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Exploring dependence between categorical variables: Benefits and limitations of using variable selection within Bayesian clustering in relation to log-linear modelling with interaction terms.

ABSTRACT: This manuscript is concerned with relating two approaches that can be used to explore complex dependence structures between categorical variables, namely Bayesian partitioning of the covariate space incorporating a variable selection procedure that highlights the covariates that drive the clustering, and log-linear modelling with interaction terms. We derive theoretical results on this relation and discuss if they can be employed to assist log-linear model determination, demonstrating advantages and limitations with simulated and real data sets. The main advantage concerns sparse contingency tables. Inferences from clustering can potentially reduce the number of covariates considered and, subsequently, the number of competing log-linear models, making the exploration of the model space feasible. Variable selection within clustering can inform on marginal independence in general, thus allowing for a more efficient exploration of the log-linear model space. However, we show that the clustering structure is not informative on the existence of interactions in a consistent manner. This work is of interest to those who utilize log-linear models, as well as practitioners such as epidemiologists that use clustering models to reduce the dimensionality in the data and to reveal interesting patterns on how covariates combine.

SUBMITTER: Papathomas M

PROVIDER: S-EPMC4896165 | biostudies-literature | 2016 Jun

REPOSITORIES: biostudies-literature

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Exploring dependence between categorical variables: Benefits and limitations of using variable selection within Bayesian clustering in relation to log-linear modelling with interaction terms.

Papathomas Michail M Richardson Sylvia S

Journal of statistical planning and inference 20160601

This manuscript is concerned with relating two approaches that can be used to explore complex dependence structures between categorical variables, namely Bayesian partitioning of the covariate space incorporating a variable selection procedure that highlights the covariates that drive the clustering, and log-linear modelling with interaction terms. We derive theoretical results on this relation and discuss if they can be employed to assist log-linear model determination, demonstrating advantages ...[more]

PMID: 27330244

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Project description:BACKGROUND: Graphical techniques can provide visually compelling insights into complex data patterns. In this paper we present a type of lasagne plot showing changes in categorical variables for participants measured at regular intervals over time and propose statistical models to estimate distributions of marginal and transitional probabilities. METHODS: The plot uses stacked bars to show the distribution of categorical variables at each time interval, with different colours to depict different categories and changes in colours showing trajectories of participants over time. The models are based on nominal logistic regression which is appropriate for both ordinal and nominal categorical variables. To illustrate the plots and models we analyse data on smoking status, body mass index (BMI) and physical activity level from a longitudinal study on women's health. To estimate marginal distributions we fit survey wave as an explanatory variable whereas for transitional distributions we fit status of participants (e.g. smoking status) at previous surveys. RESULTS: For the illustrative data the marginal models showed BMI increasing, physical activity decreasing and smoking decreasing linearly over time at the population level. The plots and transition models showed smoking status to be highly predictable for individuals whereas BMI was only moderately predictable and physical activity was virtually unpredictable. Most of the predictive power was obtained from participant status at the previous survey. Predicted probabilities from the models mostly agreed with observed probabilities indicating adequate goodness-of-fit. CONCLUSIONS: The proposed form of lasagne plot provides a simple visual aid to show transitions in categorical variables over time in longitudinal studies. The suggested models complement the plot and allow formal testing and estimation of marginal and transitional distributions. These simple tools can provide valuable insights into categorical data on individuals measured at regular intervals over time.

Project description:BackgroundThe log linear association between on-treatment LDL-C levels and ASCVD events is amplified in higher risk patient subgroups of statin versus placebo trials.ObjectivesUpdate previous systematic review to evaluate how the log linear association influences the magnitude of cardiovascular risk reduction from intensifying LDL-C lowering therapy.MethodsMEDLINE/PubMED, Clinical trials.gov, and author files were searched from 1/1/2005 through 10/30/2019 for subgroup analyses of cardiovascular outcomes trials of moderate versus high intensity statin, ezetimibe, and PCSK9 mAbs with an ASCVD endpoint (nonfatal myocardial infarction or stroke, cardiovascular death). Annualized ASCVD event rates were used to extrapolate 5-year ASCVD risk for each treatment group reported in subgroup analyses, which were grouped into a priori risk groups according to annualized placebo/control rates of ≥4%, 3-3.9%, or <3% ASCVD risk. Data were pooled using a random-effects model. Weighted least-squares regression was used to fit linear and log-linear models.ResultsSystematic review identified 96 treatment subgroups from 2 trials of moderate versus high intensity statin, 2 trials of a PCSK9 mAb versus placebo, and 1 trial of ezetimibe versus placebo. A log linear association between on-treatment LDL-C and ASCVD risk represents the association between on-treatment LDL-C levels and ASCVD event rates, especially in higher risk subgroups. Greater relative and absolute cardiovascular risk reductions from LDL-C lowering were observed when baseline LDL-C was >100 mg/dl and in extremely high risk ASCVD patient groups.ConclusionsGreater cardiovascular and mortality risk reduction benefits from intensifying LDL-C lowering therapy may be expected in those with LDL-C ≥100 mg/dl, or in extremely high risk patient groups. When baseline LDL-C <100 mg/dl, the log linear association between LDL-C and event rates suggests that treatment options other than further LDL-C lowering should also be considered for optimal risk reduction.

Dataset Information

Exploring dependence between categorical variables: Benefits and limitations of using variable selection within Bayesian clustering in relation to log-linear modelling with interaction terms.

Publications

Exploring dependence between categorical variables: Benefits and limitations of using variable selection within Bayesian clustering in relation to log-linear modelling with interaction terms.

Similar Datasets

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