Theses Doctoral

On Modeling Spatial Time-to-Event Data with Missing Censoring Type

Lu, Diane

Time-to-event data, a common occurrence in medical research, is also pertinent in the ecological context, exemplified by leaf desiccation studies using innovative optical vulnerability techniques. Such data can unveil valuable insights into the influence of various factors on the event of interest. Leveraging both spatial and temporal information, spatial survival modeling can unravel the intricate spatiotemporal dynamics governing event occurrences. Existing spatial survival models often assume the availability of the censoring type for censored cases. Various approaches have been employed to address scenarios where a "subset" of cases lacks a known "censoring indicator" (i.e., whether they are right-censored or uncensored). This uncertainty in the subset pertains to missing information regarding the censoring status. However, our study specifically centers on situations where the missing information extends to "all" censored cases, rendering them devoid of a known censoring "type" indicator (i.e., whether they are right-censored or left-censored).

The genesis of this challenge emerged from leaf hydraulic data, specifically embolism data, where the observation of embolism events is limited to instances when leaf veins transition from water-filled to air-filled during the observation period. Although it is known that all veins eventually embolize when the entire plant dries up, the critical information of whether a censored leaf vein embolized before or after the observation period is absent. In other words, the censoring type indicator is missing.

To address this challenge, we developed a Gibbs sampler for a Bayesian spatial survival model, aiming to recover the missing censoring type indicator. This model incorporates the essential embolism formation mechanism theory, accounting for dynamic patterns observed in the embolism data. The model assumes spatial smoothness between connected leaf veins and incorporates vein thickness information. Our Gibbs sampler effectively infers the missing censoring type indicator, as demonstrated on both simulated and real-world embolism data. In applying our model to real data, we not only confirm patterns aligning with existing phytological literature but also unveil novel insights previously unexplored due to limitations in available statistical tools.

Additionally, our results suggest the potential for building hierarchical models with species-level parameters focusing solely on the temporal component. Overall, our study illustrates that the proposed Gibbs sampler for the spatial survival model successfully addresses the challenge of missing censoring type indicators, offering valuable insights into the underlying spatiotemporal dynamics.


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More About This Work

Academic Units
Thesis Advisors
Zheng, Tian
Ph.D., Columbia University
Published Here
July 3, 2024