Comparison of parametric and semi-parametric methods for estimation of the parameters in frailty models in order to investigation effective factors in survival of the dental implants placement

Frailty models were utilized in survival models to take into account created heterogeneity and dependence between experimental units. Parametric and semi-parametric methods are considered for estimation of parameters in frailty models. In parametric frailty models, to frailty and baseline hazard, a parametric distribution is assumed, while the distribution for baseline hazard function is not considered in semi-parametric methods. Besides, the parameters using EM algorithm or penalized likelihood are estimated in the mentioned methods. The purpose of this study is the comparison of parametric and semi-parametric methods in frailty models.
Two hundred thirteen of the warfare victims that treated with dental implants during 2000 to 2010 were enrolled in this study. In order to investigation effective factors in survival of the dental implants placement, frailty models are fitted. Parameters are estimated using the three methods, parametric approach, semi- parametric using EM algorithm and Semi parametric using penalized likelihood. Statistical analysis was carried out using Frailtypack package in R software version 3.3.1.
Estimation of the semi parametric using penalized likelihood approach is contained a smaller magnitude of AIC as compared to parametric and semi-parametric approach of EM algorithm. Smoking and implant length are significant factors on survival implants (p In survival analysis using frailty models made more valid results in order to consider depending between survival times of experimental units. The penalized likelihood method has a better fit in order to estimate parameters in the frailty models.