The Effect of Stroke on Dementia Onset: Left-Truncation and Right-Censoring

We observe a quarter million people over a period of nine years and are interested in the effect of a stroke on the probability of dementia onset. Randomly left-truncated has a person been that was already deceased before the period. The ages at a stroke event or dementia onset are conditionally fixed right-censored, when either event may still occur, but after the period. We incorporate death and model the history of the three events by a homogeneous Markov process. The compensator for the respective counting processes is derived and Jacod's formula yields the likelihood contribution, conditional on observation. An Appendix is devoted to the role of filtrations in deriving the likelihood, for the simplification of merged non-dead states. Asymptotic normality of the estimated intensities is derived by martingale theory, relative to the size of the sample including the truncated persons. The data of a German health insurance reveals that after a stroke, the intensity of dementia onset is increased from 0.02 to 0.07, for Germans born in the first half on the 20th century. The intensity difference has a 95%-confidence interval of [0.048,0.051] and the difference halves when we extent to an age-inhomogeneous model due to Simpson's paradox.