Sequential updating via dynamic hierarchical models: A Bayesian approach to longitudinal data analysis

Most statistical analysis, theory and practice, is concerned with static models; models with a proposed set of parameters whose values are fixed across observational units. Static models implicitly assume that the quantified relationships remain the same across the design space of the data. While this is reasonable under many circumstances this can be a dangerous assumption when dealing with sequentially ordered data. The mere passage of time always brings fresh considerations and the interrelationships among parameters, or subsets of parameters, may need to be continually revised. ^ When data are gathered sequentially dynamic interim monitoring may be useful as new subject-specific parameters are introduced with each new observational unit. Sequential imputation via dynamic hierarchical models is an efficient strategy for handling missing data and analyzing longitudinal studies. Dynamic conditional independence models offers a flexible framework that exploits the Bayesian updating scheme for capturing the evolution of both the population and individual effects over time. While static models often describe aggregate information well they often do not reflect conflicts in the information at the individual level. Dynamic models prove advantageous over static models in capturing both individual and aggregate trends. Computations for such models can be carried out via the Gibbs sampler. An application using a small sample repeated measures normally distributed growth curve data is presented. ^

Motivational interviewing and feedback for college drinkers: Handling missing values with complete case analysis and multiple imputation

Objective: In this secondary data analysis, three statistical methodologies were implemented to handle cases with missing data in a motivational interviewing and feedback study. The aim was to evaluate the impact that these methodologies have on the data analysis. ^ Methods: We first evaluated whether the assumption of missing completely at random held for this study. We then proceeded to conduct a secondary data analysis using a mixed linear model to handle missing data with three methodologies (a) complete case analysis, (b) multiple imputation with explicit model containing outcome variables, time, and the interaction of time and treatment, and (c) multiple imputation with explicit model containing outcome variables, time, the interaction of time and treatment, and additional covariates (e.g., age, gender, smoke, years in school, marital status, housing, race/ethnicity, and if participants play on athletic team). Several comparisons were conducted including the following ones: 1) the motivation interviewing with feedback group (MIF) vs. the assessment only group (AO), the motivation interviewing group (MIO) vs. AO, and the intervention of the feedback only group (FBO) vs. AO, 2) MIF vs. FBO, and 3) MIF vs. MIO.^ Results: We first evaluated the patterns of missingness in this study, which indicated that about 13% of participants showed monotone missing patterns, and about 3.5% showed non-monotone missing patterns. Then we evaluated the assumption of missing completely at random by Little's missing completely at random (MCAR) test, in which the Chi-Square test statistic was 167.8 with 125 degrees of freedom, and its associated p-value was p=0.006, which indicated that the data could not be assumed to be missing completely at random. After that, we compared if the three different strategies reached the same results. For the comparison between MIF and AO as well as the comparison between MIF and FBO, only the multiple imputation with additional covariates by uncongenial and congenial models reached different results. For the comparison between MIF and MIO, all the methodologies for handling missing values obtained different results. ^ Discussions: The study indicated that, first, missingness was crucial in this study. Second, to understand the assumptions of the model was important since we could not identify if the data were missing at random or missing not at random. Therefore, future researches should focus on exploring more sensitivity analyses under missing not at random assumption.^