Discrete-Time Survival Factor Mixture Analysis for Low-Frequency Recurrent Event Histories

Abstract

In this article, the latent class analysis framework for modeling single event discrete-time survival data is extended to low-frequency recurrent event histories. A partial gap time model, parameterized as a restricted factor mixture model, is presented and illustrated using juvenile offending data. This model accommodates event-specific baseline hazard probabilities and covariate effects; event recurrences within a single time period; and accounts for within- and between-subject correlations of event times. This approach expands the family of latent variable survival models in a way that allows researchers to explicitly address questions about unobserved heterogeneity in the timing of events across the lifespan.

Figures

FIGURE 1

Sample-based hazard probabilities by (A) grouped-age intervals for first, second, and third offenses and (B) gap time intervals for second and third offenses. Note. Estimated hazard probabilities in figures corresponding to time intervals greater than one year are plotted as an approximation of the within-interval, 1-year hazard probability at the center of the interval. Full details of these calculations are available in a technical appendix upon request from the author.)

FIGURE 2

Path diagram for a low-frequency, recurrent event history process in a factor mixture framework.

FIGURE 3

Model-estimated, class-specific average hazard probabilities (located at sample mean values of all x-variables) for (A) time to first offense and (B) gap time from first to second offense and from second to third offense.