A log-linear regression model for the beta-Birnbaum-Saunders distribution with censored data

The beta-Birnbaum-Saunders (Cordeiro and Lemonte, 2011) and Birnbaum-Saunders (Birnbaum and Saunders, 1969a) distributions have been used quite effectively to model failure times for materials subject to fatigue and lifetime data. We define the log-beta-Birnbaum-Saunders distribution by the logarithm of the beta-Birnbaum-Saunders distribution. Explicit expressions for its generating function and moments are derived. We propose a new log-beta-Birnbaum-Saunders regression model that can be applied to censored data and be used more effectively in survival analysis. We obtain the maximum likelihood estimates of the model parameters for censored data and investigate influence diagnostics. The new location-scale regression model is modified for the possibility that long-term survivors may be presented in the data. Its usefulness is illustrated by means of two real data sets. (C) 2011 Elsevier B.V. All rights reserved.

Global pharmacogenomics: Impact of population diversity on the distribution of polymorphisms in the CYP2C cluster among Brazilians

The impact of biogeographical ancestry, self-reported 'race/color' and geographical origin on the frequency distribution of 10 CYP2C functional polymorphisms (CYP2C8*2, *3, *4, CYP2C9*2, *3, *5, *11, CYP2C19*2, *3 and *17) and their haplotypes was assessed in a representative cohort of the Brazilian population (n = 1034). TaqMan assays were used for allele discrimination at each CYP2C locus investigated. Individual proportions of European, African and Amerindian biogeographical ancestry were estimated using a panel of insertion-deletion polymorphisms. Multinomial log-linear models were applied to infer the statistical association between the CYP2C alleles and haplotypes (response variables), and biogeographical ancestry, self-reported Color and geographical origin (explanatory variables). The results showed that CYP2C19*3, CYP2C9*5 and CYP2C9*11 were rare alleles (<1%), the frequency of other variants ranged from 3.4% (CYP2C8*4) to 17.3% (CYP2C19*17). Two distinct haplotype blocks were identified: block 1 consists of three single nucleotide polymorphisms (SNPs) (CYP2C19*17, CYP2C19*2 and CYP2C9*2) and block 2 of six SNPs (CYP2C9*11, CYP2C9*3, CYP2C9*5, CYP2C8*2, CYP2C8*4 and CYP2C8*3). Diplotype analysis generated 41 haplotypes, of which eight had frequencies greater than 1% and together accounted for 96.4% of the overall genetic diversity. The distribution of CYP2C8 and CYP2C9 (but not CYP2C19) alleles, and of CYP2C haplotypes was significantly associated with self-reported Color and with the individual proportions of European and African genetic ancestry, irrespective of Color self-identification. The individual odds of having alleles CYP2C8*2, CYP2C8*3, CYP2C9*2 and CYP2C9*3, and haplotypes including these alleles, varied continuously as the proportion of European ancestry increased. Collectively, these data strongly suggest that the intrinsic heterogeneity of the Brazilian population must be acknowledged in the design and interpretation of pharmacogenomic studies of the CYP2C cluster in order to avoid spurious conclusions based on improper matching of study cohorts. This conclusion extends to other polymorphic pharmacogenes among Brazilians, and most likely to other admixed populations of the Americas. The Pharmacogenomics Journal (2012) 12, 267-276; doi: 10.1038/tpj.2010.89; published online 21 December 2010

Temporal Trends of Asthma Mortality Rates in Brazil from 1980 to 2010

Objective. Mortality from asthma has varied among countries during the last several decades. This study aimed to identify temporal trends of asthma mortality in Brazil from 1980 to 2010. Method. We analyzed 6840 deaths of patients aged 5-34 years that occurred in Brazil with the underlying cause of asthma. We applied a log-linear model using Poisson regression to verify peaks and trends. We also calculated the point estimation and 95% confidence interval (CI 95%) of the annual percent change (APC) of the mortality rates, and the average annual percent change (AAPC) for 2001-2010. Results. A decline was observed from 1980 to 1992 [APC = -3.4 (-5.0 to -1.8)], followed by a nonsignificant rise until 1996 [APC = 6.8 (-1.4 to 15.6)], and a new downward trend from 1997 to 2010 [APC = -2.7 (-3.9 to -1.6)]. The APCs varied according to age strata: 5-14 years from 1980 to 2010 [-0.3 (-1.1 to 0.5)]; 15-24 years from 1980 to 1991 [-2.1 (-5.0 to 0.9)], from 1992 to 1996 [6.8 (-6.7 to 22.2)], and from 1997 to 2010 [-3.9 (-5.7 to -2.0)]; 24-25 years from 1980 to 1992 [-2.5 (-4.6 to -0.3)], from 1993 to 1995 [12.0 (-21.1 to 59.1)], and from 1996-2010 [-1.7 (-3.0 to -0.4)]. AAPC from 2001 to 2010 was -1.7 (-3.0 to -0.4); the decline for this period was significant for patients over 15 years old, women, and those living in the Southeast region. Conclusion. Asthma mortality rates in Brazil have been declining since the late 1990s.

Robust statistical modeling using the Birnbaum-Saunders-t distribution applied to insurance

In this paper, we carry out robust modeling and influence diagnostics in Birnbaum-Saunders (BS) regression models. Specifically, we present some aspects related to BS and log-BS distributions and their generalizations from the Student-t distribution, and develop BS-t regression models, including maximum likelihood estimation based on the EM algorithm and diagnostic tools. In addition, we apply the obtained results to real data from insurance, which shows the uses of the proposed model. Copyright (c) 2011 John Wiley & Sons, Ltd.

Using AMS combined with mineral shape preferred orientation analysis to understand the emplacement fabrics of the Apiai gabbro-norite (Ribeira Belt, SE Brazil)

The Apiai gabbro-norite is a massive fine-grained Neoproterozoic intrusion emplaced in a core of synformal structure that deforms low-grade marine metasedimentary rocks of the Ribeira Belt of south-eastern Brazil. The lack of visible magmatic layering or any internal fabric has been a major limitation in deciding whether the emplacement occurred before or after the regional folding. To assist in the tectonic interpretations, we combine low-field anisotropy of magnetic susceptibility (AMS) and silicate shape preferred orientation (SPO) to reveal the internal structure of the mafic intrusion. Magnetic data indicate a mean susceptibility of about 10(-2) SI and a mean anisotropy degree (P) of about 1.08, essentially yielded by titanomagnetite. The magnetic and silicate foliations for P >= 1.10 are parallel to each other, while the lineations tend to scatter on the foliation plane, in agreement with the dominant oblate symmetry of the AMS and SPO ellipsoids. For lower P values, the magnetic and silicate fabrics vary from coaxial to oblique, and for P <= 1.05, their shapes and orientations can be quite distinct. The crystal size distribution (CSD) of plagioclase for P > 1.05 is log linear, in agreement with a bulk simple crystallisation history. These results combined show that for a strong SPO, corresponding to a magnetic anisotropy above 1.10, AMS is a reliable indicator of the magmatic fabric. They indicate that the Apiai gabbro-norite consists of sill-like body that was inclined gently to the north by the regional folding.

Longitudinal familial analysis of blood pressure involving parametric (co)variance functions

Abstract Background For analyzing longitudinal familial data we adopted a log-linear form to incorporate heterogeneity in genetic variance components over the time, and additionally a serial correlation term in the genetic effects at different levels of ages. Due to the availability of multiple measures on the same individual, we permitted environmental correlations that may change across time. Results Systolic blood pressure from family members from the first and second cohort was used in the current analysis. Measures of subjects receiving hypertension treatment were set as censored values and they were corrected. An initial check of the variance and covariance functions proposed for analyzing longitudinal familial data, using empirical semi-variogram plots, indicated that the observed trait dispersion pattern follows the assumptions adopted. Conclusion The corrections for censored phenotypes based on ordinary linear models may be an appropriate simple model to correct the data, ensuring that the original variability in the data was retained. In addition, empirical semi-variogram plots are useful for diagnosis of the (co)variance model adopted.

Degree of multicollinearity and variables involved in linear dependence in additive-dominant models

The objective of this work was to assess the degree of multicollinearity and to identify the variables involved in linear dependence relations in additive-dominant models. Data of birth weight (n=141,567), yearling weight (n=58,124), and scrotal circumference (n=20,371) of Montana Tropical composite cattle were used. Diagnosis of multicollinearity was based on the variance inflation factor (VIF) and on the evaluation of the condition indexes and eigenvalues from the correlation matrix among explanatory variables. The first model studied (RM) included the fixed effect of dam age class at calving and the covariates associated to the direct and maternal additive and non-additive effects. The second model (R) included all the effects of the RM model except the maternal additive effects. Multicollinearity was detected in both models for all traits considered, with VIF values of 1.03 - 70.20 for RM and 1.03 - 60.70 for R. Collinearity increased with the increase of variables in the model and the decrease in the number of observations, and it was classified as weak, with condition index values between 10.00 and 26.77. In general, the variables associated with additive and non-additive effects were involved in multicollinearity, partially due to the natural connection between these covariables as fractions of the biological types in breed composition.