Bayesian semiparametric modeling for HIV longitudinal data with censoring and skewness

Abstract

In biomedical studies, the analysis of longitudinal data based on Gaussian assumptions is common practice. Nevertheless, more often than not, the observed responses are naturally skewed, rendering the use of symmetric mixed effects models inadequate. In addition, it is also common in clinical assays that the patient's responses are subject to some upper and/or lower quantification limit, depending on the diagnostic assays used for their detection. Furthermore, responses may also often present a nonlinear relation with some covariates, such as time. To address the aforementioned three issues, we consider a Bayesian semiparametric longitudinal censored model based on a combination of splines, wavelets, and the skew-normal distribution. Specifically, we focus on the use of splines to approximate the general mean, wavelets for modeling the individual subject trajectories, and on the skew-normal distribution for modeling the random effects. The newly developed method is illustrated through simulated data and real data concerning AIDS/HIV viral loads.

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

“…Thus, to accommodate the censoring, it is interesting to generalize the t-SMEC model by considering a more flexible family of distributions, such as the scale mixtures of skew-normal (SMSN) distribution class skewness and heavy tails simultaneously. 46 A promising avenue for future research is to consider a generalization for multiple characteristics, as in Taavoni et al 47 Another could be employing more flexible nonparametric alternatives such as wavelets, as in Castro et al 48 Other interesting future research is related to censoring and missing values under the SMSN class of distributions. In this context, an extension of the works of Lin et al 49 and Lin and Wang 50 will be the topic of our subsequent papers.…”

Robust Inference for Skewed data in Health Sciences

“…It is important to note that the MDPDE is indeed an M-estimator, since its estimating equation can be written in the form i ψ(X i , θ) = 0 for a model based ψ-function; see Equation ( 6) to identify it. Further, as α → 0, the MDPDE objective function in (5) satisfies H n (θ) + 1 α → 1−the log-likelihood function, and the MDPDE estimating equation in (6) coincides with the usual score equation leading to the MLE. Hence, the MDPDEs at α > 0 can be thought of as a generalization of the MLE to achieve greater robustness against data contamination.…”

“…Clearly there is no closed form solution of the above MDPDE estimating equations in (6) and we need to solve them numerically in order to obtain the MDPDEs based on a given sample. An efficient method for the computation of the MDPDE is dicussed later in Section 3.…”

“…Now, the form of the SN density f θ in (1) and the corresponding score function u θ in (7) clearly indicates that the above IF is bounded in y for all α > 0 and unbounded at α = 0. We have presented the IFs of the three parameters (µ, σ, γ) in Figure 3 In order to compute the MDPDE, we need to minimize the objective function in (5) simultaneously with respect to the three parameters (µ, σ, γ), or equivalently solve the three estimating equations given in (6).…”

“…The corresponding data has been analyzed by several statisticians [50][51][52] and is available in the R package 'qrNLMM '. In particular Castro [6] fitted the skew-normal distribution to this data in a regression settings.…”