Costs or benefits which accumulate for individuals over time are of interest in many life history processes. Familiar examples include costs of health care for persons with chronic medical conditions, the payments to insured persons during periods of disability, and quality of life which is sometimes used in the evaluation of treatments in terminally ill patients. For convenience, here we use the term costs to refer to cost or other cumulative measures. Two important scenarios are (i) where costs are associated with the occurrence of certain events, so that total cost accumulates as a step function, and (ii) where individuals may move between various states over time, with cost accumulating at a constant rate determined by the state occupied. In both cases, there is frequently a random variable T that represents the duration of the process generating the costs. Here we consider estimation of the mean cumulative cost over a period of interest using methods based upon marginal features of the cost process and intensity based models. Robustness to adaptive censoring is discussed in the context of the multi-state methods. Data from a quality of life study of breast cancer patients are used to illustrate the methods.