AIC identifies optimal representation of longitudinal dietary variables

The Akaike Information Criterion (AIC) is a well-known tool for variable selection in multivariable modeling as well as a tool to help identify the optimal representation of explanatory variables. However, it has been discussed infrequently in the dental literature. The purpose of this paper is to demonstrate the use of AIC in determining the optimal representation of dietary variables in a longitudinal dental study.

The Iowa Fluoride Study enrolled children at birth and dental examinations were conducted at ages 5, 9, 13, and 17. Decayed or filled surfaces (DFS) trend clusters were created based on age 13 DFS counts and age 13-17 DFS increments. Dietary intake data (water, milk, 100 percent-juice, and sugar sweetened beverages) were collected semiannually using a food frequency questionnaire. Multinomial logistic regression models were fit to predict DFS cluster membership (n=344). Multiple approaches could be used to represent the dietary data including averaging across all collected surveys or over different shorter time periods to capture age-specific trends or using the individual time points of dietary data.

AIC helped identify the optimal representation. Averaging data for all four dietary variables for the whole period from age 9.0 to 17.0 provided a better representation in the multivariable full model (AIC=745.0) compared to other methods assessed in full models (AICs=750.6 for age 9 and 9-13 increment dietary measurements and AIC=762.3 for age 9, 13, and 17 individual measurements). The results illustrate that AIC can help researchers identify the optimal way to summarize information for inclusion in a statistical model.

The method presented here can be used by researchers performing statistical modeling in dental research. This method provides an alternative approach for assessing the propriety of variable representation to significance-based procedures, which could potentially lead to improved research in the dental community.