Dirichlet negative multinomial regression for overdispersed correlated count data.

A generic random effects formulation for the Dirichlet negative multinomial distribution is developed together with a convenient regression parameterization. A simulation study indicates that, even when somewhat misspecified, regression models based on the Dirichlet negative multinomial distribution have smaller median absolute error than generalized estimating equations, with a particularly pronounced improvement when correlation between observations in a cluster is high. Estimation of explanatory variable effects and sources of variation is illustrated for a study of clinical trial recruitment.

Understanding between-cluster variation in prevalence and limits for how much variation is plausible.

In clinical trials and observational studies of clustered binary data, understanding between-cluster variation is essential: in sample size and power calculations of cluster randomised trials, for example, the intra-cluster correlation coefficient is often specified. However, quantifications of between-cluster variation can be unintuitive, and an intra-cluster correlation coefficient as low as 0.04 may correspond to surprisingly large between-cluster differences. We suggest that understanding is improved through visualising the implied distribution of true cluster prevalences - possibly by assuming they follow a beta distribution - or by calculating their standard deviation, which is more readily interpretable than the intra-cluster correlation coefficient. Even so, the bounded nature of binary data complicates the interpretation of variances as primary measures of uncertainty, and entropy offers an attractive alternative. Appealing to maximum entropy theory, we propose the following rule of thumb: that plausible intra-cluster correlation coefficients and standard deviations of true cluster prevalences are both bounded above by the overall prevalence, its complement, and one third. We also provide corresponding bounds for the coefficient of variation, and for a different standard deviation and intra-cluster correlation defined on the log odds scale. Using previously published data, we observe the quantities defined on the log odds scale to be more transportable between studies with different outcomes with different prevalences than the intra-cluster correlation and coefficient of variation. The latter increase and decrease, respectively, as prevalence increases from 0% to 50%, and the same is true for our bounds. Our work will help clinical trialists better understand between-cluster variation and avoid specifying implausibly high values for the intra-cluster correlation in sample size and power calculations.

Methodological standards for the development and evaluation of clinical prediction rules: a review of the literature.

Clinical prediction rules (CPRs) that predict the absolute risk of a clinical condition or future outcome for individual patients are abundant in the medical literature; however, systematic reviews have demonstrated shortcomings in the methodological quality and reporting of prediction studies. To maximise the potential and clinical usefulness of CPRs, they must be rigorously developed and validated, and their impact on clinical practice and patient outcomes must be evaluated. This review aims to present a comprehensive overview of the stages involved in the development, validation and evaluation of CPRs, and to describe in detail the methodological standards required at each stage, illustrated with examples where appropriate. Important features of the study design, statistical analysis, modelling strategy, data collection, performance assessment, CPR presentation and reporting are discussed, in addition to other, often overlooked aspects such as the acceptability, cost-effectiveness and longer-term implementation of CPRs, and their comparison with clinical judgement. Although the development and evaluation of a robust, clinically useful CPR is anything but straightforward, adherence to the plethora of methodological standards, recommendations and frameworks at each stage will assist in the development of a rigorous CPR that has the potential to contribute usefully to clinical practice and decision-making and have a positive impact on patient care.

Potential impact of the validated Predicting Abusive Head Trauma (PredAHT) clinical prediction tool: A clinical vignette study.

BACKGROUND: The validated Predicting Abusive Head Trauma (PredAHT) tool estimates the probability of abusive head trauma (AHT) in children <3 years old with intracranial injury. OBJECTIVE: To explore the impact of PredAHT on clinicians' AHT probability estimates and child protection (CP) actions, and assess inter-rater agreement between their estimates and between their CP actions, before and after PredAHT. PARTICIPANTS AND SETTING: Twenty-nine clinicians from different specialties, at teaching and community hospitals. METHODS: Clinicians estimated the probability of AHT and indicated their CP actions in six clinical vignettes. One vignette described a child with AHT, another described a child with non-AHT, and four represented "gray" cases, where the diagnosis was uncertain. Clinicians calculated the PredAHT score, and reported whether this altered their estimate/actions. The 'think-aloud' method was used to capture the reasoning behind their responses. Analysis included linear modelling, linear mixed-effects modelling, chi-square tests, Fisher's exact tests, intraclass correlation, Gwet's AC1 coefficient and thematic analysis. RESULTS: Overall, PredAHT significantly influenced clinicians' probability estimates in all vignettes (p < 0.001), although the impact on individual clinicians varied. However, the influence of PredAHT on clinicians' CP actions was limited; after using PredAHT, 9/29 clinicians changed their CP actions in only 11/174 instances. Clinicians' AHT probability estimates and CP actions varied somewhat both before and after PredAHT. Qualitative data suggested that PredAHT may increase clinicians' confidence in their decisions when considered alongside other associated clinical, historical and social factors. CONCLUSIONS: PredAHT significantly influenced clinicians' AHT probability estimates, but had minimal impact on their CP actions.

Factors influencing child protection professionals' decision-making and multidisciplinary collaboration in suspected abusive head trauma cases: A qualitative study.

Clinicians face unique challenges when assessing suspected child abuse cases. The majority of the literature exploring diagnostic decision-making in this field is anecdotal or survey-based and there is a lack of studies exploring decision-making around suspected abusive head trauma (AHT). We aimed to determine factors influencing decision-making and multidisciplinary collaboration in suspected AHT cases, amongst 56 child protection professionals. Semi-structured interviews were conducted with clinicians (25), child protection social workers (10), legal practitioners (9, including 4 judges), police officers (8), and pathologists (4), purposively sampled across southwest United Kingdom. Interviews were recorded, transcribed and imported into NVivo for thematic analysis (38% double-coded). We identified six themes influencing decision-making: 'professional', 'medical', 'circumstantial', 'family', 'psychological' and 'legal' factors. Participants diagnose AHT based on clinical features, the history, and the social history, after excluding potential differential diagnoses. Participants find these cases emotionally challenging but are aware of potential biases in their evaluations and strive to overcome these. Barriers to decision-making include lack of experience, uncertainty, the impact on the family, the pressure of making the correct diagnosis, and disagreements between professionals. Legal barriers include alternative theories of causation proposed in court. Facilitators include support from colleagues and knowledge of the evidence-base. Participants' experiences with multidisciplinary collaboration are generally positive, however child protection social workers and police officers are heavily reliant on clinicians to guide their decision-making, suggesting the need for training on the medical aspects of physical abuse for these professionals and multidisciplinary training that provides knowledge about the roles of each agency.

Acceptability of the Predicting Abusive Head Trauma (PredAHT) clinical prediction tool: A qualitative study with child protection professionals.

The validated Predicting Abusive Head Trauma (PredAHT) tool estimates the probability of abusive head trauma (AHT) based on combinations of six clinical features: head/neck bruising; apnea; seizures; rib/long-bone fractures; retinal hemorrhages. We aimed to determine the acceptability of PredAHT to child protection professionals. We conducted qualitative semi-structured interviews with 56 participants: clinicians (25), child protection social workers (10), legal practitioners (9, including 4 judges), police officers (8), and pathologists (4), purposively sampled across southwest United Kingdom. Interviews were recorded, transcribed and imported into NVivo for thematic analysis (38% double-coded). We explored participants' evaluations of PredAHT, their opinions about the optimal way to present the calculated probabilities, and their interpretation of probabilities in the context of suspected AHT. Clinicians, child protection social workers and police thought PredAHT would be beneficial as an objective adjunct to their professional judgment, to give them greater confidence in their decisions. Lawyers and pathologists appreciated its value for prompting multidisciplinary investigations, but were uncertain of its usefulness in court. Perceived disadvantages included: possible over-reliance and false reassurance from a low score. Interpretations regarding which percentages equate to 'low', 'medium' or 'high' likelihood of AHT varied; participants preferred a precise % probability over these general terms. Participants would use PredAHT with provisos: if they received multi-agency training to define accepted risk thresholds for consistent interpretation; with knowledge of its development; if it was accepted by colleagues. PredAHT may therefore increase professionals' confidence in their decision-making when investigating suspected AHT, but may be of less value in court.

An ecometric analysis of neighbourhood cohesion.

BACKGROUND: It is widely believed that the social environment has an important influence on health, but there is less certainty about how to measure specific factors within the social environment that could link the neighbourhood of residence to a health outcome. The objectives of the study were to examine the underlying constructs captured by an adapted version of Buckner's neighbourhood cohesion scale, and to assess the reliability of the scale at the small-area-level by combining ecometric methodology with ordinal modelling of a five-point scale. METHODS: Data were analysed from 11,078 participants in the Caerphilly Health and Social Needs Study, who were sampled from within 325 UK census enumeration districts in Caerphilly county borough, Wales, UK. The responses of interest came from 15 question items designed to capture different facets of neighbourhood cohesion. Factor analysis was used to identify constructs underlying the neighbourhood cohesion item responses. Using a multilevel ecometric model, the variability present in these ordinal responses was decomposed into contextual, compositional, item-level and residual components. RESULTS: Two constructs labelled neighbourhood belonging and social cohesion were identified, and variability in both constructs was modelled at each level of the multilevel structure. The intra-neighbourhood correlations were 6.4% and 1.0% for the neighbourhood belonging and social cohesion subscales, respectively. Given the large sample size, contextual neighbourhood cohesion scores can be estimated reliably. The wide variation in the observed frequency of occurence of the scale item activities suggests that the two subscales have desirable ecometric properties. Further, the majority of between-neighbourhood variation is not explained by the socio-demographic characteristics of the individual respondents. CONCLUSION: Assessment of the properties of the adapted neighbourhood cohesion scale using factor analysis and ecometric analysis extended to an ordinal scale has shown that the items allow fine discrimination between individuals. However, large sample sizes are needed in order to accurately estimate contextual neighbourhood cohesion. The scale is therefore appropriate for use in the measurement of neighbourhood cohesion at small-area-level in future studies of neighbourhoods and health.

Study design.

A brief survey is provided of common designs for medical studies and important issues in their implementation. The designs discussed include those for laboratory studies, clinical trials, cohort studies, case-control and related studies, and diagnostic studies.

Multiple Imputation of Missing Composite Outcomes in Longitudinal Data.

In longitudinal randomised trials and observational studies within a medical context, a composite outcome-which is a function of several individual patient-specific outcomes-may be felt to best represent the outcome of interest. As in other contexts, missing data on patient outcome, due to patient drop-out or for other reasons, may pose a problem. Multiple imputation is a widely used method for handling missing data, but its use for composite outcomes has been seldom discussed. Whilst standard multiple imputation methodology can be used directly for the composite outcome, the distribution of a composite outcome may be of a complicated form and perhaps not amenable to statistical modelling. We compare direct multiple imputation of a composite outcome with separate imputation of the components of a composite outcome. We consider two imputation approaches. One approach involves modelling each component of a composite outcome using standard likelihood-based models. The other approach is to use linear increments methods. A linear increments approach can provide an appealing alternative as assumptions concerning both the missingness structure within the data and the imputation models are different from the standard likelihood-based approach. We compare both approaches using simulation studies and data from a randomised trial on early rheumatoid arthritis patients. Results suggest that both approaches are comparable and that for each, separate imputation offers some improvement on the direct imputation of a composite outcome.

Dropout in crossover and longitudinal studies: is complete case so bad?

We discuss inference for longitudinal clinical trials subject to possibly informative dropout. A selection of available methods is reviewed for the simple case of trials with two timepoints. Using data from two such clinical trials, each with two treatments, we demonstrate that different analysis methods can at times lead to quite different conclusions from the same data. We investigate properties of complete-case estimators for the type of trials considered, with emphasis on interpretation and meaning of parameters. We contrast longitudinal and crossover designs and argue that for crossover studies there are often good reasons to prefer a complete case analysis. More generally, we suggest that there is merit in an approach in which no untestable assumptions are made. Such an approach would combine a dropout analysis, an analysis of complete-case data only, and a careful statement of justified conclusions.

Socioeconomic patterning of excess alcohol consumption and binge drinking: a cross-sectional study of multilevel associations with neighbourhood deprivation.

OBJECTIVES: The influence of neighbourhood deprivation on the risk of harmful alcohol consumption, measured by the separate categories of excess consumption and binge drinking, has not been studied. The study objective was to investigate the effect of neighbourhood deprivation with age, gender and socioeconomic status (SES) on (1) excess alcohol consumption and (2) binge drinking, in a representative population survey. DESIGN: Cross-sectional study: multilevel analysis. SETTING: Wales, UK, adult population ∼2.2 million. PARTICIPANTS: 58 282 respondents aged 18 years and over to four successive annual Welsh Health Surveys (2003/2004-2007), nested within 32 692 households, 1839 census lower super output areas and the 22 unitary authority areas in Wales. PRIMARY OUTCOME MEASURE: Maximal daily alcohol consumption during the past week was categorised using the UK Department of Health definition of 'none/never drinks', 'within guidelines', 'excess consumption but less than binge' and 'binge'. The data were analysed using continuation ratio ordinal multilevel models with multiple imputation for missing covariates. RESULTS: Respondents in the most deprived neighbourhoods were more likely to binge drink than in the least deprived (adjusted estimates: 17.5% vs 10.6%; difference=6.9%, 95% CI 6.0 to 7.8), but were less likely to report excess consumption (17.6% vs 21.3%; difference=3.7%, 95% CI 2.6 to 4.8). The effect of deprivation varied significantly with age and gender, but not with SES. Younger men in deprived neighbourhoods were most likely to binge drink. Men aged 35-64 showed the steepest increase in binge drinking in deprived neighbourhoods, but men aged 18-24 showed a smaller increase with deprivation. CONCLUSIONS: This large-scale population study is the first to show that neighbourhood deprivation acts differentially on the risk of binge drinking between men and women at different age groups. Understanding the socioeconomic patterns of harmful alcohol consumption is important for public health policy development.

Analysis of censored discrete longitudinal data: estimation of mean response.

The study of longitudinal data is usually concerned with one or several response variables measured, possibly along with some covariates, at different points in time. In real-life situations this is often complicated by missing observations due to what we usually refer to as 'censoring'. In this paper we consider missingness of a monotone kind; subjects that dropout, i.e. are censored, fail to participate in the study at any of the subsequent observation times. Our scientific objective is to make inference about the mean response in a hypothetical population without any dropouts. There are several methods and approaches that address this problem, and we will present two existing methods (the linear-increments method and the inverse-probability-weighting method), as well as propose a new method, based on a discrete Markov process. We examine the performance of the corresponding estimators and compare these with respect to bias and variability. To demonstrate the effectiveness of the approaches in estimating the mean of a response variable, we analyse simulated data of different multistate models with a Markovian structure. Analyses of substantive data from (1) a study of symptoms experienced after a traumatic brain injury, and (2) a study of cognitive function among the elderly, are used as illustrations of the methods presented.

Rugby (the religion of Wales) and its influence on the Catholic church: should Pope Benedict XVI be worried?

OBJECTIVE: To explore the perceived wisdom that papal mortality is related to the success of the Welsh rugby union team. DESIGN: Retrospective observational study of historical Vatican and sporting data. MAIN OUTCOME MEASURE: Papal deaths between 1883 and the present day. RESULTS: There is no evidence of a link between papal deaths and any home nation grand slams (when one nation succeeds in beating all other competing teams in every match). There was, however, weak statistical evidence to support an association between Welsh performance and the number of papal deaths. CONCLUSION: Given the dominant Welsh performances of 2008, the Vatican medical team should take special care of the pontiff this Christmas.