| Dropout is a common problem in longitudinal cohort studies. If the probability of dropout depends on unobserved outcomes, dropout is considered missing not at random and is therefore non-ignorable. Non-ignorable missing data can be addressed using mixture model methods. We consider a Natural Spline Varying-Coefficient mixture model, which is based on a varying coefficient model with a continuous dropout distribution. We consider extensions to this method that allow the outcome to be nonlinear over time. Natural cubic B-splines are used to semi-parametrically model both time and dropout time, providing model flexibility such that the results are driven by the data. Further this method is simple to implement with commonly available statistical tools using standard software. Two approaches were considered; a B-spline transformation of the interaction of time and dropout time and a tensor product between the B-spline transformations of time and dropout time. Simulation studies were used to evaluate the performance of both methods. Simulations suggested that the interaction model was stable, but not flexible enough to capture nuances in the data. Simulations also suggested that the tensor model was flexible enough to fit the data, however because of a lack of a rectangular basis the results were extremely unstable. Finally, both methods were applied to data from the Acute Infection and Early Disease Research Program HIV cohort. |
