Survival analysis for longitudinal data

In longitudinal studies with a set of continuous or ordinal repeated response variables it may be convenient to summarise the outcome as a threshold event. Then, the time to this event becomes of interest. This is particularly true of recent Ophthalmological trials evaluating the effect of treatment on the loss of visual acuity over time. However, the practice of employing conventional survival analysis methods for testing the null hypothesis of no treatment effect in these types of studies is intrinsically flawed as the exact time to the threshold event is not measured. In this paper we obtain a general likelihood for the unknown parameters when the underlying sur- vival model is parametric. We also recover the actual information available in repeated measures data for a variety of models and compare the results with those obtained using a mis-specified model, which assumes the time to the event is one of the possibly irregularly spaced inspection times.