Censored Linear Regression Models For Irregularly Observed Longitudinal Data Using The Multivariate-t Distribution.

In acquired immunodeficiency syndrome (AIDS) studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. For such data structures, we propose a robust structure for a censored linear model based on the multivariate Student's t-distribution. To compensate for the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient expectation maximization type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by-product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step that rely on formulas for the mean and variance of a truncated multivariate Student's t-distribution. The methodology is illustrated through an application to an Human Immunodeficiency Virus-AIDS (HIV-AIDS) study and several simulation studies.

Augmented Mixed Models For Clustered Proportion Data.

Often in biomedical research, we deal with continuous (clustered) proportion responses ranging between zero and one quantifying the disease status of the cluster units. Interestingly, the study population might also consist of relatively disease-free as well as highly diseased subjects, contributing to proportion values in the interval [0, 1]. Regression on a variety of parametric densities with support lying in (0, 1), such as beta regression, can assess important covariate effects. However, they are deemed inappropriate due to the presence of zeros and/or ones. To evade this, we introduce a class of general proportion density, and further augment the probabilities of zero and one to this general proportion density, controlling for the clustering. Our approach is Bayesian and presents a computationally convenient framework amenable to available freeware. Bayesian case-deletion influence diagnostics based on q-divergence measures are automatic from the Markov chain Monte Carlo output. The methodology is illustrated using both simulation studies and application to a real dataset from a clinical periodontology study.

Evaluation Of The Effect Of Different Methods Of Microabrasion And Polishing On Surface Roughness Of Dental Enamel.

The microabrasion technique of enamel consists of selectively abrading the discolored areas or causing superficial structural changes in a selective way. In microabrasion technique, abrasive products associated with acids are used, and the evaluation of enamel roughness after this treatment, as well as surface polishing, is necessary. This in-vitro study evaluated the enamel roughness after microabrasion, followed by different polishing techniques. Roughness analyses were performed before microabrasion (L1), after microabrasion (L2), and after polishing (L3).Thus, 60 bovine incisive teeth divided into two groups were selected (n=30): G1- 37% phosphoric acid (37%) (Dentsply) and pumice; G2- hydrochloric acid (6.6%) associated with silicon carbide (Opalustre - Ultradent). Thereafter, the groups were divided into three sub-groups (n=10), according to the system of polishing: A - Fine and superfine granulation aluminum oxide discs (SofLex 3M); B - Diamond Paste (FGM) associated with felt discs (FGM); C - Silicone tips (Enhance - Dentsply). A PROC MIXED procedure was applied after data exploratory analysis, as well as the Tukey-Kramer test (5%). No statistical differences were found between G1 and G2 groups. L2 differed statistically from L1 and showed superior amounts of roughness. Differences in the amounts of post-polishing roughness for specific groups (1A, 2B, and 1C) arose, which demonstrated less roughness in L3 and differed statistically from L2 in the polishing system. All products increased enamel roughness, and the effectiveness of the polishing systems was dependent upon the abrasive used.