Non-parametric estimation of state occupation, entry and exit times with multistate current status data

As a type of multivariate survival data, multistate models have a wide range of applications, notably in cancer and infectious disease progression studies. In this article, we revisit the problem of estimation of state occupation, entry and exit times in a multistate model where various estimators have been proposed in the past under a variety of parametric and non-parametric assumptions. We focus on two non-parametric approaches, one using a product limit formula as recently proposed in Datta and Sundaram(1) and a novel approach using a fractional risk set calculation followed by a subtraction formula to calculate the state occupation probability of a transient state. A numerical comparison between the two methods is presented using detailed simulation studies. We show that the new estimators have lower statistical errors of estimation of state occupation probabilities for the distant states. We illustrate the two methods using a pubertal development data set obtained from the NHANES III.(2).