This paper discusses regression analysis of case K interval-censored failure time data, a general type of failure time data, in the presence of informative censoring with the focus on simultaneous variable selection and estimation. Although many authors have considered the challenging variable selection problem for interval-censored data, most of the existing methods assume independent or non-informative censoring. More importantly, the existing methods that allow for informative censoring are frailty model-based approaches and cannot directly assess the degree of informative censoring among other shortcomings. To address these, we propose a conditional approach and develop a penalized sieve maximum likelihood procedure for the simultaneous variable selection and estimation of covariate effects. Furthermore, we establish the oracle property of the proposed method and illustrate the appropriateness and usefulness of the approach using a simulation study. Finally we apply the proposed method to a set of real data on Alzheimer's disease and provide some new insights.