Regression modelling of interval censored data based on the adaptive ridge procedure
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We consider the Cox model with piecewise constant baseline hazard to deal with a mixed case of left-censored, interval-censored and right-censored data. Estimation is carried out with the EM algorithm by treating the true event times as unobserved variables. This estimation procedure is shown to produce a block diagonal Hessian matrix of the baseline parameters. Taking advantage of this interesting feature of the estimation procedure a L0 penalised likelihood method is implemented in order to automatically determine the number and locations of the cuts of the baseline hazard. The method is directly extended to the inclusion of exact observations and to a cure fraction. Statistical inference of the model parameters is derived from likelihood theory. Through simulation studies, the penalisation technique is shown to provide a good fit of the baseline hazard and precise estimations of the resulting regression parameters. The method is illustrated on a dental dataset where the effect of covariates on the risk of ankylosis for replanted teeth is assessed.
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