Background: Deep generative models (DGMs) present a promising avenue for generating realistic, synthetic data to augment existing healthcare datasets. However, exactly how the completeness of the original dataset affects the quality of the generated synthetic data is unclear. Objectives: In this paper, we investigate the effect of data completeness on samples generated by the most common DGM paradigms. Methods: We create both cross-sectional and panel datasets with varying missingness and subset rates and train generative adversarial networks (GANs), variational autoencoders (VAEs) and autoregressive models (Transformers) on these datasets. We then compare the distributions of generated data with original training data to measure similarity. Results: We find that increased incompleteness is directly correlated with increased dissimilarity between original and generated samples produced through DGMs. Conclusions: Care must be taken when using DGMs to generate synthetic data as data completeness issues can affect the quality of generated data in both panel and cross-sectional datasets.