Empirical estimation of life expectancy from large clinical trials: Use of left‐truncated, right‐censored survival analysis methodology

In the current era of ever-increasing health care costs, economic analyses are an essential component in the comprehensive evaluation of new medical interventions. Cost-effectiveness analysis (CEA)--the most common form of economic analysis used in medicine--aids policy-makers in determining how to allocate finite health care dollars among possible alternative therapies. CEA relates the incremental benefits of a new technology to its incremental costs in a cost-effectiveness (CE) ratio. Although the generally agreed-upon standard of presentation for the CE ratio is the lifetime perspective (incremental lifetime cost to add one life year), this perspective presents an obvious challenge to the statistical analyst. Most large clinical trials collect limited follow-up data, and yet their findings form the basis of therapeutic recommendations that often extend far beyond the limits of the empirical data. Although clinical practice guidelines do not yet require explicit modeling to examine the long-term implications of their recommendations, health policy analyses routinely rely upon such extrapolations. This paper describes methods for using empirical patient-level data to extrapolate survival in large clinical trials and cohorts beyond a limited follow-up period in which most patients remain alive in order to estimate the entire survival distribution for a cohort of patients. We accomplish this task through a novel combination of models that estimate the hazard rate not only as a function of time but also as a function of patient age. Extrapolation of survival beyond a limited time frame is made possible by capitalizing on the extensive latitude of survival information available across the range of ages represented in the data. Variations in approach are presented, and issues arising in these analyses are discussed. The proposed methodology is developed, applied, and evaluated in both a large clinical trial cohort with 5-year follow-up on over 23,000 patients and a large observational database with long-term follow-up on over 4000 patients.