In this paper, we propose a model for medical costs recorded at regular time intervals, e.g. every month, as repeated measures in the presence of a terminating event, such as death. Prior models have related monthly medical costs to time since entry, with extra costs at the final observations at the time of death. Our joint model for monthly medical costs and survival time incorporates two important new features. First, medical cost and survival may be correlated because more 'frail' patients tend to accumulate medical costs faster and die earlier. A joint random effects model is proposed to account for the correlation between medical costs and survival by a shared random effect. Second, monthly medical costs usually increase during the time period prior to death because of the intensive care for dying patients. We present a method for estimating the pattern of cost prior to death, which is applicable if the pattern can be characterized as an additive effect that is limited to a fixed time interval, say b units of time before death. This 'turn back time' method for censored observations censors cost data b units of time before the actual censoring time, while keeping the actual censoring time for the survival data. Time-dependent covariates can be included. Maximum likelihood estimation and inference are carried out through a Monte Carlo EM algorithm with a Metropolis-Hastings sampler in the E-step. An analysis of monthly outpatient EPO medical cost data for dialysis patients is presented to illustrate the proposed methods.