Title: Identifying Patterns in Behavioral Public Health Data Using Mixture Modeling with an Informative Number of Repeated Measures
Description: Finite mixture modeling is a useful statistical technique for clustering individuals based on patterns of responses. The fundamental idea of the mixture modeling approach is to assume there are latent clusters of individuals in the population which each generate their own distinct distribution of observations (multivariate or univariate) which are then mixed up together in the full population. Hence, the name mixture comes from the fact that what we observe is a mixture of distributions. The goal of this model-based clustering technique is to identify what the mixture of distributions is so that, given a particular response pattern, individuals can be clustered accordingly. Commonly, finite mixture models, as well as the special case of latent class analysis, are used on data that inherently involve repeated measures. The purpose of this dissertation is to extend the finite mixture model to allow for the number of repeated measures to be incorporated and contribute to the clustering of individuals rather than measures.

The dimension of the repeated measures or simply the count of responses is assumed to follow a truncated Poisson distribution and this information can be incorporated into what we call a dimension informative finite mixture model (DIMM). The outline of this dissertation is as follows. Paper 1 is entitled, "Dimension Informative Mixture Modeling (DIMM) for questionnaire data with an informative number of repeated measures." This paper describes the type of data structures considered and introduces the dimension informative mixture model (DIMM). A simulation study is performed to examine how well the DIMM fits the known specified truth. In the first scenario, we specify a mixture of three univariate normal distributions with different means and similar variances with different and similar counts of repeated measurements. We found that the DIMM predicts the true underlying class membership better than the traditional finite mixture model using a predicted value metric score. In the second scenario, we specify a mixture of two univariate normal distributions with the same means and variances with different and similar counts of repeated measurements.

We found that that the count-informative finite mixture model predicts the truth much better than the non-informative finite mixture model. Paper 2 is entitled, "Patterns of Physical Activity in the Northern Manhattan Study (NOMAS) Using Multivariate Finite Mixture Modeling (MFMM)." This is a study that applies a multivariate finite mixture modeling approach to examining and elucidating underlying latent clusters of different physical activity profiles based on four dimensions: total frequency of activities, average duration per activity, total energy expenditure and the total count of the number of different activities conducted. We found a five cluster solution to describe the complex patterns of physical activity levels, as measured by fifteen different physical activity items, among a US based elderly cohort. Adding in a class of individuals who were not doing any physical activity, the labels of these six clusters are: no exercise, very inactive, somewhat inactive, slightly under guidelines, meet guidelines and above guidelines.

This methodology improves upon previous work which utilized only the total metabolic equivalent (a proxy of energy expenditure) to classify individuals into inactive, active and highly active. Paper 3 is entitled, "Complex Drug Use Patterns and Associated HIV Transmission Risk Behaviors in an Internet Sample of US Men Who Have Sex With Men." This is a study that applies the count-informative information into a latent class analysis on nineteen binary drug items of drugs consumed within the past year before a sexual encounter. In addition to the individual drugs used, the mixture model incorporated a count of the total number of drugs used. We found a six class solution: low drug use, some recreational drug use, nitrite inhalants (poppers) with prescription erectile dysfunction (ED) drug use, poppers with prescription/non-prescription ED drug use and high polydrug use. Compared to participants in the low drug use class, participants in the highest drug use class were 5.5 times more likely to report unprotected anal intercourse (UAI) in their last sexual encounter and approximately 4 times more likely to report a new sexually transmitted infection (STI) in the past year. Younger men were also less likely to report UAI than older men but more likely to report an STI.