Time homogeneous Markov model has been successfully used to extend the
clas sical survival analysis to the multi-states analysis. This model assumes
that the evolution of the process is independent to the waiting time in the state.
In our clinical problem, this constraint is restrictive. The semi-Markov can be
used to extend the time-homogeneous Markov model with discrete states and
continuous time, because waiting time distributions are considered. We
propose a paramet ric semi-Markovian model applied to the malaria
serological data. We develop a semi-Markov model with time-varying
regression coefficients adapted to medical context. The purposes are
threefold. The firt is to introduce a modified Weibull distribution on the
semi-Markovian process class offering some flexibilities than those often used
as Weibull and exponential Weibull. The second is to discuss a simple
approach based on using appropriate time-dependent covariates effect in a
homogeneous semi-Markov model and to propose a non-parametric
estimation for the time-varying regression coefficients using spline functions.
The third purpose is to discuss the application of these results on semi-Markov
models to malaria serology.

Keyword : Multi-state model, Semi-Markov process, Flexible Weibull distribu
tion, Hazard function, Malaria serology, longitudinal analysis