I have clinical data from about 300 patients with repeated measures/observations of psychological distress over time. Psychological distress is measured as a continuous variable, but could be converted into a binary or categorical variable if necessary. About 60% of patients have only 2 observations and the rest have 3 or 4. The times between observations vary considerably, from a few days to a few months. I am interested in patterns of change in psychological distress over time. I have looked at various GEE models, growth models, mixed models, and time to event survival models, but am not able to find anything appropriate for this data. The varying time between observations is problematic for GEE, and the small number of repeated observations is not appropriate for mixed models. Because there are more than one possible outcomes for psychological distress (e.g. stay the same, improve, deteriorate) recurring over time, this is problematic for time to event models. Any advice on an appropriate analysis method for this data?
The small number of observations per individual isn't necessarily a problem for a mixed model. The bigger problem is often not having enough individuals or groups to get good estimates of the associated random-effect variances. See this page for details.
That said, the suggestion from @COOLSerdash to use generalized least squares (GLS) and your continuous outcome measure, modeled flexibly over time, is probably better here. You don't have to force Gaussian distributions on the random effects, as you do with a mixed model. You do have to specify a within-individual correlation structure; the continuous AR1 structure recommended is typically a good choice for data with different observation times. This answer provides some links for further reading to decide among the different ways to proceed, and for implementation of GLS in R.