Abstract: 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 limited budget, especially when the exposure variable is expensive to obtain. Alternative cost-effective sampling designs are thus desirable. We propose two-phase sampling designs with interval-censored data, where the phase II sample is enriched by selectively including more informative subjects based on the phase I information. We develop semiparametric inference procedures that properly handle interval-censoring, biased-sampling and missing data. We establish their large sample properties using empirical process theory and semiparametric theory. We also develop an R package that implements the proposed methods.