Survival data may be subject to a form of selection bias known as truncation. This thesis addresses left-truncated data, which arises when a sample is selected to include only those individuals whose truncation time precedes their event time. Statistical analyses in this thesis used joint modeling techniques, which consist of a longitudinal and survival submodel. Comparative studies of joint model methods that ignored and accounted for truncation were carried out on two real datasets and three simulations. Simulation results demonstrated that the analyses which accounted for truncation produced less biased regression parameter estimates than those that ignored truncation.