W LOD might have come from a progressor group whose observations are assumed to comply with a skew-elliptical distribution with achievable left-censoring due to a detection limit. Second, as stated above, one more principle on which the Tobit model is based on is definitely the assumption that the outcome variable is usually distributed but incompletely observed (left-censored). However, when the normality assumption is violated it might make biased final results [14, 15]. Despite the fact that the normality assumption may possibly ease mathematical complications, it might be unrealistic as the distribution of viral load measurements can be highly skewed towards the appropriate, even following log-transformation. As an example, Figure 1(a) displays the distribution of repeated viral load measurements (in organic log scale) for 44 subjects enrolled within the AIDS clinical trial study 5055 [16]. It seems that for this data set which can be analyzed in this paper, the viral load responses are highly skewed even immediately after logtransformation. Verbeke and Lesaffre[17] demonstrated that the normality assumption in linear mixed models lack robustness against skewness and outliers. Hence, a normality assumption is just not very realistic for left-censored HIV-RNA data and can be as well restrictive to supply an accurate representation on the structure that’s presented within the information.Stat Med. Author manuscript; obtainable in PMC 2014 September 30.NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author ManuscriptDagne and HuangPageAn alternative method proposed in this paper is to use more flexible parametric models primarily based on skew-elliptical distributions [18, 19] for extending the Tobit model which allow one to incorporate skewness of random errors. Multivariate skew-normal (SN) and multivariate skew-t (ST) distributions are particular instances of skew-elliptical distributions.6-Bromo-8-fluoroisoquinoline uses These models are match to AIDS data utilizing a Bayesian method.21950-36-7 Formula It is noted that the ST distribution reduces to the SN distribution when degrees of freedom are substantial.PMID:34645436 As a result, we use an ST distribution to develop joint models and related statistical methodologies, but it is often simply extended to other skew-elliptical distributions like SN distribution. The reminder from the paper is organized as follows. In Section two, we develop semiparametric mixture Tobit models with multivariate ST distributions in complete generality. In Section three, we present the Bayesian inferential procedure and followed by a simulation study in Section four. The proposed methodologies are illustrated applying the AIDS data set in Section five. Ultimately, the paper concludes with discussions in Section six.NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscript2. Semiparametric Bayesian mixture Tobit models2.1. Motivating data Our study was motivated by the AIDS clinical trial study (A5055) viewed as in [16, 20]. This study was a Phase I/II, randomized, open-label, 24-week comparative study in the pharmacokinetic, tolerability and ARV effects of two regimens of indinavir (IDV) and ritonavir (RTV), plus two nucleoside analogue reverse transcriptase inhibitors (NRTIs) on HIV-1-infected subjects failing protease inhibitor (PI)-containing ARV therapies. Forty 4 subjects who failed their very first PI-containing regimens were randomized to among two IDV/ RTV regimens: IDV 800 mg twice day-to-day (q12h) + RTV 200 mg q12h and IDV 400 mg q12h + RTV 400 mg q12h. RNA viral load was measured in copies/mL at study days 0, 7, 14, 28, 56, 84, 112, 140 and 168 of follow-up. Covariates like.
