The utility of our approach is demonstrated through simulation studies, as well as in an analysis of data from a case-control study conducted among African-Americans, comparing whether the similarity in haplotypes (ie, sets of adjacent genetic loci inherited from the same parent) occurring in a case and a control participant differs from the similarity in haplotypes occurring in 2 control participants., (Copyright © 2018 John Wiley & Sons, Ltd.)

A major challenge of genomics data is to detect interactions displaying functional associations from large-scale observations. In this study, a new cPLS-algorithm combining partial least squares approach with negative binomial regression is suggested to reconstruct a genomic association network for high-dimensional next-generation sequencing count data. The suggested approach is applicable to the raw counts data, without requiring any further pre-processing steps. In the settings investigated, the cPLS-algorithm outperformed the two widely used comparative methods, graphical lasso, and weighted correlation network analysis. In addition, cPLS is able to estimate the full network for thousands of genes without major computational load. Finally, we demonstrate that cPLS is capable of finding biologically meaningful associations by analyzing an example data set from a previously published study to examine the molecular anatomy of the craniofacial development.

Propensity score based statistical methods, such as matching, regression, stratification, inverse probability weighting (IPW), and doubly robust (DR) estimating equations, have become popular in estimating average treatment effect (ATE) and average treatment effect among treated (ATT) in observational studies. Propensity score is the conditional probability receiving a treatment assignment with given covariates, and propensity score is usually estimated by logistic regression. However, a misspecification of the propensity score model may result in biased estimates for ATT and ATE. As an alternative, the generalized boosting method (GBM) has been proposed to estimate the propensity score. GBM uses regression trees as weak predictors and captures nonlinear and interactive effects of the covariate. For GBM-based propensity score, only IPW methods have been investigated in the literature. In this article, we provide a comparative study of the commonly used propensity score based methods for estimating ATT and ATE, and examine their performances when propensity score is estimated by logistic regression and GBM, respectively. Extensive simulation results indicate that the estimators for ATE and ATT may vary greatly due to different methods. We concluded that (i) regression may not be suitable for estimating ATE and ATT regardless of the estimation method of propensity score; (ii) IPW and stratification usually provide reliable estimates of ATT when propensity score model is correctly specified; (iii) the estimators of ATE based on stratification, IPW, and DR are close to the underlying true value of ATE when propensity score is correctly specified by logistic regression or estimated using GBM., (© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Clustered data are often encountered in biomedical studies, and to date, a number of approaches have been proposed to analyze such data. However, the phenomenon of informative cluster size (ICS) is a challenging problem, and its presence has an impact on the choice of a correct analysis methodology. For example, Dutta and Datta (2015, Biometrics) presented a number of marginal distributions that could be tested. Depending on the nature and degree of informativeness of the cluster size, these marginal distributions may differ, as do the choices of the appropriate test. In particular, they applied their new test to a periodontal data set where the plausibility of the informativeness was mentioned, but no formal test for the same was conducted. We propose bootstrap tests for testing the presence of ICS. A balanced bootstrap method is developed to successfully estimate the null distribution by merging the re-sampled observations with closely matching counterparts. Relying on the assumption of exchangeability within clusters, the proposed procedure performs well in simulations even with a small number of clusters, at different distributions and against different alternative hypotheses, thus making it an omnibus test. We also explain how to extend the ICS test to a regression setting and thereby enhancing its practical utility. The methodologies are illustrated using the periodontal data set mentioned earlier. Copyright © 2017 John Wiley & Sons, Ltd., (Copyright © 2017 John Wiley & Sons, Ltd.)

Community water fluoridation is an important public health measure to prevent dental caries, but it continues to be somewhat controversial. The Iowa Fluoride Study (IFS) is a longitudinal study on a cohort of Iowa children that began in 1991. The main purposes of this study (http://www.dentistry.uiowa.edu/preventive-fluoride-study) were to quantify fluoride exposures from both dietary and nondietary sources and to associate longitudinal fluoride exposures with dental fluorosis (spots on teeth) and dental caries (cavities). We analyze a subset of the IFS data by a marginal regression model with a zero-inflated version of the Conway-Maxwell-Poisson distribution for count data exhibiting excessive zeros and a wide range of dispersion patterns. In general, we introduce two estimation methods for fitting a ZICMP marginal regression model. Finite sample behaviors of the estimators and the resulting confidence intervals are studied using extensive simulation studies. We apply our methodologies to the dental caries data. Our novel modeling incorporating zero inflation, clustering, and overdispersion sheds some new light on the effect of community water fluoridation and other factors. We also include a second application of our methodology to a genomic (next-generation sequencing) dataset that exhibits underdispersion., (© 2015, The International Biometric Society.)

Ignorance of the mechanisms responsible for the availability of information presents an unusual problem for analysts. It is often the case that the availability of information is dependent on the outcome. In the analysis of cluster data we say that a condition for informative cluster size (ICS) exists when the inference drawn from analysis of hypothetical balanced data varies from that of inference drawn on observed data. Much work has been done in order to address the analysis of clustered data with informative cluster size; examples include Inverse Probability Weighting (IPW), Cluster Weighted Generalized Estimating Equations (CWGEE), and Doubly Weighted Generalized Estimating Equations (DWGEE). When cluster size changes with time, i.e., the data set possess temporally varying cluster sizes (TVCS), these methods may produce biased inference for the underlying marginal distribution of interest. We propose a new marginalization that may be appropriate for addressing clustered longitudinal data with TVCS. The principal motivation for our present work is to analyze the periodontal data collected by Beck et al. (1997, Journal of Periodontal Research 6, 497-505). Longitudinal periodontal data often exhibits both ICS and TVCS as the number of teeth possessed by participants at the onset of study is not constant and teeth as well as individuals may be displaced throughout the study., (© 2015, The International Biometric Society.)

Background: It has been long well known that genes do not act alone; rather groups of genes act in consort during a biological process. Consequently, the expression levels of genes are dependent on each other. Experimental techniques to detect such interacting pairs of genes have been in place for quite some time. With the advent of microarray technology, newer computational techniques to detect such interaction or association between gene expressions are being proposed which lead to an association network. While most microarray analyses look for genes that are differentially expressed, it is of potentially greater significance to identify how entire association network structures change between two or more biological settings, say normal versus diseased cell types., Results: We provide a recipe for conducting a differential analysis of networks constructed from microarray data under two experimental settings. At the core of our approach lies a connectivity score that represents the strength of genetic association or interaction between two genes. We use this score to propose formal statistical tests for each of following queries: (i) whether the overall modular structures of the two networks are different, (ii) whether the connectivity of a particular set of "interesting genes" has changed between the two networks, and (iii) whether the connectivity of a given single gene has changed between the two networks. A number of examples of this score is provided. We carried out our method on two types of simulated data: Gaussian networks and networks based on differential equations. We show that, for appropriate choices of the connectivity scores and tuning parameters, our method works well on simulated data. We also analyze a real data set involving normal versus heavy mice and identify an interesting set of genes that may play key roles in obesity., Conclusions: Examining changes in network structure can provide valuable information about the underlying biochemical pathways. Differential network analysis with appropriate connectivity scores is a useful tool in exploring changes in network structures under different biological conditions. An R package of our tests can be downloaded from the supplementary website http://www.somnathdatta.org/Supp/DNA.

We consider the problem of comparing two outcome measures when the pairs are clustered. Using the general principle of within-cluster resampling, we obtain a novel signed-rank test for clustered paired data. We show by a simple informative cluster size simulation model that only our test maintains the correct size under a null hypothesis of marginal symmetry compared to four other existing signed rank tests; further, our test has adequate power when cluster size is noninformative. In general, cluster size is informative if the distribution of pair-wise differences within a cluster depends on the cluster size. An application of our method to testing radiation toxicity trend is presented.

Multistage models are used to describe individuals (or experimental units) moving through a succession of "stages" corresponding to distinct states (e.g., healthy, diseased, diseased with complications, dead). The resulting data can be considered to be a form of multivariate survival data containing information about the transition times and the stages occupied. Traditional survival analysis is the simplest example of a multistage model, where individuals begin in an initial stage (say, alive) and move irreversibly to a second stage (death). In this article, we consider general multistage models with a directed tree structure (progressive models) in which individuals traverse through stages in a possibly non-Markovian manner. We construct nonparametric estimators of stage occupation probabilities and marginal cumulative transition hazards. Empirical calculations of these quantities are not possible due to the lack of complete data. We consider current status information which represents a more severe form of censoring than the commonly used right censoring. Asymptotic validity of our estimators can be justified using consistency results for nonparametric regression estimators. Finite-sample behavior of our estimators is studied by simulation, in which we show that our estimators based on these limited data compare well with those based on complete data. We also apply our method to a real-life data set arising from a cardiovascular diseases study in Taiwan.

We provide non-parametric estimates of the marginal cumulative distribution of stage occupation times (waiting times) and non-parametric estimates of marginal cumulative incidence function (proportion of persons who leave stage j for stage j' within time t of entering stage j) using right-censored data from a multi-stage model. We allow for stage and path dependent censoring where the censoring hazard for an individual may depend on his or her natural covariate history such as the collection of stages visited before the current stage and their occupation times. Additional external time dependent covariates that may induce dependent censoring can also be incorporated into our estimates, if available. Our approach requires modelling the censoring hazard so that an estimate of the integrated censoring hazard can be used in constructing the estimates of the waiting times distributions. For this purpose, we propose the use of an additive hazard model which results in very flexible (robust) estimates. Examples based on data from burn patients and simulated data with tracking are also provided to demonstrate the performance of our estimators., (Published in 2002 by John Wiley & Sons, Ltd.)