Uncertainty-Aware Missing-Data Multimodal Latent for Fetal-Growth Analysis
Objective: Routine third-trimester examination yields fetal biometry, maternal, Doppler and fetal-cardiac measurements, acquired at clinical discretion and therefore often incomplete. We show that these four measurement blocks are close to mutually uninformative, and that this single property determines what a representation of them can impute, what it can audit, and what fetal size alone cannot indicate. Methods: A linear-Gaussian factor model (K = 8 by parallel analysis, VARIMAX-rotated) was fitted to 25 measurements in four blocks from 977 fetuses (169 SGA, 61 severe; 77 LGA). Posterior precision sums contributions from observed measurements only, so missing values are marginalized rather than imputed. Data quality was screened using the standardized residual between each measurement and its reconstruction. Results: Predicting any one block from the other three gives an out-of-fold R2 of 0.023. The representation is a continuous growth spectrum with no cluster structure (Hartigan dip p = 0.99, gap statistic k = 1, three-cluster silhouette 0.07) ordering fetuses by birthweight centile (Spearman rho = 0.55). Among 169 SGA fetuses the haemodynamic redistribution axis separated the 25 adverse outcomes (AUC 0.70, 0.585-0.808) where measured size did not (0.60, 0.451-0.738). With Doppler censored, the marginalized interval covered held-out measurements in 97% and 93% of cases against nominal 95% and 90%. The reconstruction residual flagged 38 of 977 records, 36 confirmed transcription errors in the registry. Conclusion: Marginalizing missing measurements yields a representation whose uncertainty reflects the available data, and whose reconstruction residual doubles as a data-quality screen. Because the blocks are nearly independent, confirmed flags are within-block errors, and a synthetic benchmark gives the coupling needed before cross-block detection becomes available.