In longitudinal studies with missingness, shared parameter models (SPM) provide appropriate framework for the joint modeling of the measurements and missingness process. These models use a set of random effects to account for the interdependence between two processes. Sometimes the longitudinal responses may not be fitted well by using a linear model and some non-parametric methods have to be used. Also, parametric assumptions are typically made for the random effects distribution, and violation of those may affect the parameter estimates and standard errors. To overcome these problems, we propose a semi-parametric model for the joint modelling of longitudinal markers and a missing not at random mechanism. In this model, because of the flexibility in nonparametric regression models, the relationship between the response variables and the covariates has been modeled by semi-parametric mixed effect model. Also, we do not assume any parametric assumption for the random effects distribution and we allow it to be unspecified. The parameter estimations are made using a vertex exchange method. In order to evaluate the performance of the proposed model, we compare SPM using regression spline (Spline-SPM) and semi-parametric SPM (SpSPM) models. We also conduct a simulation study with different parametric assumptions for the random effects distribution. A real example from a recent HIV study is analyzed for illustration of the proposed approach.
Baghfalaki, Taban; Sefidi, Saeide; and Ganjali, Mojtaba
A Semi-parametric Approach for Analyzing Longitudinal Measurements with Non-ignorable Missingness Using Regression Spline,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 10,
1, Article 13.
Available at: https://digitalcommons.pvamu.edu/aam/vol10/iss1/13