The relations between baseline covariates and the outcome of AUDs were evaluated with a series of discrete-time survival analyses (DTSA) conducted using a latent hazard function representing the event time distribution. The discrete-time hazard is the conditional probability that an individual will be diagnosed with an AUD in a time period, given that he was not diagnosed in any earlier time period (Singer & Willett, 2003). The DTSA model has been described as “a number of logistic regressions fitting the incremental probability of survival” (page 185; Asparouhov et al., 2006), which informs both whether and when an event of interest (here, an AUD diagnosis) occurs. A related indicator of event occurrence is the survival function, which is the sample’s cumulative probability of not being diagnosed with an AUD over time, and which is expressed as a function of the hazard function (Muthen & Masyn, 2005). This survival function has been shown to approximate the Cox regression model used in traditional continuous time survival models, and is preferred when the data are categorical and the number of categories is less than 20 (Asparouhov et al., 2006).
