Middle censoring refers to data that becomes unobservable if it falls within a random interval (L,R). For some individuals the exact values are available while for others the corresponding intervals of censorship are observed. Left censoring, right censoring and double censoring are special cases of this middle censoring by suitable choices of this censoring interval. Here, we develop new methods for analyzing data subject to middle-censoring when covariates are present. The techniques discussed include parametric models as well as semi-parametric models such as the Cox's Proportional Hazards model and the Accelerated Failure Times model.

In survival studies the values of some covariates may change over time. As such, it is natural to incorporate such time-dependent covariates into the model to be used in survival analysis. The model used in this research integrates both time-independent and time-dependent covariates for middle censored data. Both semiparametric and parametric models are considered when time-dependent covariates are present. Next, discrete lifetime data that follow a geometric distribution, that is subject to middle censoring is considered. Here, we include an extension and generalization to the case where covariates are present and present an alternate approach and proofs which exploit the simple relationship between the geometric and exponential distributions. Also, considered are estimation problems for middle censored data with two independent competing risks, both for parametric and semiparametric context.

Simulation studies are performed to demonstrate the usefulness and accuracy of the methods developed here, and illustrated with a practical example using data from a Stanford Heart Transplant study.