On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

Lognormal distribution has abundant applications in various fields. In literature, most inferences on the two parameters of the lognormal distribution are based on Type-I censored sample data. However, exact measurements are not always attainable especially when the observation is below or above the detection limits, and only the numbers of measurements falling into predetermined intervals can be recorded instead. This is the so-called grouped data. In this paper, we will show the existence and uniqueness of the maximum likelihood estimators of the two parameters of the underlying lognormal distribution with Type-I censored data and grouped data. The proof was first established under the case of normal distribution and extended to the lognormal distribution through invariance property. The results are applied to estimate the median and mean of the lognormal population.

The association of depression and perceived stress with beta cell function between African and Haitian Americans with and without type 2 diabetes

Background: Diabetes and diabetes-related complications are major causes of morbidity and mortality in the United States. Depressive symptoms and perceived stress have been identified as possible risk factors for beta cell dysfunction and diabetes. The purpose of this study was to assess associations between depression symptoms and perceived stress with beta cell function between African and Haitian Americans with and without type 2 diabetes. Participants and Methods: Informed consent and data were available for 462 participants (231 African Americans and 231 Haitian Americans) for this cross-sectional study. A demographic questionnaire developed by the Primary Investigator was used to collect information regarding age, gender, smoking, and ethnicity. Diabetes status was determined by self-report and confirmed by fasting blood glucose. Anthropometrics (weight, and height and waist circumference) and vital signs (blood pressure) were taken. Blood samples were drawn after 8 10 hours over-night fasting to measure lipid panel, fasting plasma glucose and serum insulin concentrations. The homeostatic model assessment, version 2 (HOMA2) computer model was used to calculate beta cell function. Depression was assessed using the Beck Depression Inventory-II (BDI-II) and stress levels were assessed using the Perceived Stress Scale (PSS). Results: Moderate to severe depressive symptoms were more likely for persons with diabetes (p = 0.030). There were no differences in perceived stress between ethnicity and diabetes status (p = 0.283). General linear models for participants with and without type 2 diabetes using beta cell function as the dependent variable showed no association with depressive symptoms and perceived stress; however, Haitian Americans had significantly lower beta cell function than African Americans both with and without diabetes and adjusting for age, gender, waist circumference and smoking. Further research is needed to compare these risk factors in other race/ethnic groups.

Perceived Stress and Self‑rated Health of Haitian and African Americans with and without Type 2 Diabetes

Background: Blacks have a higher incidence of diabetes and its related complications. Self-rated health (SRH) and perceived stress indicators are associated with chronic diseases. The aim of this study was to examine the associations between SRH, perceived stress and diabetes status among two Black ethnicities. Materials and Methods: The cross-sectional study included 258 Haitian Americans and 249 African Americans with (n = 240) and without type 2 diabetes (n = 267) (N = 507). Recruitment was performed by community outreach. Results: Haitian-Americans were less likely to report ‘fair to poor’ health as compared to African Americans [OR=0.58 (95% CI: 0.35, 0.95), P = 0.032]; yet, Haitian Americans had greater perceived stress than African Americans (P = 0.002). Having diabetes was associated with ‘fair to poor’ SRH [OR=3.14 (95% CI: 2.09, 4.72),P < 0.001] but not perceived stress (P = 0.072). Haitian-Americans (P = 0.023), females (P = 0.003) and those participants having ‘poor or fair’ SRH (P < 0.001) were positively associated with perceived stress (Nagelkerke R2=0.151). Conclusion: Perceived stress associated with ‘poor or fair’ SRH suggests that screening for perceived stress should be considered part of routine medical care; albeit, further studies are required to confirm our results. The findings support the need for treatment plans that are patient-centered and culturally relevant and that address psychosocial issues.

Social determinants of fruit and vegetable intake and validation of Pro-Children Eating Habits Questionnaire for 3rd and 5th grade children

BACKGROUND: The Pro Children Eating Habits Questionnaire has been evaluated as a valid and reliable tool in Europe to measure determinants of fruit and vegetable intake for children; however, it has not been validation for United States populations. The purpose of this study was to (1) assess the reliability and discrimination validity of fruit and vegetable correlates for the Pro Children Eating Habits Questionnaire; (2) investigate the predictive validity of determinants of fruit and vegetable consumption for multi-ethnic elementary school children; and, (3) to assess the association of social determinants with fruit and vegetable consumption. METHODS: One hundred and thirty elementary school students from the 3rd and 5th grades completed this cross-sectional study. RESULTS: Fruit and vegetable determinants, had satisfactory internal consistencies. No differences were found between the test and the retest for the individual questions with the exception of the question for mean perceived vegetable intake. The discriminatory validity indicated the questionnaire could show differences across grade and gender levels for barriers of fruit and vegetables but not for other factors. Grade together with gender explained barriers to eating fruit and vegetables. Greater availability of fruit in the home and school was associated with higher frequency of consumption. CONCLUSIONS: The results of this study indicate the Pro-Children Eating Habits Questionnaire may be a reliable and valid tool for assessing fruit and vegetable consumption of children in the United States.

Dietary Intake Of Flavonoids And HDL- And LDL- Cholesterol In Two Black Ethnicities With And Without Type 2 Diabetes

Flavonoids are a class of over 6,500 plant metabolites that have been associated with reduced mortality from cardiovascular disease. A cross-sectional analysis of dietary flavonoids and serum cholesterol in 507 Blacks with and without type 2 diabetes (258 Haitian-Americans and 249 African-Americans) showed differences by ethnicity and diabetes status. Haitian-Americans consumed more of most flavonoids as compared to African-Americans. Individuals with type 2 diabetes consumed less of most flavonoids as compared to those without diabetes. Flavonoids were differentially associated with low-density lipoprotein cholesterol (LDL) and high-density lipoprotein cholesterol (HDL) by diabetes status. Flavanones were associated with lower LDL for participants without diabetes and higher LDL for those with diabetes, independent of ethnicity and adjusted for age, gender, cholesterol medications, daily energy, dietary fat, body mass index (BMI), and smoking. Flavan-3-ols were positively related to LDL while polyflavonoids (theaflavin and polymers, proanthocyanidins) were inversely related to LDL for the group without diabetes only. Higher anthocyanidins and flavan-3-ols and lower polyflavonoids were associated with higher HDL (same adjustments) for those without diabetes, whereas no flavonoids were associated with HDL for individuals with type 2 diabetes.