Regression modelling of interval censored data based on the adaptive ridge procedure

Olivier Bouaziz (1, 2, 3, 4) , Eva Lauridsen (5) , Grégory Nuel (6)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 UPD5 - Université Paris Descartes - Paris 5
3 IUT - Paris Descartes - Institut Universitaire de Technologie Paris Descartes
4 USPC - Université Sorbonne Paris Cité
5 UCPH - University of Copenhagen = Københavns Universitet
6 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

A new method for the analysis of time to ankylosis complication on a dataset of replanted teeth is proposed. In this context of left-censored, interval-censored and right-censored data, a Cox model with piecewise constant baseline hazard is introduced. 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 method a L0 penalised likelihood method is implemented in order to automatically determine the number and locations of the cuts of the baseline hazard. This procedure allows to detect specific areas of time where patients are at greater risks for ankylosis. The method can be directly extended to the inclusion of exact observations and to a cure fraction. Theoretical results are obtained which allow to derive statistical inference of the model parameters from asymptotic 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.

Mots clés: Cure model; Interval censoring; Pe-nalised likelihood; Piecewise constant hazard; EM algorithm; Adaptive Ridge procedure; Penalised likelihood

Domaines: Méthodologie [stat.ME]

Olivier Bouaziz, Eva Lauridsen, Grégory Nuel. Regression modelling of interval censored data based on the adaptive ridge procedure. Journal of Applied Statistics, 2021. ⟨hal-01959728v2⟩