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Editor’s Choice : Bayesian Analysis of Transition Model for Longitudinal Ordinal Response Data: Application to Insomnia Data
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Abstract: In this paper, we present a Bayesian framework for analyzing longitudinal ordinal response data. In analyzing longitudinal data, the possibility of correlations between responses given by the same individual needs to be taken into account. Various models can be used to handle such correlations such as marginal modeling, random effect modeling and transition (Markov) modeling. Here a transition modeling is used and a Bayesian approach is presented for analyzing longitudinal data. A cumulative logistic regression model and the Bayesian method, using MCMC, are implemented for obtaining the parameters estimates. Our approach is applied on a two-period longitudinal Insomnia data where the Bayesian estimate for measure of association, , between the initial and follow-up ordinal responses is obtained in each level of a treatment variable. Then, the sensitivity of posterior summaries to changes of prior hyperparameters is investigated. We also use Bayes factor criterion for testing some important hypotheses. Keywords: Bayesian Analysis, Bayes Factor, Conditional Predictive Ordinate, Logistic Regression, Markov Model.Download Full Article |
Editor’s Choice : Comparison of Post Hoc Multiple Pairwise Testing Procedures as Applied to Small k-Group Logrank Tests
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Abstract: The logrank test is widely used to compare groups on distribution of survival time in the presence of censoring. There is no convention for post hoc pairwise comparisons after a significant omnibus k-group logrank test. This simulation study compares four post hoc pairwise testing procedures: Bonferroni, Dunn-Šidák,Hochberg, and unadjusted post hoc logrank test procedure. Evaluation criteria include, familywise type I error rate, correct decision rate, number of correctly rejected pairs, and false discovery rate. We demonstrated that when conditioned upon rejection of the omnibus test, multiplicity adjustments may be unnecessary and can be overly conservative when k is at most 4, or number of comparisons is no greater than 6. This is supported by the results that the performance of the unadjusted post hoclogrank test procedure is preferred over the others on all criteria except for the false discovery rate. The Hochberg procedure appears to be superior among the adjustments examined. Data from a clinical trial for suicide prevention illustrate these approaches where number of comparison groups is often limited. Keywords: Logrank test, multiplicity adjustment, post hoc tests, survival analysis.Download Full Article |
Editor’s Choice : Development and Validation of Models to Predict Hospital Admission for Emergency Department Patients
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Abstract: Background: Boarding, or patients waiting to be admitted to hospital, has been shown as a significant contributing factor at overcrowding in emergency departments (ED). Predicting hospital admission at triage has been proposed as having the potential to help alleviate ED overcrowding. The objective of this paper is to develop and validate a model to predict hospital admission at triage to help alleviate ED overcrowding. Methods: Administrative records between April 1, 2010 and November 31, 2010 in an adult ED were used to derive and validate two prediction models, one based on Coxian phase type distribution (the PH model), the other based on logistic regression. Separate data sets were used for model development (data between April 1, 2010 and July 31, 2010) and validation (data between August 1, 2010 and November 31, 2010). Results: There were a total of 14,542 ED visits and 2,602 (17.89%) hospital admissions in the derivation cohort. In both models, acuity levels, model of arrival, and main reason of the visit are strong predictors of hospital admission; number of patients at the ED, as well as gender, are also predictors, albeit with ORs closer to 1. Patient age and timing of visits are not strong predictors. The PH model has an AUC of 0.89 compared with AUC of 0.83 for logistic regression model; with a cut- off value of 0.50, the PH model correctly predicted 86.3% of visits, compared to 84.4% for the logistic regression model. Results of the validation cohort were similar: the PH model has an AUC of 0.88, compared to AUC of 0.83 for the logistic model. Conclusions: PH and logistic models can be used to provide reasonably accurate prediction of hospital admission for ED patients, with the PH model offering more accurate predictions. Keywords: Hospital admission, Emergency department, Wait times, Overcrowding, Coxian phase type distribution.Download Full Article |
Editor’s Choice : Conditional Two Level Mixture with Known Mixing Proportions: Applications to School and Student Level Overweight and Obesity Data from Birmingham, England
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Abstract: Two Level (TL) models allow the total variation in the outcome to be decomposed as level one and level two or ‘individual and group’ variance components. Two Level Mixture (TLM) models can be used to explore unobserved heterogeneity that represents different qualitative relationships in the outcome. In this paper, we extend the standard TL model by introducing constraints to guide the TLM algorithm towards a more appropriate data partitioning. Our constraints-based methods combine the mixing proportions estimated by parametric Expectation Maximization (EM) of the outcome and the random component from the TL model. This forms new two level mixing conditional (TLMc) approach by means of prior information. The new framework advantages are: 1. avoiding trial and error tactic used by TLM for choosing the best BIC (Bayesian Information Criterion), 2. permitting meaningful parameter estimates for distinct classes in the coefficient space and finally 3. allowing smaller residual variances. We show the benefit of our method using overweight and obesity from Body Mass Index (BMI) for students in year 6. We apply these methods on hierarchical BMI data to estimate student multiple deprivation and school Club effects. Keywords: Parametric Expectation Maximization, Multilevel Mixture, Conditional Multilevel Mixture Known Mix, Overweight and Obesity Data.Download Full Article |
Editor’s Choice : Enriched-Data Problems and Essential Non-Identifiability
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Abstract: There are two principal ways in which statistical models extend beyond the data available. First, the data may be coarsened, that is, what is actually observed is less detailed than what is planned, owing to, for example, attrition, censoring, grouping, or a combination of these. Second, the data may be augmented, that is, the observed data are hypothetically but conveniently supplemented with structures such as random effects, latent variables, latent classes, or component membership in mixture distributions. These two settings together will be referred to as enriched data. Reasons for modelling enriched data include the incorporation of substantive information, such as the need for predictions, advantages in interpretation, and mathematical and computational convenience. The fitting of models for enriched data combine evidence arising from empirical data with non-verifiable model components, i.e., that are purely assumption driven. This has important implications for the interpretation of statistical analyses in such settings. While widely known, the exploration and discussion of these issues is somewhat scattered. The user should be fully aware of the potential dangers and pitfalls that follows from this. Therefore, we provide a unified framework for enriched data and show in general that to any given model an entire class of models can be assigned, with all of its members producing the same fit to the observed data but arbitrary regarding the unobservable parts of the enriched data. The implications of this are explored for several specific settings, namely that of latent classes, finite mixtures, factor analysis, random-effects models, and incomplete data. The results are applied to a range of relevant examples. Keywords: Compound-symmetry, empirical bayes, enriched data, exponential random effects, gamma random effects, linear mixed model, missing at random, missing completely at random, non-future dependence, pattern-mixture model, selection model, shared-parameter model..Download Full Article |