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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]

Spatial scan statistics are widely used tools for the detection of disease clusters. Especially, the circular spatial scan statistic proposed by Kulldorff along with SaTScan software has been used in a wide variety of epidemiological studies and disease surveillance. However, as it cannot detect non-circular, irregularly shaped clusters, many authors have proposed non-circular spatial scan statistics. Above all, the flexible spatial scan statistic proposed by Tango and Takahashi along with FleXScan software has also been used. However, it does not seem to be well recognized that these spatial scan statistics, especially SaTScan, tend to detect the most likely cluster, much larger than the true cluster by absorbing neighboring regions with nonelevated risk of disease occurrence. Therefore, if researchers reported the detected most likely cluster as they are, it might lead to a criticism to them due to the fact that some regions with nonelevated risk are included in the detected most likely cluster. In this paper, to avoid detecting such undesirable and misleading clusters which might cause a social concern, we shall propose the use of the restricted likelihood ratio proposed by Tango and illustrate the procedure with two kinds of mortality data in Japan. [ABSTRACT FROM AUTHOR]

Agreement studies are of paramount importance in various scientific domains. When several observers classify objects on categorical scales, agreement can be quantified through multirater kappa coefficients. In most statistical packages, the standard error of these coefficients is only available under the null hypothesis that the coefficient is equal to zero, preventing the construction of confidence intervals in the general case. The aim of this paper is triple. First, simple analytic formulae for the standard error of multirater kappa coefficients will be given in the general case. Second, these formulae will be extended to the case of multilevel data structures. The formulae are based on simple matrix algebra and are implemented in the R package "multiagree". Third, guidelines on the choice between the different mulitrater kappa coefficients will be provided. [ABSTRACT FROM AUTHOR]

Dependent censoring often arises in biomedical studies when time to tumour progression (e.g., relapse of cancer) is censored by an informative terminal event (e.g., death). For meta-analysis combining existing studies, a joint survival model between tumour progression and death has been considered under semicompeting risks, which induces dependence through the study-specific frailty. Our paper here utilizes copulas to generalize the joint frailty model by introducing additional source of dependence arising from intra-subject association between tumour progression and death. The practical value of the new model is particularly evident for meta-analyses in which only a few covariates are consistently measured across studies and hence there exist residual dependence. The covariate effects are formulated through the Cox proportional hazards model, and the baseline hazards are nonparametrically modeled on a basis of splines. The estimator is then obtained by maximizing a penalized log-likelihood function. We also show that the present methodologies are easily modified for the competing risks or recurrent event data, and are generalized to accommodate left-truncation. Simulations are performed to examine the performance of the proposed estimator. The method is applied to a meta-analysis for assessing a recently suggested biomarker CXCL12 for survival in ovarian cancer patients. We implement our proposed methods in R joint.Cox package. [ABSTRACT FROM AUTHOR]

Common limitations of clustering methods include the slow algorithm convergence, the instability of the pre-specification on a number of intrinsic parameters, and the lack of robustness to outliers. A recent clustering approach proposed a fast search algorithm of cluster centers based on their local densities. However, the selection of the key intrinsic parameters in the algorithm was not systematically investigated. It is relatively difficult to estimate the "optimal" parameters since the original definition of the local density in the algorithm is based on a truncated counting measure. In this paper, we propose a clustering procedure with adaptive density peak detection, where the local density is estimated through the nonparametric multivariate kernel estimation. The model parameter is then able to be calculated from the equations with statistical theoretical justification. We also develop an automatic cluster centroid selection method through maximizing an average silhouette index. The advantage and flexibility of the proposed method are demonstrated through simulation studies and the analysis of a few benchmark gene expression data sets. The method only needs to perform in one single step without any iteration and thus is fast and has a great potential to apply on big data analysis. A user-friendly R package ADPclust is developed for public use. [ABSTRACT FROM AUTHOR]

Community intervention trials are becoming increasingly popular as a tool for evaluating the effectiveness of health education and intervention strategies. Typically, units such as households, schools, towns, counties, are randomized to receive either intervention or control, then outcomes are measured on individuals within each of the units of randomization. It is well recognized that the design and analysis of such studies must account for the clustering of subjects within the units of randomization. Furthermore, there are usually both subject level and cluster level covariates that must be considered in the modelling process. While suitable methods are available for continuous outcomes, data analysis is more complicated when dichotomous outcomes are measured on each subject. This paper will compare and contrast several of the available methods that can be applied in such settings, including random effects models, generalized estimating equations and methods based on the calculation of 'design effects', as implemented in the computer package SUDAAN. For completeness, the paper will also compare these methods of analysis with more simplistic approaches based on the summary statistics. All the methods will be applied to a case study based on an adolescent anti-smoking intervention in Australia. The paper concludes with some general discussion and recommendations for routine design and analysis. [ABSTRACT FROM AUTHOR]

This paper investigates the impact of the number of studies on meta-analysis and meta-regression within the random-effects model framework. It is frequently neglected that inference in random-effects models requires a substantial number of studies included in meta-analysis to guarantee reliable conclusions. Several authors warn about the risk of inaccurate results of the traditional DerSimonian and Laird approach especially in the common case of meta-analysis involving a limited number of studies. This paper presents a selection of likelihood and non-likelihood methods for inference in meta-analysis proposed to overcome the limitations of the DerSimonian and Laird procedure, with a focus on the effect of the number of studies. The applicability and the performance of the methods are investigated in terms of Type I error rates and empirical power to detect effects, according to scenarios of practical interest. Simulation studies and applications to real meta-analyses highlight that it is not possible to identify an approach uniformly superior to alternatives. The overall recommendation is to avoid the DerSimonian and Laird method when the number of meta-analysis studies is modest and prefer a more comprehensive procedure that compares alternative inferential approaches. R code for meta-analysis according to all of the inferential methods examined in the paper is provided. [ABSTRACT FROM AUTHOR]

Data in many experiments arise as curves and therefore it is natural to use a curve as a basic unit in the analysis, which is termed functional data analysis (FDA). In longitudinal studies, recent developments in FDAhave extended classical linear models and linear mixed effects models to functional linear models (also termed varying-coefficient models) and functional mixed effects models. In this paper we focus our review on the functional mixed effects models using smoothing splines, because functional linear models are special cases of this more general framework. Due to the connection between smoothing splines and linear mixed effects models, functional mixed effects models can be fitted using existing software such as SAS Proc Mixed. A case study is presented as an illustration. [ABSTRACT FROM AUTHOR]

All models of this paper involve R x C contingency tables in which the total frequency is fixed (full multinomial model), or in which the row totals are fixed (product multinomial model). For the most part, we assume that the column categories are ordered. For the full multinomial model the null hypothesis of interest is independence, i.e., the (ij)th cell probability is the product of the marginal probabilities of the ith row and jth column. In the product multinomial model the null hypothesis is that the R multinomial distributions have the same vector of cell probabilities. Our review includes (1) a careful listing of two-sided and one-sided alternatives, and (2) methodology to reduce the loss of efficiency of tests because of the discreteness of the model (The methodologies discussed are efficient in several senses. Tests are exact. Tests have very favorable and robust power properties. Tests make use of back-up statistics, thereby providing a finer grid of p-values. In some special cases, e.g., a 2 x C table and a one-sided alternative, conditional p-values are found, within seconds, simply by entering row frequencies into a given website. Thus, computational efficiency is exceptional.), and (3) a critique of some exact linear permutation tests (that are conditional on row and column margins) for both two-sided and some one-sided alternatives. Furthermore, recommendations as to which tests to use for specific alternatives are made. [ABSTRACT FROM AUTHOR]

Since the early work of RA Fisher, exact methods have been recognized as important tools in data analysis because they provide valid statistical inference even with small sample sizes, or with sparse or skewed data. With the recent advance of computational power and the availability of commercial software packages, exact methods have gained substantial popularity over the past two decades. However, most of these exact methods have been devoted to testing classical null hypotheses of no differences, and until recently little was known about exact methods dealing with non-inferiority or equivalence hypotheses. The presence of nuisance parameters in testing non-inferiority/equivalence hypotheses presents a special challenge for exact methods because of the intense computational requirement. In this paper, we review exact methods available for proving non-inferiority or equivalence of two treatments with a dichotomous endpoint. First, we present the general methodology for conducting exact tests for non-inferiority or equivalence; we then discuss several unconditional and conditional methods available for constructing hypothesis tests and confidence intervals based on three commonly used measures, namely, the difference, relative risk, and odds ratio of two independent proportions or rates. Finally, we illustrate with several examples the application of these exact methods in analysing and planning non-inferiority or equivalence trials. [ABSTRACT FROM AUTHOR]

Economic evaluation of health care interventions based on decision analytic modelling can generate valuable information for health policy decision makers. However, the usefulness of the results obtained depends on the quality of the data input into the model; that is, the accuracy of the estimates for the costs, effectiveness, and transition probabilities between the different health states of the model. The aim of this paper is to review the use of Bayesian decision models in economic evaluation and to demonstrate how the individual components required for decision analytical modelling (i.e., systematic review incorporating meta-analyses, estimation of transition probabilities, evaluation of the model, and sensitivity analysis) may be addressed simultaneously in one coherent Bayesian model evaluated using Markov Chain Monte Carlo simulation implemented in the specialist Bayesian statistics software WinBUGS. To illustrate the method described, a simple probabilistic decision model is developed to evaluate the cost implications of using prophylactic antibiotics in caesarean section to reduce the incidence of wound infection. The advantages of using the Bayesian statistical approach outlined compared to the conventional classical approaches to decision analysis include the ability to: (i) perform all necessary analyses, including all intermediate analyses (e.g., meta-analyses) required to derive model parameters, in a single coherent model; (ii) incorporate expert opinion either directly or regarding the relative credibility of different data sources; (iii) use the actual posterior distributions for parameters of interest (opposed to making distributional assumptions necessary for the classical formulation); and (iv) incorporate uncertainty for all model parameters. [ABSTRACT FROM AUTHOR]

The analysis of marker data from HIV positive patients has been the motivation for many new developments in applied statistics. As well as reviewing these methods, this paper considers the extent to which programs to implement them are available in current software. Particular areas of development have been the joint modelling of markers and survival outcomes, non-linear random effects models that are of particular relevance for studying the efficacy of treatments and the use of Bayesian computational methods for inference from marker data. The package WinBUGS is recommended as being particularly well suited to the analysis of marker data. [ABSTRACT FROM AUTHOR]

Cluster randomized trials are increasingly common in general practice (family medicine). This paper will consider the design and analysis of such trials and emphasize the similarities and differences with trials in education, heath promotion and public health. Issues discussed are the estimation and range of values of the intra-cluster correlation coefficient found in general practice, and the associated sample size problems. There are problems with widely varying numbers of subjects per cluster, which leads to planning and analysis difficulties. Ethical issues in these trials, and considerations such as the principle of intention to treat are also considered. An example of the type of analysis available for a continuous outcome variable is given, and the available software is summarized briefly. [ABSTRACT FROM AUTHOR]

Continuous outcomes with preponderance of zero values are ubiquitous in data that arise from biomedical studies, for example studies of addictive disorders. This is known to lead to violation of standard assumptions in parametric inference and enhances the risk of misleading conclusions unless managed properly. Two-part models are commonly used to deal with this problem. However, standard two-part models have limitations with respect to obtaining parameter estimates that have marginal interpretation of covariate effects which are important in many biomedical applications. Recently marginalized two-part models are proposed but their development is limited to log-normal and log-skew-normal distributions. Thus, in this paper, we propose a finite mixture approach, with Weibull mixture regression as a special case, to deal with the problem. We use extensive simulation study to assess the performance of the proposed model in finite samples and to make comparisons with other family of models via statistical information and mean squared error criteria. We demonstrate its application on real data from a randomized controlled trial of addictive disorders. Our results show that a two-component Weibull mixture model is preferred for modeling zero-heavy continuous data when the non-zero part are simulated from Weibull or similar distributions such as Gamma or truncated Gauss. [ABSTRACT FROM AUTHOR]

Two-part mixed effects models are often used for analyzing longitudinal data with many zeros. Typically, these models are formulated with binary and continuous components separately with random effects that are correlated between the two components. Researchers have developed maximum-likelihood and Bayesian approaches for fitting these models that often require using particular software packages or very specialized software. We propose an imputation approach that will allow practitioners to separately use standard linear and generalized linear mixed models to estimate the fixed effects for two-part mixed effects models with complex random effects structures. An approximation to the conditional distribution of positive measurements given an individual's pattern of non-zero measurements is proposed that can be easily estimated and then imputed from. We show that for a wide range of parameter values, the imputation approach results in nearly unbiased estimation and can be implemented with standard software. We illustrate the proposed imputation approach for the analysis of longitudinal clinical trial data with many zeros. [ABSTRACT FROM AUTHOR]

We describe a procedure for imputing missing values of time-dependent covariates in a discrete time Cox model using the chained equations method. The procedure multiply imputes the missing values for each time-period in a time-sequential manner, using covariates from the current and previous time-periods as well as the survival outcome. The form of the outcome variable used in the imputation model depends on the functional form of the time-dependent covariate(s) and differs from the case of Cox regression with only baseline covariates. This time-sequential approach provides an approximation to a fully conditional approach. We illustrate the procedure with data on diabetics, evaluating the association of their glucose control with the risk of selected cancers. Using simulations we show that the suggested estimator performed well (in terms of bias and coverage) for completely missing at random, missing at random and moderate non-missing-at-random patterns. However, for very strong non-missing-at-random patterns, the estimator was seriously biased and the coverage was too low. The procedure can be implemented using multiple imputation with the Fully conditional Specification (FCS) method (MI procedure in SAS with FCS statement or similar packages in other software, e.g. MICE in R). For use with event times on a continuous scale, the events would need to be grouped into time-intervals. [ABSTRACT FROM AUTHOR]

Often in biomedical research, we deal with continuous (clustered) proportion responses ranging between zero and one quantifying the disease status of the cluster units. Interestingly, the study population might also consist of relatively disease-free as well as highly diseased subjects, contributing to proportion values in the interval [0, 1]. Regression on a variety of parametric densities with support lying in (0, 1), such as beta regression, can assess important covariate effects. However, they are deemed inappropriate due to the presence of zeros and/or ones. To evade this, we introduce a class of general proportion density, and further augment the probabilities of zero and one to this general proportion density, controlling for the clustering. Our approach is Bayesian and presents a computationally convenient framework amenable to available freeware. Bayesian case-deletion influence diagnostics based on q-divergence measures are automatic from the Markov chain Monte Carlo output. The methodology is illustrated using both simulation studies and application to a real dataset from a clinical periodontology study. [ABSTRACT FROM AUTHOR]

In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time-varying coefficients. [ABSTRACT FROM AUTHOR]

Motivated by a study exploring spatiotemporal trends in emergency department use, we develop a class of two-part hurdle models for the analysis of zero-inflated areal count data. The models consist of two components-one for the probability of any emergency department use and one for the number of emergency department visits given use. Through a hierarchical structure, the models incorporate both patient- and region-level predictors, as well as spatially and temporally correlated random effects for each model component. The random effects are assigned multivariate conditionally autoregressive priors, which induce dependence between the components and provide spatial and temporal smoothing across adjacent spatial units and time periods, resulting in improved inferences. To accommodate potential overdispersion, we consider a range of parametric specifications for the positive counts, including truncated negative binomial and generalized Poisson distributions. We adopt a Bayesian inferential approach, and posterior computation is handled conveniently within standard Bayesian software. Our results indicate that the negative binomial and generalized Poisson hurdle models vastly outperform the Poisson hurdle model, demonstrating that overdispersed hurdle models provide a useful approach to analyzing zero-inflated spatiotemporal data. [ABSTRACT FROM AUTHOR]

We combine conjugate and normal random effects in a joint model for outcomes, at least one of which is non-Gaussian, with particular emphasis on cases in which one of the outcomes is of survival type. Conjugate random effects are used to relax the often-restrictive mean-variance prescription in the non-Gaussian outcome, while normal random effects account for not only the correlation induced by repeated measurements from the same subject but also the association between the different outcomes. Using a case study in chronic heart failure, we show that model fit can be improved, even resulting in impact on significance tests, by switching to our extended framework. By first taking advantage of the ease of analytical integration over conjugate random effects, we easily estimate our framework, by maximum likelihood, in standard software. [ABSTRACT FROM AUTHOR]

Multivariate meta-analysis is becoming increasingly popular and official routines or self-programmed functions have been included in many statistical software. In this article, we review the statistical methods and the related software for multivariate meta-analysis. Emphasis is placed on Bayesian methods using Markov chain Monte Carlo, and codes in WinBUGS are provided. The various model-fitting options are illustrated in two examples and specific guidance is provided on how to run a multivariate meta-analysis using various software packages. [ABSTRACT FROM PUBLISHER]

Logistic regression is frequently used in many areas of applied statistics. The maximum likelihood estimates (MLE) of the logistic regression parameters are usually computed using the iterative Newton-Raphson method. It is well known that these estimates are biased. Several methods are proposed to correct the bias of these estimates. Among them Firth (1993) and Cordeiro and McCullagh (1991) proposed two promising methods. The conditional exact method (CMLE) is popular for small-sample estimates, and is available in many software packages. In this article we compare these methods in terms of their bias. In general, our extensive simulations show that the methods proposed by Cordeiro and McCullagh and by Firth work well, though Cordeiro and McCullagh is slightly better in our simulations. In case of separation, Firth or CMLE can be used; however, a judicious approach is required when there is a wide variation in results. Two real data analyses are given exhibiting these properties. The data analysis also includes bootstrap results. [ABSTRACT FROM AUTHOR]