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The main objective of this paper is to evaluate the influence of individual subjects exerted on a random-effects model for repeated measures, where the random effects follow a mixture distribution. The diagnostic tool is based on local influence with perturbation scheme that explicitly targets influences resulting from perturbing the mixture component probabilities. Bruckers, Molenberghs, Verbeke, and Geys (2016) considered a similar model, but focused on influences stemming from perturbing a subject's likelihood contributions as a whole. We also compare the two types of perturbation. Our results are illustrated using linear mixed models fitted to data from three studies. A simulation study is also conducted in order to strengthen the result from case studies., (© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

A key question in clinical practice is accurate prediction of patient prognosis. To this end, nowadays, physicians have at their disposal a variety of tests and biomarkers to aid them in optimizing medical care. These tests are often performed on a regular basis in order to closely follow the progression of the disease. In this setting, it is of interest to optimally utilize the recorded information and provide medically relevant summary measures, such as survival probabilities, which will aid in decision making. In this work, we present and compare two statistical techniques that provide dynamically updated estimates of survival probabilities, namely landmark analysis and joint models for longitudinal and time-to-event data. Special attention is given to the functional form linking the longitudinal and event time processes, and to measures of discrimination and calibration in the context of dynamic prediction., (© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

A fast way is proposed based on the multiple outputation idea (Hoffman et al., ; Follmann et al., ) to calculate the precision of parameter estimates for high-dimensional multivariate joint models using a pairwise approach (Fieuws and Verbeke, ; Fieuws et al., ). Simulation results as well as data analysis shows possibly more than 2500 times faster computations using the proposed method. In our real data illustration, the time gain is more than 330 times., (© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

In this paper, we propose a method to cluster multivariate functional data with missing observations. Analysis of functional data often encompasses dimension reduction techniques such as principal component analysis (PCA). These techniques require complete data matrices. In this paper, the data are completed by means of multiple imputation, and subsequently each imputed data set is submitted to a cluster procedure. The final partition of the data, summarizing the partitions obtained for the imputed data sets, is obtained by means of ensemble clustering. The uncertainty in cluster membership, due to missing data, is characterized by means of the agreement between the members of the ensemble and fuzziness of the consensus clustering. The potential of the method was brought out on the heart failure (HF) data. Daily measurement for four biomarkers (heart rate, diastolic, and systolic blood pressure, weight) were used to cluster the patients. To normalize the distributions of the longitudinal outcomes, the data were transformed with a natural logarithm function. A cubic spline base with 69 basis functions was employed to smooth the profiles. The proposed algorithm indicates the existence of a latent structure and divides the HF patients into two clusters, showing a different evolution in blood pressure values and weight. In general, cluster results are sensitive to choices made. Likewise for the proposed approach, alternative choices for the distance measure, procedure to optimize the objective function, choice of the scree-test threshold, or the number of principal components, to be used in the approximation of the surrogate density, could all influence the final partition. For the HF data set, the final partition depends on the number of principal components used in the procedure., (© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

We consider models for hierarchical count data, subject to overdispersion and/or excess zeros. Molenberghs et al. () and Molenberghs et al. () extend the Poisson-normal generalized linear-mixed model by including gamma random effects to accommodate overdispersion. Excess zeros are handled using either a zero-inflation or a hurdle component. These models were studied by Kassahun et al. (). While flexible, they are quite elaborate in parametric specification and therefore model assessment is imperative. We derive local influence measures to detect and examine influential subjects, that is subjects who have undue influence on either the fit of the model as a whole, or on specific important sub-vectors of the parameter vector. The latter include the fixed effects for the Poisson and for the excess-zeros components, the variance components for the normal random effects, and the parameters describing gamma random effects, included to accommodate overdispersion. Interpretable influence components are derived. The method is applied to data from a longitudinal clinical trial involving patients with epileptic seizures. Even though the data were extensively analyzed in earlier work, the insight gained from the proposed diagnostics, statistically and clinically, is considerable. Possibly, a small but important subgroup of patients has been identified., (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

The intraclass correlation is commonly used with clustered data. It is often estimated based on fitting a model to hierarchical data and it leads, in turn, to several concepts such as reliability, heritability, inter-rater agreement, etc. For data where linear models can be used, such measures can be defined as ratios of variance components. Matters are more difficult for non-Gaussian outcomes. The focus here is on count and time-to-event outcomes where so-called combined models are used, extending generalized linear mixed models, to describe the data. These models combine normal and gamma random effects to allow for both correlation due to data hierarchies as well as for overdispersion. Furthermore, because the models admit closed-form expressions for the means, variances, higher moments, and even the joint marginal distribution, it is demonstrated that closed forms of intraclass correlations exist. The proposed methodology is illustrated using data from agricultural and livestock studies., (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

A surrogate endpoint is intended to replace a clinical endpoint for the evaluation of new treatments when it can be measured more cheaply, more conveniently, more frequently, or earlier than that clinical endpoint. A surrogate endpoint is expected to predict clinical benefit, harm, or lack of these. Besides the biological plausibility of a surrogate, a quantitative assessment of the strength of evidence for surrogacy requires the demonstration of the prognostic value of the surrogate for the clinical outcome, and evidence that treatment effects on the surrogate reliably predict treatment effects on the clinical outcome. We focus on these two conditions, and outline the statistical approaches that have been proposed to assess the extent to which these conditions are fulfilled. When data are available from a single trial, one can assess the "individual level association" between the surrogate and the true endpoint. When data are available from several trials, one can additionally assess the "trial level association" between the treatment effect on the surrogate and the treatment effect on the true endpoint. In the latter case, the "surrogate threshold effect" can be estimated as the minimum effect on the surrogate endpoint that predicts a statistically significant effect on the clinical endpoint. All these concepts are discussed in the context of randomized clinical trials in oncology, and illustrated with two meta-analyses in gastric cancer., (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

The increasing cost of drug development has raised the demand for surrogate endpoints when evaluating new drugs in clinical trials. However, over the years, it has become clear that surrogate endpoints need to be statistically evaluated and deemed valid, before they can be used as substitutes of "true" endpoints in clinical studies. Nowadays, two paradigms, based on causal-inference and meta-analysis, dominate the scene. Nonetheless, although the literature emanating from these paradigms is wide, till now the relationship between them has largely been left unexplored. In the present work, we discuss the conceptual framework underlying both approaches and study the relationship between them using theoretical elements and the analysis of a real case study. Furthermore, we show that the meta-analytic approach can be embedded within a causal-inference framework on the one hand and that it can be heuristically justified why surrogate endpoints successfully evaluated using this approach will often be appealing from a causal-inference perspective as well, on the other. A newly developed and user friendly R package Surrogate is provided to carry out the evaluation exercise., (© 2014, The International Biometric Society.)

We consider a conceptual correspondence between the missing data setting, and joint modeling of longitudinal and time-to-event outcomes. Based on this, we formulate an extended shared random effects joint model. Based on this, we provide a characterization of missing at random, which is in line with that in the missing data setting. The ideas are illustrated using data from a study on liver cirrhosis, contrasting the new framework with conventional joint models., (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

In the analyses of incomplete longitudinal clinical trial data, there has been a shift, away from simple methods that are valid only if the data are missing completely at random, to more principled ignorable analyses, which are valid under the less restrictive missing at random assumption. The availability of the necessary standard statistical software nowadays allows for such analyses in practice. While the possibility of data missing not at random (MNAR) cannot be ruled out, it is argued that analyses valid under MNAR are not well suited for the primary analysis in clinical trials. Rather than either forgetting about or blindly shifting to an MNAR framework, the optimal place for MNAR analyses is within a sensitivity-analysis context. One such route for sensitivity analysis is to consider, next to selection models, pattern-mixture models or shared-parameter models. The latter can also be extended to a latent-class mixture model, the approach taken in this article. The performance of the so-obtained flexible model is assessed through simulations and the model is applied to data from a depression trial.

Generalized linear mixed models (GLMMs) have become a frequently used tool for the analysis of non-Gaussian longitudinal data. Estimation is based on maximum likelihood theory, which assumes that the underlying probability model is correctly specified. Recent research is showing that the results obtained from these models are not always robust against departures from the assumptions on which these models are based. In the present work we have used simulations with a logistic random-intercept model to study the impact of misspecifying the random-effects distribution on the type I and II errors of the tests for the mean structure in GLMMs. We found that the misspecification can either increase or decrease the power of the tests, depending on the shape of the underlying random-effects distribution, and it can considerably inflate the type I error rate. Additionally, we have found a theoretical result which states that whenever a subset of fixed-effects parameters, not included in the random-effects structure equals zero, the corresponding maximum likelihood estimator will consistently estimate zero. This implies that under certain conditions a significant effect could be considered as a reliable result, even if the random-effects distribution is misspecified.

It is shown how hierarchical biomedical data, such as coming from longitudinal clinical trials, meta-analyses, or a combination of both, can be used to provide evidence for quantitative strength of reliability, agreement, generalizability, and related measures that derive from association concepts. When responses are of a continuous, Gaussian type, the linear mixed model is shown to be a versatile framework. At the same time, the framework is embedded in the generalized linear mixed models, such that non-Gaussian, e.g., binary, outcomes can be studied as well. Similarities and, above all, important differences are studied. All developments are exemplified using clinical studies in schizophrenia, with focus on the endpoints Clinician's Global Impression (CGI) or Positive and Negative Syndrome Scale (PANSS).

The differential reinforcement of low-rate 72 seconds schedule (DRL-72) is a standard behavioral test procedure for screening potential antidepressant compounds. The protocol for the DRL-72 experiment, proposed by Evenden et al. (1993), consists of using a crossover design for the experiment and one-way ANOVA for the statistical analysis. In this paper we discuss the choice of several crossover designs for the DRL-72 experiment and propose to estimate the treatment effects using either generalized linear mixed models (GLMM) or generalized estimating equation (GEE) models for clustered binary data.

Recent scientific evolutions force us to rethink our profession's position on the scientific map, in relation to our neighboring professions, the ones with which we traditionally have strong collaborative links as well as the newly emerging fields, but also within our own, diverse professional group. We will show that great inspiration can be drawn from our own history, in fact from the early days of the Society. A recent inspiring example has been set by the late Rob Kempton, who died suddenly just months before he was to become President of the International Biometric Society.

We put a perspective on the strengths and limitations of statistical methods for the evaluation of surrogate endpoints. Whereas using several trials overcomes some of the limitations of a single-trial framework (Prentice, 1989, Statistics in Medicine 8, 431-440), arguably the evaluation of surrogate endpoints can never be done using only statistical evidence but such evidence should be seen as but one component in a decision-making process that involves, among others, a number of clinical and biological considerations. We briefly present a hierarchical framework that incorporates ideas from Prentice's work and is uniformly applicable to different types of surrogate and true clinical outcomes.

This article describes three multivariate projection methods and compares them for their ability to identify clusters of biological samples and genes using real-life data on gene expression levels of leukemia patients. It is shown that principal component analysis (PCA) has the disadvantage that the resulting principal factors are not very informative, while correspondence factor analysis (CFA) has difficulties interpreting distances between objects. Spectral map analysis (SMA) is introduced as an alternative approach to the analysis of microarray data. Weighted SMA outperforms PCA, and is at least as powerful as CFA, in finding clusters in the samples, as well as identifying genes related to these clusters. SMA addresses the problem of data analysis in microarray experiments in a more appropriate manner than CFA, and allows more flexible weighting to the genes and samples. Proper weighting is important, since it enables less reliable data to be down-weighted and more reliable information to be emphasized.

The problem of testing a dose-response relationship in the presence of exchangeably correlated binary data has been addressed using a variety of models. Most commonly used approaches are derived from likelihood or generalized estimating equations and rely on large-sample theory to justify their inferences. However, while earlier work has determined that these methods may perform poorly for small or sparse samples, there are few alternatives available to those faced with such data. We propose an exact trend test for exchangeably correlated binary data when groups of correlated observations are ordered. This exact approach is based on an exponential model derived by Molenberghs and Ryan (1999) and Ryan and Molenberghs (1999) and provides natural analogues to Fisher's exact test and the binomial trend test when the data are correlated. We use a graphical method with which one can efficiently compute the exact tail distribution and apply the test to two examples.

Diggle and Kenward (1994, Applied Statistics 43, 49-93) proposed a selection model for continuous longitudinal data subject to nonrandom dropout. It has provoked a large debate about the role for such models. The original enthusiasm was followed by skepticism about the strong but untestable assumptions on which this type of model invariably rests. Since then, the view has emerged that these models should ideally be made part of a sensitivity analysis. This paper presents a formal and flexible approach to such a sensitivity assessment based on local influence (Cook, 1986, Journal of the Royal Statistical Society, Series B 48, 133-169). The influence of perturbing a missing-at-random dropout model in the direction of nonrandom dropout is explored. The method is applied to data from a randomized experiment on the inhibition of testosterone production in rats.

Most models for incomplete data are formulated within the selection model framework. This paper studies similarities and differences of modeling incomplete data within both selection and pattern-mixture settings. The focus is on missing at random mechanisms and on categorical data. Point and interval estimation is discussed. A comparison of both approaches is done on side effects in a psychiatric study.

The validation of surrogate endpoints has been studied by Prentice (1989, Statistics in Medicine 8, 431-440) and Freedman, Graubard, and Schatzkin (1992, Statistics in Medicine 11, 167-178). We extended their proposals in the cases where the surrogate and the final endpoints are both binary or normally distributed. Letting T and S be random variables that denote the true and surrogate endpoint, respectively, and Z be an indicator variable for treatment, Prentice's criteria are fulfilled if Z has a significant effect on T and on S, if S has a significant effect on T, and if Z has no effect on T given S. Freedman relaxed the latter criterion by estimating PE, the proportion of the effect of Z on T that is explained by S, and by requiring that the lower confidence limit of PE be larger than some proportion, say 0.5 or 0.75. This condition can only be verified if the treatment has a massively significant effect on the true endpoint, a rare situation. We argue that two other quantities must be considered in the validation of a surrogate endpoint: RE, the effect of Z on T relative to that of Z on S, and gamma Z, the association between S and T after adjustment for Z. A surrogate is said to be perfect at the individual level when there is a perfect association between the surrogate and the final endpoint after adjustment for treatment. A surrogate is said to be perfect at the population level if RE is 1. A perfect surrogate fulfills both conditions, in which case S and T are identical up to a deterministic transformation. Fieller's theorem is used for the estimation of PE, RE, and their respective confidence intervals. Logistic regression models and the global odds ratio model studied by Dale (1986, Biometrics, 42, 909-917) are used for binary endpoints. Linear models are employed for continuous endpoints. In order to be of practical value, the validation of surrogate endpoints is shown to require large numbers of observations.

Test statistics for the homogeneity of the risk difference for a series of 2 x 2 tables when the data are sparse is proposed. A weighted least squares statistic is commonly used to test for equality of the risk difference over the tables; however, when the data are sparse, this statistic can have anticonservative Type I error rates. Simulation is used to compare the proposed test statistics to the weighted least squares statistic. The weighted least squares statistic has the most anticonservative Type I error rates of all the statistics compared. We suggest the use of one of our proposed test statistics instead of the weighted least squares statistic.

Data are analysed from a longitudinal psychiatric study in which there are no dropouts that do not occur completely at random. A marginal proportional odds model is fitted that relates the response (severity of side effects) to various covariates. Two methods of estimation are used: generalized estimating equations (GEE) and maximum likelihood (ML). Both the complete set of data and the data from only those subjects completing the study are analysed. For the completers-only data, the GEE and ML analyses produce very similar results. These results differ considerably from those obtained from the analyses of the full data set. There are also marked differences between the results obtained from the GEE and ML analysis of the full data set. The occurrence of such differences is consistent with the presence of a non-completely-random dropout process and it can be concluded in this example that both the analyses of the completers only and the GEE analysis of the full data set produce misleading conclusions about the relationships between the response and covariates.