Parametric Event Sequence Analysis: An Application to an Analysis of Gender and Racial/Ethnic Differences in Patterns of Drug-Use Progression

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Abstract
This article introduces novel statistical models for the sequence analysis of events. The models are formulated to analyze occurrence, association, and sequencing among events as an extension of log-linear models. A set of parameters characterizes marginal odds and odds ratios of frequencies summed across sequence patterns for each combination of the occurrence/nonoccurrence of events. These parameters are used for the analysis of the occurrence and association of events. Another set of parameters characterizes conditional odds and odds ratios among sequence patterns within each combination of the occurrence/nonoccurrence of events. These parameters are used for the analysis of sequencing of events. The models permit a decomposition of the likelihood function into a marginal likelihood component that includes only parameters for occurrence and association among events and a conditional likelihood component that includes only parameters for sequencing among events. The models are then extended further for regressions with covariates. An application analyzes gender and racial/ethnic differences in patterns of drug use progression. Sequential patterns of initiations and association among initiations are analyzed for three groups of drugs: alcoholic beverages, cigarettes, and marijuana. Findings that cross-validate previous findings based on different datasets and findings that are novel are reported.

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