Modeling Semi-Continuous Outcomes in Longitudinal Studies:Methods and Applications

Very often researchers may encounter continuous outcome measures with a large number of observed values clustered at zero, called a semi-continuous measure. Such an outcome has a mixture of two distributions representing occurrence (non-zero vs. zero values) and intensity (amount of non-zero values) of the outcome measure. As the likelihood of occurrence and the intensity of non-zero values are often correlated with each other, the traditional econometric approach of modeling the two parts of outcome measures separately is inappropriate. The recently developed analytical methods, such as the Mixed-Effect Mixed Distribution Model and the two-part latent growth model (LGM) are often used to model semi-continuous outcome measures. This study demonstrates application of the two-part LGM. In the model the original distribution of outcome measure is decomposed into two parts (i.e., likelihood vs. amount), which are considered as two associated growth processes, and are modeled simultaneously. The data used for model demonstration were collected in a natural history study (N=248) of rural stimulant users in rural counties in Western Ohio. Frequency of crack-cocaine use in the past 30 days measured at the baseline and every 6 months in the first two years of study period were used for the model. Both unconditional and conditional two-part LGMs are demonstrated.