Performance of several types of beta-binomial models in comparison to standard approaches for meta-analyses with very few studies.

BACKGROUND: Meta-analyses are used to summarise the results of several studies on a specific research question. Standard methods for meta-analyses, namely inverse variance random effects models, have unfavourable properties if only very few (2 - 4) studies are available. Therefore, alternative meta-analytic methods are needed. In the case of binary data, the "common-rho" beta-binomial model has shown good results in situations with sparse data or few studies. The major concern of this model is that it ignores the fact that each treatment arm is paired with a respective control arm from the same study. Thus, the randomisation to a study arm of a specific study is disrespected, which may lead to compromised estimates of the treatment effect. Therefore, we extended this model to a version that respects randomisation. The aim of this simulation study was to compare the "common-rho" beta-binomial model and several other beta-binomial models with standard meta-analyses models, including generalised linear mixed models and several inverse variance random effects models. METHODS: We conducted a simulation study comparing beta-binomial models and various standard meta-analysis methods. The design of the simulation aimed to consider meta-analytic situations occurring in practice. RESULTS: No method performed well in scenarios with only 2 studies in the random effects scenario. In this situation, a fixed effect model or a qualitative summary of the study results may be preferable. In scenarios with 3 or 4 studies, most methods satisfied the nominal coverage probability. The "common-rho" beta-binomial model showed the highest power under the alternative hypothesis. The beta-binomial model respecting randomisation did not improve performance. CONCLUSION: The "common-rho" beta-binomial appears to be a good option for meta-analyses of very few studies. As residual concerns about the consequences of disrespecting randomisation may still exist, we recommend a sensitivity analysis with a standard meta-analysis method that respects randomisation.

Bayesian joint modelling of benefit and risk in drug development.

To gain regulatory approval, a new medicine must demonstrate that its benefits outweigh any potential risks, ie, that the benefit-risk balance is favourable towards the new medicine. For transparency and clarity of the decision, a structured and consistent approach to benefit-risk assessment that quantifies uncertainties and accounts for underlying dependencies is desirable. This paper proposes two approaches to benefit-risk evaluation, both based on the idea of joint modelling of mixed outcomes that are potentially dependent at the subject level. Using Bayesian inference, the two approaches offer interpretability and efficiency to enhance qualitative frameworks. Simulation studies show that accounting for correlation leads to a more accurate assessment of the strength of evidence to support benefit-risk profiles of interest. Several graphical approaches are proposed that can be used to communicate the benefit-risk balance to project teams. Finally, the two approaches are illustrated in a case study using real clinical trial data.

Deletion diagnostics for the generalised linear mixed model with independent random effects.

The Generalised linear mixed model (GLMM) is widely used for modelling environmental data. However, such data are prone to influential observations, which can distort the estimated exposure-response curve particularly in regions of high exposure. Deletion diagnostics for iterative estimation schemes commonly derive the deleted estimates based on a single iteration of the full system holding certain pivotal quantities such as the information matrix to be constant. In this paper, we present an approximate formula for the deleted estimates and Cook's distance for the GLMM, which does not assume that the estimates of variance parameters are unaffected by deletion. The procedure allows the user to calculate standardised DFBETAs for mean as well as variance parameters. In certain cases such as when using the GLMM as a device for smoothing, such residuals for the variance parameters are interesting in their own right. In general, the procedure leads to deleted estimates of mean parameters, which are corrected for the effect of deletion on variance components as estimation of the two sets of parameters is interdependent. The probabilistic behaviour of these residuals is investigated and a simulation based procedure suggested for their standardisation. The method is used to identify influential individuals in an occupational cohort exposed to silica. The results show that failure to conduct post model fitting diagnostics for variance components can lead to erroneous conclusions about the fitted curve and unstable confidence intervals.

Estimation of Effect Heterogeneity in Rare Events Meta-Analysis.

The paper outlines several approaches for dealing with meta-analyses of count outcome data. These counts are the accumulation of occurred events, and these events might be rare, so a special feature of the meta-analysis is dealing with low counts including zero-count studies. Emphasis is put on approaches which are state of the art for count data modelling including mixed log-linear (Poisson) and mixed logistic (binomial) regression as well as nonparametric mixture models for count data of Poisson and binomial type. A simulation study investigates the performance and capability of discrete mixture models in estimating effect heterogeneity. The approaches are exemplified on a meta-analytic case study investigating the acceptance of bibliotherapy.

The effect of random-effects misspecification on classification accuracy.

Mixed models are a useful way of analysing longitudinal data. Random effects terms allow modelling of patient specific deviations from the overall trend over time. Correlation between repeated measurements are captured by specifying a joint distribution for all random effects in a model. Typically, this joint distribution is assumed to be a multivariate normal distribution. For Gaussian outcomes misspecification of the random effects distribution usually has little impact. However, when the outcome is discrete (e.g. counts or binary outcomes) generalised linear mixed models (GLMMs) are used to analyse longitudinal trends. Opinion is divided about how robust GLMMs are to misspecification of the random effects. Previous work explored the impact of random effects misspecification on the bias of model parameters in single outcome GLMMs. Accepting that these model parameters may be biased, we investigate whether this affects our ability to classify patients into clinical groups using a longitudinal discriminant analysis. We also consider multiple outcomes, which can significantly increase the dimensions of the random effects distribution when modelled simultaneously. We show that when there is severe departure from normality, more flexible mixture distributions can give better classification accuracy. However, in many cases, wrongly assuming a single multivariate normal distribution has little impact on classification accuracy.

Spatial generalised linear mixed models based on distances.

Risk models derived from environmental data have been widely shown to be effective in delineating geographical areas of risk because they are intuitively easy to understand. We present a new method based on distances, which allows the modelling of continuous and non-continuous random variables through distance-based spatial generalised linear mixed models. The parameters are estimated using Markov chain Monte Carlo maximum likelihood, which is a feasible and a useful technique. The proposed method depends on a detrending step built from continuous or categorical explanatory variables, or a mixture among them, by using an appropriate Euclidean distance. The method is illustrated through the analysis of the variation in the prevalence of Loa loa among a sample of village residents in Cameroon, where the explanatory variables included elevation, together with maximum normalised-difference vegetation index and the standard deviation of normalised-difference vegetation index calculated from repeated satellite scans over time.

Occupancy dynamics of South American sea-lions in Brazilian haul-outs / Dinâmica de ocupação do leão-marinho-do-sul no Brasil

Along the Brazilian coast only two haul-outs of South American sea lions (Otaria flavescens) are known: Ilha dos Lobos and Molhe Leste, both located in the southernmost state of Brazil, Rio Grande do Sul. Most sea lions observed in these haul-outs are adult and sub-adult males. It is supposed that the species' presence in these areas is due to food supply and absence of parental assistance by males. This study analysed the use of these haul-outs by O. flavescens between 1993 and 2002 based on counting data of observed individuals. Bayesian generalised linear mixed models were used to evaluate differences in abundance between areas, long term trends and seasonal patterns. Results showed that for O. flavescens abundance had a long term trend of increased average occupancy over the study period, with seasonal variation reaching the highest within-year value in August (Ilha dos Lobos) and October (Molhe Leste). The novel application of this powerful statistical modelling approach resulted in a useful tool to quantify occupancy dynamic.

Ao longo da costa do Brasil apenas duas colônias não-reprodutivas de leões-marinhos-do-sul (Otaria flavescens) são conhecidas: Ilha dos Lobos e Molhe Leste, ambas localizadas no estado do Rio Grande do Sul. A maioria dos leões-marinhos observados nestas colônias são machos adultos e sub-adultos. Supõe-se que a presença da espécie nestas áreas está relacionada ao forrageamento e a ausência de cuidado parental pelos machos. Este estudo analisou a dinâmica de ocupação e abundância de O. flavescens nas colônias não-reprodutivas entre 1993 e 2002, baseado em uma série temporal de dados de contagens de indivíduos. Modelos lineares generalizados mistos Bayesianos foram usados para avaliar diferença na abundância entre áreas, tendência de uso em longo prazo e padrões sazonais. Os resultados mostram que a abundância de O. flavescens variou sazonalmente, atingindo pico intra-anual em agosto (Ilha dos Lobos) e outubro (Molhe Leste), acompanhado de um aumento da ocupação média dos refúgios ao longo do período de estudo. A nova aplicação desta poderosa forma de modelagem estatística mostrou-se útil para quantificar a dinâmica de ocupação.