Local regression when the responses are Interval-Censored

Abstract

Conditional expectation imputation and local-likelihood methods are contrasted with a midpoint imputation method for bivariate regression involving interval-censored responses. Although the methods can be extended in principle to higher order polynomials, our focus is on the local constant case. Comparisons are based on simulations of data scattered about three target functions with normally distributed errors. Two censoring mechanisms are considered: the first is analogous to current-status data in which monitoring times occur according to a homogeneous Poisson process; the second is analogous to a coarsening mechanism such as would arise when the response values are binned. We find that, according to a pointwise MSE criterion, no method dominates any other when interval sizes are fixed, but when the intervals have a variable width, the local-likelihood method often performs better than the other methods, and midpoint imputation performs the worst. Several illustrative examples are presented.