A note on the likelihood and moments of the skew-normal distribution

In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood equation are established, which seem to hold in more general setting

Coffee, Alcohol, Smoking, Physical Activity and QT Interval Duration: Results from the Third National Health and Nutrition Examination Survey

Abnormalities in the electrocardiographic QT interval duration have been associated with an increased risk of ventricular arrhythmias and sudden cardiac death. However, there is substantial uncertainty about the effect of modifiable factors such as coffee intake, cigarette smoking, alcohol consumption, and physical activity on QT interval duration.We studied 7795 men and women from the Third National Health and Nutrition Survey (NHANES III, 1988-1994). Baseline QT interval was measured from the standard 12-lead electrocardiogram. Coffee and tea intake, alcohol consumption, leisure-time physical activities over the past month, and lifetime smoking habits were determined using validated questionnaires during the home interview.In the fully adjusted model, the average differences in QT interval comparing participants drinking ≥6 cups/day to those who did not drink any were -1.2 ms (95% CI -4.4 to 2.0) for coffee, and -2.0 ms (-11.2 to 7.3) for tea, respectively. The average differences in QT interval duration comparing current to never smokers was 1.2 ms (-0.6 to 2.9) while the average difference in QT interval duration comparing participants drinking ≥7 drinks/week to non-drinkers was 1.8 ms (-0.5 to 4.0). The age, race/ethnicity, and RR-interval adjusted differences in average QT interval duration comparing men with binge drinking episodes to non-drinkers or drinkers without binge drinking were 2.8 ms (0.4 to 5.3) and 4.0 ms (1.6 to 6.4), respectively. The corresponding differences in women were 1.1 (-2.9 to 5.2) and 1.7 ms (-2.3 to 5.7). Finally, the average differences in QT interval comparing the highest vs. the lowest categories of total physical activity was -0.8 ms (-3.0 to 1.4).Binge drinking was associated with longer QT interval in men but not in women. QT interval duration was not associated with other modifiable factors including coffee and tea intake, smoking, and physical activity

Diabetes Risk in Older Mexican Americans: Effects of Language Acculturation, Generation and Socioeconomic Status

The effect of language acculturation, socioeconomic status (SES), and immigrant generation on development of diabetes among Mexican Americans was evaluated in the Hispanic Established Population for the Epidemiologic Study of the Elderly (HEPESE). HEPESE is a longitudinal cohort study of 3,050 non-institutionalized Mexican Americans aged 65 years at baseline (1993-1994) from 5 Southwestern states. Diabetes incidence was ascertained in 4 follow-up surveys to 2004-05 by respondent self-reported physician-diagnosis of diabetes, high blood glucose, or sugar in the urine. Language of interview, immigrant generation, gender, age, education, family history of diabetes, smoking status, alcohol use, health insurance type and self-reported height and weight were assessed. High socioeconomic status (SES) was defined by high school graduation and non-Medicaid insurance. Cox's proportional hazards models were fit to evaluate the effects of language acculturation, generation and SES on incident diabetes. 845 of 3,050 (27.7%) Mexican Americans had diabetes at baseline and were younger, more educated, and more likely to have health insurance than those without diabetes. Risk of developing diabetes increased for Spanish-speaking respondents with low SES from 1st to 3rd generation (HR = 1.76, 95% CI = 1.02-3.03) and from 2nd to 3rd generation (HR = 2.15, 95% CI = 1.20-3.84). Among English-speaking, high SES participants, generation had a protective effect on developing diabetes: HR = 0.45 (95% CI = 0.22-0.91) when comparing 3rd versus 1st generation. The effect of language acculturation and immigrant generation on incident diabetes is moderated by SES status in HEPESE participants