Informative Missingness to Generate Irregular Clinical Time Series

Technical Summary: Informative Missingness to Generate Irregular Clinical Time Series

Problem Statement
Laboratory tests in Electronic Health Records (EHRs) are collected irregularly, where the absence of a test order is often as informative as the measurement itself. This "informative missingness" reflects clinician decisions and patient physiology, particularly in Missing-Not-At-Random (MNAR) settings where the decision to test depends on unobserved or partially observed clinical states. Existing generative modeling approaches often treat missingness as a preprocessing artifact to be imputed or focus on near-regular signals (e.g., vital signs), failing to capture the joint distribution of lab values and their observation patterns (sampling bursts and timing). Consequently, standard imputation benchmarks do not necessarily validate whether a generator can reproduce the complex coupling between patient physiology and clinical testing behavior.

Methodology
The authors propose a diffusion-based framework adapted from the TimeDiff architecture to generate clinical time series that jointly model continuous laboratory values and discrete missingness patterns.

• Dataset: The study utilizes the DACMI (Data Analytics Challenge on Missing data Imputation) benchmark, derived from MIMIC-III. This dataset includes 13 common blood laboratory variables. The authors constructed a paired representation where each time step contains continuous lab values and a binary missingness mask (0 for observed, 1 for missing).
• Preprocessing:
  • Temporal Alignment: Chart times were discretized into 4-hour intervals to minimize artificial missingness.
  • Windowing: Admissions were segmented into non-overlapping 7-day windows (42 time steps). Admissions exceeding this duration were split into consecutive windows.
  • Normalization: Features underwent log or Box-Cox transformations followed by z-score standardization to approximate Gaussianity.
  • Input Representation: The model input consists of 26 channels: 13 standardized lab values and 13 binary masks.
  • Delta Conditioning: To encode observation recency, a delta conditioning tensor was introduced. For each lab and time index, this value represents the number of steps since the most recent observation, normalized to $[0, 1)$. This auxiliary context guides the denoising network without being part of the final generated output.
• Model Architecture & Training:
  • The approach extends TimeDiff to handle mixed continuous (Gaussian) and discrete (binary) variables via complementary diffusion objectives.
  • Loss Modification: The numerical (Gaussian) loss was modified to exclude truly missing lab values, treating missingness as an absence rather than noisy values.
  • Optimization: The model was trained for 200,000 steps using the Adam optimizer. A weighting factor ($\lambda = 10^{-5}$) was applied to the discrete missingness loss relative to the continuous value loss to balance the objectives.
  • Sampling: 16,000 synthetic windows were generated by iteratively denoising random noise.

Key Contributions

1. Joint Generation Pipeline: A diffusion-based framework that generates both lab values and their observation indicators simultaneously, specifically targeting irregular labs and informative missingness to support downstream inference.
2. Loss Function Adaptation: A modification of the TimeDiff numerical loss to explicitly exclude missing values from the reconstruction error, ensuring missingness is modeled as an absence.
3. MNAR-Preserving Protocol: A practical preprocessing and windowing strategy designed to preserve MNAR-like structures (where sampling frequency reflects clinical decisions) while remaining compatible with diffusion training.
4. Comprehensive Evaluation: An evaluation strategy utilizing univariate distributions, joint embeddings of values and masks, and trajectory similarity metrics (EMD and DTW) to assess realism in both physiology and sampling behavior.

Results

• Univariate Distributions: The synthetic data closely matched real patient trajectories for individual lab distributions. For example, the synthetic density for Hemoglobin matched the real histogram around the main mode and upper tail, while White Blood Cells count (highly right-skewed) was well-preserved in high-density regions and tail profiles.
• Joint Embeddings: Using UMAP with a Dynamic Time Warping (DTW) distance metric on all 26 channels (13 values + 13 masks), the synthetic and real data distributions showed substantial overlap, indicating high-quality generation without out-of-support instances.
• Quantitative Metrics:
  • Delta Conditioning: Models utilizing delta conditioning achieved lower mean Earth Mover's Distance (EMD) and DTW scores compared to those without conditioning, bringing them closer to Real–Real reference values.
  • Missingness Prevalence: While the model improved joint structure, the synthetic missingness prevalence was consistently lower than observed in real data (e.g., mean real prevalence 0.79 vs. synthetic 0.74), suggesting the model still underestimates the frequency of unobserved measurements.
• Trajectory Similarity: DTW distances for trajectories were generally low, indicating that the temporal dynamics of the generated data align well with real data when restricted to observed time points.

Significance and Claims
The authors position this work as a preliminary step toward developing clinical foundation models. They claim that diffusion models are a promising foundation for generating realistic synthetic lab data under MNAR-like missingness by capturing clinically meaningful dependencies between physiology and testing behavior.

The primary significance lies in the ability to produce synthetic priors that preserve key physiology–missingness relationships. These priors are intended to serve as the initial component for training Prior-Data Fitted Networks, which the authors plan to investigate in extended work for leveraging informative missingness in downstream tasks like imputation and forecasting under distribution shifts. The paper explicitly states that these results are preliminary evidence of the model's capability to capture coupled processes, rather than a complete validation of downstream clinical utility.