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Intensive care unit (ICU) data consist of high-frequency multivariate time series, including vital signs, laboratory results, and hemodynamic variables, which are crucial for clinical decision-making and predictive modeling. However, these data are frequently incomplete due to monitor interruptions, clinical workflows, and selective measurement, with missing rates ranging from 20% to over 80% depending on the variable. Missingness in ICU time series is often not random, as sicker patients tend to be monitored more frequently, creating a missing not at random (MNAR) mechanism. Conventional imputation methods such as mean filling, interpolation, and multiple imputation assume random missingness and therefore introduce bias and distort clinical signals under MNAR conditions. We propose a variational recurrent neural network (VRNN) with stochastic attention to impute ICU time series under MNAR settings. The framework integrates latent state modeling of physiological dynamics, stochastic attention over observed measurements using Gumbel-Softmax sampling, and a missingness pattern encoder that explicitly models the observation process. An imputation decoder generates probabilistic estimates of missing values conditioned on latent states, attention context, and missingness structure. This framework enables uncertainty-aware and potentially unbiased imputation in ICU time series by jointly modeling physiological dynamics and missingness mechanisms. It combines variational inference and stochastic attention to address systematic bias in conventional approaches, with future work needed to validate performance on real-world ICU datasets.