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Finite mixture models have been used to model population heterogeneity and to relax distributional assumptions. These models are also convenient tools for clustering and classification of complex data such as, for example, repeated-measurements data. The performance of model-based clustering algorithms is sensitive to influential and outlying observations. Methods for identifying outliers in a finite mixture model have been described in the literature. Approaches to identify influential observations are less common. In this paper, we apply local-influence diagnostics to a finite mixture model with known number of components. The methodology is illustrated on real-life data. ; The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Financial support from the IAP research Network P7/06 of the Belgian government (Belgian Science Policy) is gratefully acknowledged.

Quantitative risk assessment involves the determination of a safe level of exposure. Recent techniques use the estimated dose‐response curve to estimate such a safe dose level. Although such methods have attractive features, a low‐dose extrapolation is highly dependent on the model choice. Fractional polynomials,(1) basically being a set of (generalized) linear models, are a nice extension of classical polynomials, providing the necessary flexibility to estimate the dose‐response curve. Typically, one selects the best‐fitting model in this set of polynomials and proceeds as if no model selection were carried out. We show that model averaging using a set of fractional polynomials reduces bias and has better precision in estimating a safe level of exposure (say, the benchmark dose), as compared to an estimator from the selected best model. To estimate a lower limit of this benchmark dose, an approximation of the variance of the model‐averaged estimator, as proposed by Burnham and Anderson,(2) can be used. However, this is a conservative method, often resulting in unrealistically low safe doses. Therefore, a bootstrap‐based method to more accurately estimate the variance of the model averaged parameter is proposed.

Although some major risk studies have been done for Campylobacter jejuni, its dose response is not well characterized. Only a single human study is available, providing dose‐response information for only a single isolate. As substantial heterogeneity in infectivity has been acknowledged for other pathogens, it remains unknown how well this single study represents the dose‐response relation for this pathogen. As future human challenge studies with Campylobacter are unlikely, we have to find other means of studying its infectivity. Several dose‐response studies have been done using chickens as host organisms. These studies may be used to obtain quantitative information on the variation in infectivity among different isolates of this pathogen. A hierarchical Bayesian model is well suited to describe heterogeneity, and we demonstrate how the beta‐Poisson model of microbial infection may be adapted to allow for within‐ and between‐isolate variation. Isolates tested in chickens can be categorized into two distinct groups: lab‐adapted and fresh isolates, and we show how the hierarchical dose‐response model can be used to quantitatively describe their differences. Fresh isolates show higher colonization potential and less within‐isolate variation than lab isolates. The results indicate that Campylobacter jejuni is highly infectious in chickens. Different isolates show great variation in infectivity, especially between lab and fresh isolates, indicating that human clinical (volunteer) studies on infectivity must be interpreted cautiously.

This work investigates how generalizability, an extension of reliability, can be defined and estimated based on longitudinal data sequences resulting from, for example, clinical studies. Useful and intuitive approximate expressions are derived based on generalized linear mixed models. Data from four double-blind, randomized clinical trials into schizophrenia motivate the research and are used to estimate generalizability for a binary response parameter. ; The authors are thankful to J&J PRD for their kind permission to use their data. Financial support from the IAP research network #P6/03 of the Belgian Government (Belgian Science Policy) is gratefully acknowledged.

This paper proposes a flexible modeling approach for so-called comet assay data regularly encountered in pre-clinical research. While such data consist of non-Gaussian outcomes in a multi-level hierarchical structure, traditional analyses typically completely or partly ignore this hierarchical nature by summarizing measurements within a cluster. Non-Gaussian outcomes are often modeled using exponential family models. This is true not only for binary and count data, but also for, e.g., time-to-event outcomes. Two important reasons for extending this family are: (1) the possible occurrence of overdispersion, meaning that the variability in the data may not be adequately described by the models which often exhibit a prescribed mean-variance link, and (2) the accommodation of a hierarchical structure in the data, owing to clustering in the data. The first issue is dealt with through so-called overdispersion models. Clustering is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. In the case of time-to-event data, one encounters, for example, the gamma frailty model (Duchateau and Janssen 2007). While both of these issues may occur simultaneously, models combining both are uncommon. Molenberghs et al (2010) proposed a broad class of generalized linear models accommodating overdispersion and clustering through two separate sets of random effects. Here, we use this method to model data from a comet assay with a three-level hierarchical structure. Whereas a conjugate gamma random effect is used for the overdispersion random effect, both gamma and Normal random effects are considered for the hierarchical random effect. Apart from model formulation, we place emphasis on Bayesian estimation. Our proposed method has upper hand over the traditional analysis in that it: (1) uses the appropriate distribution stipulated in the literature; (2) deals with the complete hierarchical nature; and (3) uses all information instead of summary measures. The fit of the model to the comet assay is compared against the background of more conventional model fits. Results indicate the toxicity of 1,2-Dimethylhydrazine dihydrochloride at different dose levels (low, medium, and high). ; IAP research network of the Belgian Government (Belgian Science Policy) (P6/03 ) - Fund for Scientific Research-Flanders (F.W.O.)

This work aims at investigating marginal correlation within and between longitudinal data sequences. Useful and intuitive approximate expressions are derived based on generalized linear mixed models. Data from four double-blind randomized clinical trials are used to estimate the intra-class coefficient of reliability for a binary response. Additionally, the correlation between such a binary response and a continuous response is derived to evaluate the criterion validity of the binary response variable and the established continuous response variable. ; Financial support from the IAP research network #P6/03 of the Belgian Government (Belgian Science Policy) is gratefully acknowledged.

In repeated dose-toxicity studies, many outcomes are repeatedly measured on the same animal to study the toxicity of a compound of interest. This is only one example in which one is confronted with the analysis of many outcomes, possibly of a different type. Probably the most common situation is that of an amalgamation of continuous and categorical outcomes. A possible approach towards the joint analysis of two longitudinal outcomes of a different nature is the use of random-effects models (Models for Discrete Longitudinal Data. Springer Series in Statistics. Springer: New York, 2005). Although a random-effects model can easily be extended to jointly model many outcomes of a different nature, computational problems arise as the number of outcomes increases. To avoid maximization of the full likelihood expression, Fieuws and Verbeke (Biometrics 2006; 62:424-431) proposed a pairwise modeling strategy in which all possible pairs are modeled separately, using a mixed model, yielding several different estimates for the same parameters. These latter estimates are then combined into a single set of estimates. Also inference, based on pseudo-likelihood principles, is indirectly derived from the separate analyses. In this paper, we extend the approach of Fieuws and Verbeke (Biometrics 2006; 62:424-431) in two ways: the method is applied to different types of outcomes and the full pseudo-likelihood expression is maximized at once, leading directly to unique estimates as well as direct application of pseudo-likelihood inference. This is very appealing when interested in hypothesis testing. The method is applied to data from a repeated dose-toxicity study designed for the evaluation of the neurofunctional effects of a psychotrophic drug. The relative merits of both methods are discussed. Copyright (c) 2008 John Wiley & Sons, Ltd. ; We gratefully acknowledge the support from the Institute for the Promotion of Innovation by Science andTechnology (IWT) in Flanders, Belgium, and from the IAP Research Network no. P5/24 of the Belgian Government (Belgian Science Policy).

Multivariate longitudinal or clustered data are commonly encountered in clinical trials and toxicological studies. Typically, there is no single standard endpoint to assess the toxicity or efficacy of the compound of interest, but co-primary endpoints are available to assess the toxic effects or the working of the compound. Modeling the responses jointly is thus appealing to draw overall inferences using all responses and to capture the association among the responses. Non-Gaussian outcomes are often modeled univariately using exponential family models. To accommodate both the overdispersion and hierarchical structure in the data, Molenberghs et al. A family of generalized linear models for repeated measures with normal and conjugate random effects. Statistical Science 2010; 25:325347 proposed using two separate sets of random effects. This papers considers a model for multivariate data with hierarchically clustered and overdispersed non-Gaussian data. Gamma random effect for the over-dispersion and normal random effects for the clustering in the data are being used. The two outcomes are jointly analyzed by assuming that the normal random effects for both endpoints are correlated. The association structure between the response is analytically derived. The fit of the joint model to data from a so-called comet assay are compared with the univariate analysis of the two outcomes. ; Financial support from the IAP research network #P6/03 of the Belgian Government (Belgian Science Policy) and the Research Foundation Flanders is gratefully acknowledged.

Neuron experiments produce high-dimensional data structures. Therefore, application of smoothing techniques in the analysis of neuronal data from electrophysiological experiments has received considerable attention of late. We investigate the use of penalized splines in the analysis of neuronal data. This is first illustrated when interested in the temporal trend of a single neuron. An approach to investigate the maximal firing rate, based on the penalizedspline model is proposed. Determination of the time of maximal firing rate is based on non-linear optimization of the objective function with the corresponding confidence intervals constructed based on the first-order derivative function. To distinguish between the curves from different experimental conditions in a moment-by-moment sense, bias adjusted simulation-based simultaneous confidence bands leading to global inference in the time domain are constructed. The bands are an extension of the approach proposed by Ruppert et al. (2003). These methods are in a second step extended towards the analysis of a population of neurons via a marginal or population-averaged model. ; The first four authors gratefully acknowledge the financial support from the IAP researchnetwork nr. P5/24 of the Belgian Government (Belgian Science Policy) and from the Institute for the Promotion ofInnovation by Science and Technology (IWT) in Flanders, Belgium.The research of Carlos Acun˜a was supported by the Ministerio de Educacion y Ciencia (MEC) grantBFU2006-06657. Work of Josee L. Pardo-Vaazquez and Vı´ctor Leboraan was supported by pre-doctoral MEC fellow-ships.The research of Christel Faes, Geert Molenberghs, and Carmen Cadarso-Suaarez was partially supported by theMinisterio de Educacion y Ciencia (MEC) grant MTM2005-00818.

The use of semi-parametric mixed models has proven useful in a wide variety of settings. Here. we focus on the application of the methodology ill file particular Case Of a cross-over design with relatively long. sequences of repeated measurements Within each treatment period and for each subject. Other than an overall measure of the difference between each One of file experimental groups and the control group. specific time point comparisons may also be of interest. TO that effect. We propose file use of flexible semi-parametric mixed models, enabling file construction of simulation-based simultaneous confidence bands. The bands take into account both between- and within-subject variabilities, while simultaneously correcting for Multiple time point comparisons. Owing to the relatively long sequences of Measurements per Subject, the presence of serially correlated errors is anticipated and investigated. WC illustrate how several formulations of semi-parametric mixed models call be fitted and the construction of simulation-based simultaneous confidence bands using SAS PROC MIXED. Copyright (C) 2008 John Wiley & Sons, Ltd. ; We gratefully acknowledge the financial support from the IAP research network no. P5/24 of the Belgian Government (Belgian Science Policy) and from th

AbstractEstimation of microorganism concentration in samples (bacterial cells or viral particles) has been a focal point in biomedical experiments for more than a century. Serial dilution of the samples is often used to estimate the target concentrations in immunology, virology, and pharmaceutical industry. A new methodology, called joint likelihood estimation (JLE), is proposed to estimate particles such as the number of microorganisms in a sample from counts obtained by serially diluting the sample. It models count data from the entire single dilution series rather than using only specific dilutions. The theoretical framework is based on the binomial and the Poisson distributions and is consistent with the actual experimental process. The estimator of the target concentration is obtained by MLE with derived joint likelihood functions of the observed counts including right‐censored values. Simulations demonstrated that the new JLE method significantly increases precision and accuracy of the estimate compared to the existing methods. It can be applied to a variety of studies with similar experimental designs, especially when the number of particles in the neat sample is very large.

The drug development process involves identifying a compound and assessing its merit through rigorous pre-clinical and clinical trials. The pre-clinical stage is designed to assess the chemical properties of the new drug, as well as to determine the steps for synthesis and purification. In this stage of drug development, circumstances might dictate the use of alternative endpoints than the originally anticipated clinically relevant endpoint. In this regard, identification and evaluation of surrogate endpoints is of paramount importance. The validation methods make it possible to quantify degrees of association between the clinically relevant endpoint, also termed the true endpoint, and the alternative, surrogate endpoint. In this paper, we adapt the surrogate marker evaluation methodology of Alonso et al. (2003); (2006), developed for the case of two longitudinal outcomes, to the situation where either a longitudinal surrogate and cross sectional true endpoint is recorded, or vice versa. The work is motivated by a preclinical experiment conducted to assess association between corticosterone (CORT), heart rate, and blood pressure in rats, the data from which are then subjected to analysis. It was found that there is a weak relationship between CORT and behavior, and between CORT on the one hand and heart rate and blood pressure on the other hand, but a reasonably high degree of association was registered between heart rate and behavior. ; Financial support from the IAP research network #P6/03 of the Belgian Government (Belgian Science Policy) is gratefully acknowledged.