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The quantile regression model has increasingly become a useful approach for analyzing survival data due to its easy interpretation and flexibility in exploring the dynamic relationship between a time-to-event outcome and the covariates. In this paper, we consider the quantile regression model for survival data with missing censoring indicators. Based on the augmented inverse probability weighting technique, two weighted estimating equations are developed and corresponding easily implemented algorithms are suggested to solve the estimating equations. Asymptotic properties of the resultant estimators and the resampling-based inference procedures are established. Finally, the finite sample performances of the proposed approaches are investigated in simulation studies and a real data application. [ABSTRACT FROM AUTHOR]

This paper presents a new model-based generalized functional clustering method for discrete longitudinal data, such as multivariate binomial and Poisson distributed data. For this purpose, we propose a multivariate functional principal component analysis (MFPCA)-based clustering procedure for a latent multivariate Gaussian process instead of the original functional data directly. The main contribution of this study is two-fold: modeling of discrete longitudinal data with the latent multivariate Gaussian process and developing of a clustering algorithm based on MFPCA coupled with the latent multivariate Gaussian process. Numerical experiments, including real data analysis and a simulation study, demonstrate the promising empirical properties of the proposed approach. [ABSTRACT FROM AUTHOR]

In clustering problems, to model the intrinsic structure of unlabeled data, the latent variable models are frequently used. These model-based clustering methods often provide a clustering rule minimizing the total false assignment error. However, in many clustering applications, it is desirable to treat false assignment errors for a certain cluster differently. In this paper, we introduce the false assignment rate for clustering and estimate it by using the extended likelihood approach. We propose VRclust, a novel clustering rule that controls various errors differently across clusters. Real data examples illustrate the usage of estimation of false assignment rate and a simulation study shows that error controls are consistent as the sample size increases. [ABSTRACT FROM AUTHOR]

For the analysis of competing risks data, three different types of hazard functions have been considered in the literature, namely the cause-specific hazard, the sub-distribution hazard, and the marginal hazard function. Accordingly, medical researchers can fit three different types of the Cox model to estimate the effect of covariates on each of the hazard function. While the relationship between the cause-specific hazard and the sub-distribution hazard has been extensively studied, the relationship to the marginal hazard function has not yet been analyzed due to the difficulties related to non-identifiability. In this paper, we adopt an assumed copula model to deal with the model identifiability issue, making it possible to establish a relationship between the sub-distribution hazard and the marginal hazard function. We then compare the two methods of fitting the Cox model to competing risks data. We also extend our comparative analysis to clustered competing risks data that are frequently used in medical studies. To facilitate the numerical comparison, we implement the computing algorithm for marginal Cox regression with clustered competing risks data in the R joint.Cox package and check its performance via simulations. For illustration, we analyze two survival datasets from lung cancer and bladder cancer patients. [ABSTRACT FROM AUTHOR]

In this paper, we propose a generalization of the power series cure rate model for the number of competing causes related to the occurrence of the event of interest. The model includes distributions not yet used in the cure rate models context, such as the Borel, Haight and Restricted Generalized Poisson distributions. The model is conveniently parameterized in terms of the cure rate. Maximum likelihood estimation based on the Expectation Maximization algorithm is discussed. A simulation study designed to assess some properties of the estimators is carried out, showing the good performance of the proposed estimation procedure in finite samples. Finally, an application to a bone marrow transplant data set is presented. [ABSTRACT FROM AUTHOR]

It is well known that the standard F test is severely affected by heteroskedasticity in unbalanced analysis of covariance models. Currently available potential remedies for such a scenario are based on heteroskedasticity-consistent covariance matrix estimation (HCCME). However, the HCCME approach tends to be liberal in small samples. Therefore, in the present paper, we propose a combination of HCCME and a wild bootstrap technique, with the aim of improving the small-sample performance. We precisely state a set of assumptions for the general analysis of covariance model and discuss their practical interpretation in detail, since this issue may have been somewhat neglected in applied research so far. We prove that these assumptions are sufficient to ensure the asymptotic validity of the combined HCCME-wild bootstrap analysis of covariance. The results of our simulation study indicate that our proposed test remedies the problems of the analysis of covariance F test and its heteroskedasticity-consistent alternatives in small to moderate sample size scenarios. Our test only requires very mild conditions, thus being applicable in a broad range of real-life settings, as illustrated by the detailed discussion of a dataset from preclinical research on spinal cord injury. Our proposed method is ready-to-use and allows for valid hypothesis testing in frequently encountered settings (e.g., comparing group means while adjusting for baseline measurements in a randomized controlled clinical trial). [ABSTRACT FROM AUTHOR]

After the diagnosis of a disease, one major objective is to predict cumulative probabilities of events such as clinical relapse or death from the individual information collected up to a prediction time, usually including biomarker repeated measurements. Several competing estimators have been proposed, mainly from two approaches: joint modelling and landmarking. These approaches differ by the information used, the model assumptions and the complexity of the computational procedures. This paper aims to review the two approaches, precisely define the derived estimators of dynamic predictions and compare their performances notably in case of misspecification. The ultimate goal is to provide key elements for the use of individual dynamic predictions in clinical practice. Prediction of two competing causes of prostate cancer progression from the history of prostate-specific antigen is used as a motivated example. We formally define the quantity to estimate and its estimators, propose techniques to assess the uncertainty around predictions and validate them. We then conduct an in-depth simulation study compare the estimators in terms of prediction error, discriminatory power, efficiency and robustness to model assumptions. We show that prediction tools should be handled with care, in particular by properly specifying models and estimators. [ABSTRACT FROM AUTHOR]

Real phenomena often leads to challenges in data. One of these is outliers or influential values. Especially in a small sample, these values can have a major influence on the modeling process. In the beta regression framework, this issue has been addressed mainly in two ways: the assumption of a different response model and the application of a minimum density power divergence estimation (MDPDE) procedure. In this paper, however, we propose a simple hierarchical Bayesian methodology in the context of a varying dispersion beta response model that is robust to outliers, as shown through an extensive simulation study and analysis of two real data sets. To robustify Bayesian modeling, a heavy-tailed Student's t prior with uniform degrees of freedom is adopted for the regression coefficients. This proposal results in a wieldy implementation procedure which avails practical use of the approach. [ABSTRACT FROM AUTHOR]

Count outcomes with excessive zeros are common in behavioral and social studies, and zero-inflated count models such as zero-inflated Poisson (ZIP) and zero-inflated Negative Binomial (ZINB) can be applied when such zero-inflated count data are used as response variable. However, when the zero-inflated count data are used as predictors, ignoring the difference of structural and random zeros can result in biased estimates. In this paper, a generalized estimating equation (GEE)-type mixture model is proposed to jointly model the response of interest and the zero-inflated count predictors. Simulation studies show that the proposed method performs well for practical settings and is more robust for model misspecification than the likelihood-based approach. A case study is also provided for illustration. [ABSTRACT FROM AUTHOR]

Joint modelling of longitudinal and time-to-event data has received much attention recently. Increasingly, extensions to standard joint modelling approaches are being proposed to handle complex data structures commonly encountered in applied research. In this paper, we propose a joint model for hierarchical longitudinal and time-to-event data. Our motivating application explores the association between tumor burden and progression-free survival in non-small cell lung cancer patients. We define tumor burden as a function of the sizes of target lesions clustered within a patient. Since a patient may have more than one lesion, and each lesion is tracked over time, the data have a three-level hierarchical structure: repeated measurements taken at time points (level 1) clustered within lesions (level 2) within patients (level 3). We jointly model the lesion-specific longitudinal trajectories and patient-specific risk of death or disease progression by specifying novel association structures that combine information across lower level clusters (e.g. lesions) into patient-level summaries (e.g. tumor burden). We provide user-friendly software for fitting the model under a Bayesian framework. Lastly, we discuss alternative situations in which additional clustering factor(s) occur at a level higher in the hierarchy than the patient-level, since this has implications for the model formulation. [ABSTRACT FROM AUTHOR]

Data on rates, percentages, or proportions arise frequently in many different applied disciplines like medical biology, health care, psychology, and several others. In this paper, we develop a robust inference procedure for the beta regression model, which is used to describe such response variables taking values in (0, 1) through some related explanatory variables. In relation to the beta regression model, the issue of robustness has been largely ignored in the literature so far. The existing maximum likelihood-based inference has serious lack of robustness against outliers in data and generate drastically different (erroneous) inference in the presence of data contamination. Here, we develop the robust minimum density power divergence estimator and a class of robust Wald-type tests for the beta regression model along with several applications. We derive their asymptotic properties and describe their robustness theoretically through the influence function analyses. Finite sample performances of the proposed estimators and tests are examined through suitable simulation studies and real data applications in the context of health care and psychology. Although we primarily focus on the beta regression models with a fixed dispersion parameter, some indications are also provided for extension to the variable dispersion beta regression models with an application. [ABSTRACT FROM AUTHOR]

Publication bias can significantly limit the validity of meta-analysis when trying to draw conclusion about a research question from independent studies. Most research on detection and correction for publication bias in meta-analysis focus mainly on funnel plot-based methodologies or selection models. In this paper, we formulate publication bias as a truncated distribution problem, and propose new parametric solutions. We develop methodologies of estimating the underlying overall effect size and the severity of publication bias. We distinguish the two major situations, in which publication bias may be induced by: (1) small effect size or (2) large p-value. We consider both fixed and random effects models, and derive estimators for the overall mean and the truncation proportion. These estimators will be obtained using maximum likelihood estimation and method of moments under fixed- and random-effects models, respectively. We carried out extensive simulation studies to evaluate the performance of our methodology, and to compare with the non-parametric Trim and Fill method based on funnel plot. We find that our methods based on truncated normal distribution perform consistently well, both in detecting and correcting publication bias under various situations. [ABSTRACT FROM AUTHOR]

Age-dependent dynamics is an important characteristic of many infectious diseases. Age-group epidemic models describe the infection dynamics in different age-groups by allowing to set distinct parameter values for each. However, such models are highly nonlinear and may have a large number of unknown parameters. Thus, parameter estimation of age-group models, while becoming a fundamental issue for both the scientific study and policy making in infectious diseases, is not a trivial task in practice. In this paper, we examine the estimation of the so-called next-generation matrix using incidence data of a single entire outbreak, and extend the approach to deal with recurring outbreaks. Unlike previous studies, we do not assume any constraints regarding the structure of the matrix. A novel two-stage approach is developed, which allows for efficient parameter estimation from both statistical and computational perspectives. Simulation studies corroborate the ability to estimate accurately the parameters of the model for several realistic scenarios. The model and estimation method are applied to real data of influenza-like-illness in Israel. The parameter estimates of the key relevant epidemiological parameters and the recovered structure of the estimated next-generation matrix are in line with results obtained in previous studies. [ABSTRACT FROM AUTHOR]

When developing prediction models for application in clinical practice, health practitioners usually categorise clinical variables that are continuous in nature. Although categorisation is not regarded as advisable from a statistical point of view, due to loss of information and power, it is a common practice in medical research. Consequently, providing researchers with a useful and valid categorisation method could be a relevant issue when developing prediction models. Without recommending categorisation of continuous predictors, our aim is to propose a valid way to do it whenever it is considered necessary by clinical researchers. This paper focuses on categorising a continuous predictor within a logistic regression model, in such a way that the best discriminative ability is obtained in terms of the highest area under the receiver operating characteristic curve (AUC). The proposed methodology is validated when the optimal cut points' location is known in theory or in practice. In addition, the proposed method is applied to a real data-set of patients with an exacerbation of chronic obstructive pulmonary disease, in the context of the IRYSS-COPD study where a clinical prediction rule for severe evolution was being developed. The clinical variable PCO2 was categorised in a univariable and a multivariable setting. [ABSTRACT FROM AUTHOR]

A common objective in longitudinal studies is to characterize the relationship between a longitudinal response process and a time-to-event data. Ordinal nature of the response and possible missing information on covariates add complications to the joint model. In such circumstances, some influential observations often present in the data may upset the analysis. In this paper, a joint model based on ordinal partial mixed model and an accelerated failure time model is used, to account for the repeated ordered response and time-to-event data, respectively. Here, we propose an influence function-based robust estimation method. Monte Carlo expectation maximization method-based algorithm is used for parameter estimation. A detailed simulation study has been done to evaluate the performance of the proposed method. As an application, a data on muscular dystrophy among children is used. Robust estimates are then compared with classical maximum likelihood estimates. [ABSTRACT FROM AUTHOR]

Anderson Gray McKendrick's 1926 paper, 'Applications of mathematics to medical problems', was the earliest reference cited in Dempster et al.'s 1977 paper that defined and popularized the EM algorithm. McKendrick's paper was prominently featured by Joseph Oscar Irwin in his 1962 inaugural address as the President of the Royal Statistical Society (in the UK), entitled 'The place of mathematics in medical and biological statistics'. The link of McKendrick's work to the EM algorithm is due to an improvement made by Irwin on a novel method McKendrick used for estimating an infection rate when the observed data do not distinguish between those individuals who are not susceptible to the infection and those who are susceptible, but do not develop symptoms. This article examines this link, along the way illustrating the central ideas underlying the EM algorithm as well as its properties; the examination also suggests a profiling strategy for speeding up EM, which may be worthy of general investigation. McKendrick's data on an epidemic of cholera are used for illustration and to compare EM with Irwin's method as well as the Newton-Raphson algorithm. Issues beyond computation are also discussed whenever appropriate. [ABSTRACT FROM AUTHOR]

This paper reviews applications of the method of multiple imputation to dealing with multilevel data that have several kinds of imperfections. These are classified into two broad categories: missing values and imprecise measurement (corrupted recording). The role of the model describing the data imperfections is emphasized. With multiple imputation, these imperfections and information about the processes underlying them can be taken into account. The inferences drawn exploit all the collected information and appropriately reflect the information contained in the data. [ABSTRACT FROM AUTHOR]

This paper reviews recent developments by the Washington/Brown groups for the study of anatomical shape in the emerging new discipline of computational anatomy. Parametric representations of anatomical variation for computational anatomy are reviewed, restricted to the assumption of small deformations. The generation of covariance operators for probabilistic measures of anatomical variation on coordinatized submanifolds is formulated as an empirical procedure. Populations of brains are mapped to common coordinate systems, from which template coordinate systems are constructed which are closest to the population of anatomies in a minimum distance sense. Variation of several one-, two- and three-dimensional manifolds, i.e. sulci, surfaces and brain volumes are examined via Gaussian measures with mean and covariances estimated directly from maps of templates to targets. Methods are presented for estimating the covariances of vector fields from a family of empirically generated maps, posed as generalized spectrum estimation indexed over the submanifolds. Covariance estimation is made parametric, analogous to autoregressive modelling, by introducing small deformation linear operators for constraining the spectrum of the fields. [ABSTRACT FROM AUTHOR]

Most problems in computational statistics involve optimization of an objective function such as a loglikelihood, a sum of squares, or a log posterior function. The EM algorithm is one of the most effective algorithms for maximization because it iteratively transfers maximization from a complex function to a simple, surrogate function. This theoretical perspective clarifies the operation of the EM algorithm and suggests novel generalizations. Besides simplifying maximization, optimization transfer usually leads to highly stable algorithms with well-understood local and global convergence properties. Although convergence can be excruciatingly slow, various devices exist for accelerating it. Beginning with the EM algorithm, we review in this paper several optimization transfer algorithms of substantial utility in medical statistics. [ABSTRACT FROM AUTHOR]