Vascular access for haemodialysis is of paramount importance. Although studies have found that central venous catheter is often associated with poor outcomes and switching to arteriovenous fistula is beneficial, it has not been fully elucidated how the effect of switching of access on outcomes changes over time and whether the effect depends on switching time. Analysis of the longitudinal data needs to account for changes over multiple time indices. In this paper we propose a flexible model that jointly models the change over treatment time, the trend over calendar time, the change associated with treatment switching and time-varying effects of covariates. The effect of switching may depend on both the time of switching and time since switching. All unknown functions are modeled nonparametrically using local linear smoothers and estimated using a backfitting procedure. Large sample properties are studied. Simulation studies show excellent finite-sample performance. Our methods are applied to investigate the effect of vascular access change on albumin in dialysis patients. It is concluded that the benefit of switching from central venous catheter to arteriovenous fistula depends on the time of switching, the sooner the better.