Biomarker data collected over time, alongside event data that may be recurrent or terminal, and other (possibly temporal) covariate data, are commonplace. Such data are often used to understand a disease's progression over time and characterize the relationship between biomarker data and the event outcome simultaneously using joint models. We consider a five-component longitudinal sub-model for a joint model with integrated fractional Brownian motion (IFBM) and Cox proportional hazards model that serves as the event sub-model, which includes a time-dependent true longitudinal trajectory, the rate of decline of the true longitudinal trajectory, and a set of baseline covariates. We perform a simulation study and analysis of the NHLBI LAM registry data set and the Cystic Fibrosis data acquired at the Cincinnati Children's Hospital Medical Center. We used forced expiratory volume in one second (FEV1) in liters as the longitudinal biomarker and lung-transplant/death as the composite event. Baseline is defined as the time at which the first pulmonary function test was performed.