  Data from multi-modality provide complementary information in clinical
prediction, but missing data in clinical cohorts limits the number of subjects
in multi-modal learning context. Multi-modal missing imputation is challenging
with existing methods when 1) the missing data span across heterogeneous
modalities (e.g., image vs. non-image); or 2) one modality is largely missing.
In this paper, we address imputation of missing data by modeling the joint
distribution of multi-modal data. Motivated by partial bidirectional generative
adversarial net (PBiGAN), we propose a new Conditional PBiGAN (C-PBiGAN) method
that imputes one modality combining the conditional knowledge from another
modality. Specifically, C-PBiGAN introduces a conditional latent space in a
missing imputation framework that jointly encodes the available multi-modal
data, along with a class regularization loss on imputed data to recover
discriminative information. To our knowledge, it is the first generative
adversarial model that addresses multi-modal missing imputation by modeling the
joint distribution of image and non-image data. We validate our model with both
the national lung screening trial (NLST) dataset and an external clinical
validation cohort. The proposed C-PBiGAN achieves significant improvements in
lung cancer risk estimation compared with representative imputation methods
(e.g., AUC values increase in both NLST (+2.9\%) and in-house dataset (+4.3\%)
compared with PBiGAN, p$<$0.05).
