  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.
