Model Based Data Augmentation for Left-Truncated Lifetime Data : Theory and Simulation

Left-truncation or censoring of lifetime observation occurs in many applications. For instance, a crack on the body of a plane may become visible after it starts, a study may permit a process that has progressed to certain level, or a clinical trial may admit a subject who contracted the disease at an unspecified point of time, etc. Typically, the left-truncated observations are either discarded or misused when this type of data is analyzed. If a large portion of the data is left truncated, it may result in a significant loss of information. Moreover, any statistical analysis conducted on the data may be severely biased toward the non-truncated (complete) observations. When auxiliary information is available for the lifetimes of interest, a simple likelihood based model incorporating this auxiliary information can be constructed to estimate the truncated segment of the lifetimes. Using the estimated as well as the complete set of data, maximization of the conditional expectation of the log-likelihood function given the known part of the truncated data will provide a valid upgrade for the parameter estimates. When left-truncated observations are present in the data, this likelihood-based approach is theoretically appealing and sound therefore, has great potentiality over models based on the complete observations alone. We examine this approach through extensive simulation