Prediction of transition probabilities in multi-state models with nested case-control data

Music City Center 

Multi-state models are widely used to study complex interrelated life events. In resource-limited settings, nested case-control (NCC) sampling may be employed to extract subsamples from a cohort for events of interest, followed by a conditional likelihood analysis. However, conditioning restricts the reuse of NCC data for studying additional events. An alternative approach constructs pseudolikelihoods using inverse probability weighting (IPW) with NCC data. Existing IPW-based methods focus on estimating relative risks for multiple or secondary outcomes. We extend these methods to predict transition probabilities under general multi-state models and evaluate their efficiency. We propose two novel approaches for more efficient prediction and derive explicit variance estimators. The first approach calibrates the design weights using cohort-level information, while the second jointly models transitions from the same state. A simulation study demonstrates that either approach substantially improves efficiency and that their combined application yields further gains. We illustrate these methods with real data from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial (PLCO).

Cox regression

Multi-state models

Nested case-control design

Pseudolikelihood

Transition probability

Weight calibration 

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