Parametric models of irregular longitudinal data are needed for Bayesian inference and may be more robust to misspecification of the visit process compared to semiparametric approaches. Robustness of univariate parametric models has been assessed under the assumption of a memoryless visit process; however, it would be useful to assess this more generally, exploring scenarios where the intensity of a visit depends on the time elapsed since the last visit. We investigate the robustness of univariate parametric models under an informative visit process that is based on the physician’s recommendation on when the patient should return, and compare the performance of the univariate approach to a novel parametric joint model. Using simulation studies, we show that in most cases, the standard linear mixed model estimates parameters of interest with little bias, and for the specific cases where the univariate model is biased, we show how our joint model can eliminate or reduce the bias.