THE LOG-BURR XII REGRESSION MODEL FOR GROUPED SURVIVAL DATA

The log-Burr XII regression model for grouped survival data is evaluated in the presence of many ties. The methodology for grouped survival data is based on life tables, where the times are grouped in k intervals, and we fit discrete lifetime regression models to the data. The model parameters are estimated by maximum likelihood and jackknife methods. To detect influential observations in the proposed model, diagnostic measures based on case deletion, so-called global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to these measures, the total local influence and influential estimates are also used. We conduct Monte Carlo simulation studies to assess the finite sample behavior of the maximum likelihood estimators of the proposed model for grouped survival. A real data set is analyzed using a regression model for grouped data.

Association between diet and polymorphisms in individuals with statin-controlled dyslipidaemia grouped according to oxidative stress biomarkers

The objective of this study was to investigate whether differences in diet and in single-nucleotide polymorphisms (SNPs) found in paraoxonase-1 (PON-1), 3-hydroxy-3-methylglutaryl-coenzyme A reductase (HMGCR), cholesterol ester transfer protein (CETP) and apolipoprotein E (APOE) genes, are associated with oxidative stress biomarkers and consequently with susceptibility of low-density cholesterol (LDL) to oxidation. A multivariate approach was applied to a group of 55 patients according to three biomarkers: plasma antioxidant activity, malondialdehyde and oxidized LDL (oxLDL) concentrations. Individuals classified in Cluster III showed the worst prognoses in terms of antioxidant activity and oxidative status. Individuals classified in Cluster I presented the lowest oxidative status, while individuals grouped in Cluster II presented the highest levels of antioxidant activity. No difference in nutrient intake was observed among the clusters. Significantly higher gamma- and delta-tocopherol concentrations were observed in those individuals with the highest levels of antioxidant activity. No single linear regression was statistically significant, suggesting that mutant alleles of the SNPs selected did not contribute to the differences observed in oxidative stress response. Although not statistically significant, the p value of the APO E coefficient for oxLDL response was 0.096, indicating that patients who carry the TT allele of the APO E gene tend to present lower plasma oxLDL concentrations. Therefore, the differences in oxidative stress levels observed in this study could not be attributed to diet or to the variant alleles of PON-1, CETP, HMGCR or APO E. This data supports the influence of gamma-tocopherol and delta-tocopherol on antioxidant activity, and highlights the need for further studies investigating APO E alleles and LDL oxidation.