Extending multivariate Student's‐t$$ t $$ semiparametric mixed models for longitudinal data with censored responses and heavy tails

Abstract

Thismodel allows us to consider a flexible, functional dependence of an outcome variable over the covariates using nonparametric regression. Moreover, the proposed model takes into account the correlation between observations by using random effects. Penalized likelihood equations are applied to derive the maximum likelihood estimates that appear to be robust against outlying observations with respect to the Mahalanobis distance. We estimate nonparametric functions using smoothing splines under an EM-type algorithm framework. Finally, the proposed approach's performance is evaluated through extensive simulation studies and an application to two datasets from acquired immunodeficiency syndrome clinical trials.

Flexible modeling of multiple nonlinear longitudinal trajectories with censored and non-ignorable missing outcomes

“…This can also be observed from Figure 1 that the mean trajectories for log 10 (RNA) under the MNLMM are apparently different from those under the MNLMM-CM with MNAR and MCAR scenarios, whereas those with MNAR and MCAR look quite close. Figure 2 depicts the Q-Q plots for the empirical Bayes estimates of the random effects in model (23). Observing these plots, there is no clear evidence of non-normality in the estimated random effects.…”

“…Dagne and Huang 22 pursued a Bayesian semiparametric mixture Tobit model with skew- t errors to assess the simultaneous impact of left censoring, skewness, and measurement errors in covariates on inference. Mattos et al 23 considered an extension of the semiparametric mixed model based on the Student’s t-distribution, where log 10(RNA) measurements with left-censoring are treated as a primary outcome, and CD4 and CD8 T-cells are considered as covariates. All the aforementioned methods can be used only in the situation of single-outcome longitudinal trajectories.…”