  Readily available proxies for time of disease onset such as time of the first
diagnostic code can lead to substantial risk prediction error if performing
analyses based on poor proxies. Due to the lack of detailed documentation and
labor intensiveness of manual annotation, it is often only feasible to
ascertain for a small subset the current status of the disease by a follow up
time rather than the exact time. In this paper, we aim to develop risk
prediction models for the onset time efficiently leveraging both a small number
of labels on current status and a large number of unlabeled observations on
imperfect proxies. Under a semiparametric transformation model for onset and a
highly flexible measurement error models for proxy onset time, we propose the
semisupervised risk prediction method by combining information from proxies and
limited labels efficiently. From an initial estimator solely based on the
labelled subset, we perform a one-step correction with the full data augmenting
against a mean zero rank correlation score derived from the proxies. We
establish the consistency and asymptotic normality of the proposed
semi-supervised estimator and provide a resampling procedure for interval
estimation. Simulation studies demonstrate that the proposed estimator performs
well in finite sample. We illustrate the proposed estimator by developing a
genetic risk prediction model for obesity using data from Partners Biobank
Electronic Health Records (EHR).
