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.
翻译:提议在重新种植的牙齿的数据集中采用一种新的分析时间到肾上腺炎并发症的时间分析方法。在左侧检查、间隔检查和右侧检查数据的情况下,采用了带有小片常数基准危险的Cox模型;通过将真实事件时间作为未观测的变量,对EM算法进行了估计;这一估计程序显示可以产生基线参数的区块二角Hessian矩阵。利用估算方法的这一令人感兴趣的特征,采用了L0惩罚可能性方法,以便自动确定削减基线危险的次数和地点。这一程序可以查明病人在哪些具体时间方面处于更大的亚性螺旋病风险。该方法可以直接扩大到包括精确的观察和治疗分数。取得了理论结果,从而能够从无症状可能性理论中得出模型参数的统计推理推理。通过模拟研究,模拟技术显示,惩罚方法能够提供与基准危险相当的准确估计结果回归参数。