Outcome†dependent sampling with interval†censored failure time data

Epidemiologic studies and disease prevention trials often seek to relate an exposure variable to a failure time that suffers from interval†censoring. When the failure rate is low and the time intervals are wide, a large cohort is often required so as to yield reliable precision on the exposure†failure†time relationship. However, large cohort studies with simple random sampling could be prohibitive for investigators with a limited budget, especially when the exposure variables are expensive to obtain. Alternative cost†effective sampling designs and inference procedures are therefore desirable. We propose an outcome†dependent sampling (ODS) design with interval†censored failure time data, where we enrich the observed sample by selectively including certain more informative failure subjects. We develop a novel sieve semiparametric maximum empirical likelihood approach for fitting the proportional hazards model to data from the proposed interval†censoring ODS design. This approach employs the empirical likelihood and sieve methods to deal with the infinite†dimensional nuisance parameters, which greatly reduces the dimensionality of the estimation problem and eases the computation difficulty. The consistency and asymptotic normality of the resulting regression parameter estimator are established. The results from our extensive simulation study show that the proposed design and method works well for practical situations and is more efficient than the alternative designs and competing approaches. An example from the Atherosclerosis Risk in Communities (ARIC) study is provided for illustration.