Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

Micronutrient intakes and their associations with markers of inflammation, subclinical atherosclerosis, cardiovascular disease, type II diabetes and metabolic syndrome

We investigated cross-sectional associations between intakes of zinc, magnesium, heme- and non heme iron, beta-carotene, vitamin C and vitamin E and inflammation and subclinical atherosclerosis in the Multi-Ethnic Study of Atherosclerosis (MESA). We also investigated prospective associations between those micronutrients and incident MetS, T2D and CVD. Participants between 45-84 years of age at baseline were followed between 2000 and 2007. Dietary intake was assessed at baseline using a 120-item food frequency questionnaire. Multivariable linear regression and Cox proportional hazard regression models were used to evaluate associations of interest. Dietary intakes of non-heme iron and Mg were inversely associated with tHcy concentrations (geometric means across quintiles: 9.11, 8.86, 8.74, 8.71, and 8.50 µmol/L for non-heme iron, and 9.20, 9.00, 8.65, 8.76, and 8.33 µmol/L for Mg; ptrends <0.001). Mg intake was inversely associated with high CC-IMT; odds ratio (95% CI) for extreme quintiles 0.76 (0.58, 1.01), ptrend: 0.002. Dietary Zn and heme-iron were positively associated with CRP (geometric means: 1.73, 1.75, 1.78, 1.88, and 1.96 mg/L for Zn and 1.72, 1.76, 1.83, 1.86, and 1.94 mg/L for heme-iron). In the prospective analysis, dietary vitamin E intake was inversely associated with incident MetS and with incident CVD (HR [CI] for extreme quintiles - MetS: 0.78 [0.62-0.97] ptrend=0.01; CVD: 0.69 [0.46-1.03]; ptrend =0.04). Intake of heme-iron from red meat and Zn from red meat, but not from other sources, were each positively associated with risk of CVD (HR [CI] - heme-iron from red meat: 1.65 [1.10-2.47] ptrend = 0.01; Zn from red meat: 1.51 [1.02 - 2.24] ptrend =0.01) and MetS (HR [CI] - heme-iron from red meat: 1.25 [0.99-1.56] ptrend =0.03; Zn from red meat: 1.29 [1.03-1.61]; ptrend = 0.04). All associations evaluated were similar across different strata of gender, race-ethnicity and alcohol intake. Most of the micronutrients investigated were not associated with the outcomes of interest in this multi-ethnic cohort. These observations do not provide consistent support for the hypothesized association of individual nutrients with inflammatory markers, MetS, T2D, or CVD. However, nutrients consumed in red meat, or consumption of red meat as a whole, may increase risk of MetS and CVD.^

Public service use by residents of Jackson Hinds Gardens before and after enrollment

Homelessness is associated with high use of public services such as health care and criminal justice services. Intervention designs to reverse homelessness have broadly fallen into two categories: either standard care which employs requisitely addressing the causes of homelessness, or housing first, which emphasizes provision of permanent housing without requisitely addressing the causes of homelessness. Multiple cities have recently commenced housing first interventions. Locally, Houston’s first housing first development is the Jackson Hinds Gardens project. The purpose of this study is to analyze the public service use of residents of housing first in Houston. Residents of Jackson Hinds Gardens who have been enrolled for at least 6 months were evaluated for public service use for an equal amount of time preceding and during their residence at Jackson Hinds. Resident interactions with county health services and criminal justice entities were determined by electronic database searches; these data were supplemented by life experience interview data. Service usage values pre- and post-enrollment at Jackson Hinds Gardens were compared by paired t-test analyses. We found that ER and inpatient usage decreased following enrollment in Jackson Hinds, although these reductions were not significant. In contrast, outpatient care and number of medications significantly increased following enrollment. These analyses inform on the effects of housing first in another major city, as well as informing the ethical considerations regarding housing first versus standard care. ^

Nutritional factors and the risk of cervical dysplasia

A case comparison study of 159 women was conducted to test the hypotheses that women with cervical dysplasia had a higher prevalence of low dietary intakes of carotenoids, vitamin C, and folacin than women without cervical dysplasia, and that there would be no association between the risk of having cervical dysplasia and dietary intake of retinol. Information regarding the prevalence of known risk factors for cervical dysplasia, early age at first intercourse, multiple sexual partners, early age at first pregnancy, history of having sexually transmitted diseases, cigarette smoking, and sociodemographic data was collected. Dietary intake was estimated using a 97 item quantified food frequency questionnaire designed to obtain information on consumption of all sources of retinol, carotenoids, vitamin C and folacin. Univariate analyses showed that the presence of cervical dysplasia was positively and significantly associated with all the risk factors. In analyses of the association of the dietary variables with cervical dysplasia, information on carotenoid intake was calculated in two ways, as total carotenoid intake and as intake of lycopene and other carotenoids. While there appeared to be an inverse association between the presence of cervical dysplasia and intakes of lycopene and folacin, lower intake of retinol, total carotenoids, other carotenoids (non-lycopene carotenoids) or vitamin C did not increase the risk of having cervical dysplasia. Multivariable analyses showed that, in comparison to women who usually consume 105 RE/day of lycopene, the odds of having cervical dysplasia for women who consume 31-104 RE/day and 30 RE/day or less were 1.31 and 1.66 respectively. The odds of having cervical dysplasia in women who consume 199-396 mcg/day and 198 mcg/day or less of folacin were 2.66 and 2.97 respectively as compared to women who usually consume 397 mcg/day or more. These results suggest the importance of re-evaluating existing dietary data and planning in future studies to evaluate the associations of lycopene and folacin with cervical cancer, as well as to extend these results to other diet/cancer investigations. ^

The relationship between calcium and fluoride intake, pregnancy and lactation and the risk of height loss in white women

This study was designed to investigate the effect of calcium and fluoride intake, and parity and lactation on the risk of spinal osteoporosis. Height loss was used as a surrogate measure for spinal fractures by taking advantage of documented changes in height found during the 25-year follow-up of the Charleston Heart Study cohort. Women who had lost 2-4" in height or who had no change in height during the follow-up period were defined as case and comparison subjects respectively. Calcium intake when the subjects were "about 25" and in the recent past, average intake of fluoride over 25 years, and parity and history of breastfeeding were ascertained by questionnaire from 54 case and 77 comparison subjects. Low calcium intake in the past decreased the risk of height loss (age-adjusted OR = 0.3, 95%CI: 0.1-0.96) although several potentially important confounding variables could not be adjusted for. There was no association between risk of height loss and present calcium intake (OR = 0.8, 95%CI: 0.3-2.6 for low versus high intake) after adjustment for past calcium intake. High fluoride intake decreased the risk of height loss (adjusted OR = 0.4, 95%CI: 0.1-1.2). The effect of fluoride or calcium intake in the present was modified by the level of the other nutrient. Compared to a low intake of both calcium and fluoride, a high intake of one increased the risk of height loss (crude OR = 3.3 for high fluoride/low calcium, crude OR = 6.0 for high calcium/low fluoride) although a high intake of both was slightly protective (crude OR = 0.7). It is estimated that a "high" nutrient intake in this population was greater than 850mg/day for calcium and 2mg/day for fluoride. After adjustment for age, increasing parity decreased the risk of height loss in women who had never breastfed (OR = 0.2, 95%CI: 0.01-1.7 for 4 or more children). Women who had breastfed were also at lower risk of height loss than nulliparous women (OR = 0.3, 95%CI: 0.1-1.2 for 4 or more children) although at any level of parity, breastfeeding women had a greater risk of height loss than did non-breastfeeding women. ^

Cardiovascular disease risk factors in Hispanic children identified through a diabetic proband

Prevalence and mortality rates for non-insulin dependent (Type II) diabetes mellitus are two to five times greater in the Mexican-American population than in the general U.S. population. Diabetes has been associated with risk factors which increases the likelihood of developing atherosclerosis. Relatives of noninsulin dependent diabetic probands are at increased risk of developing diabetes; and offspring of diabetic parents are at greater risk. Elevation in risk factor levels clearly began to develop prior to adulthood. Therefore an excess of these risk factors are expected among offspring and relatives of diabetics.^ The purposes of this study were to describe levels of risk factors within a group of Mexican American children who were identified through a diabetic proband, and to determine if there was a relationship between risk factor levels and heritability. Data from three hundred and seventy-six children and adolescents between the ages of 7 and 13 years, inclusively, were analyzed. These children were identified through a diabetic proband who participated in the Diabetes Alert Study. This study group was compared to a representative sample of Mexican American children, who participated in the Hispanic Health and Nutrition Examination Survey.^ For females, there were statistically significant associations between upper body fat distribution and increased systolic and diastolic blood pressure after adjusting for age and measures of fatness. Body mass index was positively related to and explained a significant portion of the variability in systolic blood pressure, total cholesterol, and HDL-cholesterol, for males only. No relationship was found between degree of relationship to the diabetic proband and risk factor levels. The most likely explanations for this were insufficient sample size to detect differences, and/or incomplete ascertainment of pedigree information.^ Although there was evidence that these Mexican American children are fatter and have more central fat distribution than non-Hispanic children, there is no evidence of increased risk for diabetes and/or cardiovascular disease at these ages. ^

A case-comparison study of weight fluctuations during young adulthood and coronary artery disease during middle age

The hypothesis that large fluctuations in weight during young adulthood are associated with the degree of coronary artery disease was investigated by comparing patterns of weight change of patients with angiographically defined diseased or normal arteries. Participants (n = 823) were selected from men and women aged 40-74 years who had undergone angiography at North Carolina Baptist Hospital during 1987-88. Weight history from age 20 to 40 was assessed with a mailed questionnaire. Per cent prevalence of "yo-yo dieting" adjusted for age, race, and coronary disease risk factors in patients who had 0, 1, 2, 3, or more than 3 diseased arteries was 8.6, 8.8, 3.7, 5.6 and 7.1 per cent respectively (p = 0.313). These results do not support the research hypothesis. However, since the results may have been confound by neuroticism, they should not be interpreted as strong evidence against this hypothesis. ^

Total cholesterol and anthropometric measurements distributions in a cross-sectional study of school children

Cross-sectional age and sex specific distributions of serum total cholesterol were described for 1091 children age 6-18 years, in The Woodlands, Texas. Associations of serum total cholesterol with five anthropometric measurements (weight, height, body mass index, arm circumference, and triceps skinfold thickness) were examined by correlation and regression analyses. Examination of serum total cholesterol distributions showed lower levels in boys than in girls for most of the age groups studied. Mean levels of total cholesterol peaked at age 9 for boys and 8 for girls. Serum total cholesterol leveled off until age 14 for boys and 11 for girls, and then dropped through age 18 for both boys and girls. These results support the hypothesis that serum total cholesterol concentration drops at pre-adolescence.^ Age adjusted correlations were observed between serum total cholesterol and triceps skinfold thickness for both boys and girls. This association was stronger in boys. Triceps skinfold thickness and arm circumference were consistently the strongest correlates for serum total cholesterol in boys. Weight and arm circumference were consistently the strongest correlates for serum total cholesterol in girls. ^

The effect of specific carotenoids on lung cancer risk

A population-based case-comparison study of histologically confirmed lung cancer among white male and female residents of six Texas coastal counties was conducted from 1979-1982. Dietary information as well as information concerning smoking, alcohol consumption, occupational and residential exposures, and family history of cancer was obtained from 149 living cases and 359 comparison subjects.^ These data support the findings of previous studies that reported a protective association of total carotene intake with lung cancer (OR = 4.07, CI = 3.36-4.78), and no association for total Vitamin A or retinol. Of six specific carotenoids examined, these data reveal a statistically significant protective effect for alpha carotene (OR = 3.58, CI = 2.85-4.31), and an elevated, although non-significant effect for beta carotene (OR = 1.46, CI = 0.61-2.31). No consistent significant effect was found for cryptoxanthin, other xanthins, lutein or lycopene.^ Similar results were found for both males and females, and for both squamous cell and adenocarcinoma subtypes, although loss of power resulting from stratification may have rendered the celltype specific results more imprecise. These results should be considered with caution until confirmed by other studies, however, they suggest the importance of evaluating specific carotenoids in future diet-lung cancer investigations. ^

A survey of statural changes with age in the adult population of the United States

A study of the patterns of height loss with age in the Anglo, black, and Mexican-American populations of the United States has been undertaken. The study was based on data gathered by the United States Public Health Service in the Second National Health and Nutrition Examination Survey and the Hispanic Health and Nutrition Examination Survey. Estimates of height loss were obtained by subtracting present stature from a calculated maximum attained height derived from sex- and race/ethnic-specific regression equations relating stature to subischial length. Anglo women have greater height losses than Anglo, black, or Mexican-American males, and black or Mexican-American females. Between 24 and 74 years of age, Anglo women average 3.8 cm. loss in stature. The black populations lose less height than Anglos or Mexican-Americans. Mexican-Americans lose less height than Anglos from 24 to 54 years and then have a greatly increased height loss so that by age 74 their total height loss is the same as Anglos. Standing height, sitting height, body mass index, and the Poverty Index were found to be negatively correlated with height loss. Age was positively correlated to height loss. The most important determinants of the magnitude of height loss with age were sex and ethnicity. ^

The prevalence of bulimia nervosa and bulimic behaviors among university students in Texas

This cross-sectional study examined by questionnaire the prevalence of bulimia nervosa and bulimic behaviors in a sample of 1175 undergraduate students enrolled in two state-supported universities in Texas. In one university, the student population was predominantly white; in the other, it was predominantly black. Fifty-nine percent of the respondents were female and 41% were male. Information regarding age, sex, ethnicity, college major, college year, marital status, housing arrangements, religion, socioeconomic status, height, weight, dieting behaviors, and family history of alcoholism, drug abuse, and depression was collected. Bulimia status was assessed using the Revised Bulimia Test (BULIT-R), which is based on the DSM-III-R criteria for bulimia nervosa. Only 1.3% of the females and 0.4% of the males were classified as having bulimia nervosa. The prevalence of bulimic behaviors was considerably higher; 6.4% of the females and 3.6% of the males were classified as having bulimic behaviors. Univariate analysis showed the following factors to be significantly associated with bulimic behaviors: female gender, single marital status, high BMI, a family history of alcoholism, drug abuse, or depression, and certain dieting behaviors. In the present study, ethnicity did not prove to be a significant factor associated with bulimia nervosa or bulimic behaviors. Multivariate analysis showed that, in comparison to normal/underweight individuals, the odds of having bulimic behaviors for severely overweight subjects were 2.23 (95% CI: 1.43, 3.50). Students who were dieting at the time of the study were 3.22 times (95% CI: 2.05, 5.06) as likely to have bulimic behaviors as were students who had never dieted. This study concludes there is a need to distinguish between bulimia nervosa and bulimic behaviors when estimating prevalence of a population. ^

Nonpurging binge eaters versus nonbinge eaters and treatment retention for adult obesity

Dropout from obesity treatment has been a major factor associated with weight control failure, with few reliable predictors of dropouts or completers. Previous studies have tended to treat obese people as a homogeneous group with standard behavior modification-based interventions. Current research indicates there may be subgroups within the obese population, binge eaters and nonbinge eaters, who have different dropout rates. Current studies also recommend focusing on the subset of this subgroup that does not engage in purging (vomiting, laxative abuse, or excessive exercise) to compensate for binge eating. This research uses a secondary dataset (N = 156) from a prospective study in which participants were randomized to a Food Dependency (FD) and a Behavioral Self-Management (BSM) group for weight reduction. Criteria for subjects in the original study included (1) scoring higher on the existing Binge Eating Scale (BES) in order to ensure enrollment of more binge eaters and (2) no compensatory purging behavior for binge eating. Subjects were then reclassified in this study as binge eaters or nonbinge eaters using the more stringent proposed 1994 DSM-IV criteria for Binge Eating Disorder (BED). Subjects were followed for dropout. Variables studied were binge status, age at obesity onset, age at study baseline, class instructor, number of previous weight loss attempts, race, marital status, body mass index (BMI kg/m$\sp2$), type of intervention, work status, educational level, and social support. Stepwise backward regression Cox survival analysis indicated binge status had a consistent, statistically significant protective effect on dropout in which binge eaters were half as likely to dropout versus nonbinge eaters (p = 0.04). Cox proportional hazards analysis indicated no statistical difference in dropout by type of intervention (FD, p = 0.13; BSM, p = 0.80) when controlling for binge status. All other variables did not reach significance, which is consistent with the literature. Implications of these findings suggest that (1) the proposed 1994 DSM-IV criteria for BED is a more useful classification that the existing DSM-III-R criteria, and (2) the identification of subgroups among obese subjects is an important step in dropout and weight loss intervention research. Future research can confirm this finding. ^

The association between CD4+ lymphocyte count and measures of body composition in HIV-infected men

Purpose. This project was designed to describe the association between wasting and CD4 cell counts in HIV-infected men in order to better understand the role of wasting in progression of HIV infection.^ Methods. Baseline and prevalence data were collected from a cross-sectional survey of 278 HIV-infected men seen at the Houston Veterans Affairs Medical Center Special Medicine Clinic, from June 1, 1991 to January 1, 1994. A follow-up study was conducted among those at risk, to investigate the incidence of wasting and the association between wasting and low CD4 cell counts. Wasting was described by four methods. Z-scores for age-, sex-, and height-adjusted weight; sex-, and age-adjusted mid-arm muscle circumference (MAMC); and fat-free mass; and the ratio of extra-cellular mass (ECM) to body-cell mass (BCM) $>$ 1.20. FFM, ECM, and BCM were estimated from bioelectrical impedance analysis. MAMC was calculated from triceps skinfold and mid-arm circumference. The relationship between wasting and covariates was examined with logistic regression in the cross-sectional study, and with Poisson regression in the follow-up study. The association between death and wasting was examined with Cox's regression.^ Results. The prevalence of wasting ranged from 5% (weight and ECM:BCM) to almost 14% (MAMC and FFM) among the 278 men examined. The odds of wasting, associated with baseline CD4 cell count $<$200, was significant for each method but weight, and ranged from 4.6 to 12.7. Use of antiviral therapy was significantly protective of MAMC, FFM and ECM:BCM (OR $\approx$ 0.2), whereas the need for antibacterial therapy was a risk (OR 3.1, 95% CI 1.1-8.7). The average incidence of wasting ranged from 4 to 16 per 100 person-years among the approximately 145 men followed for 160 person-years. Low CD4 cell count seemed to increase the risk of wasting, but statistical significance was not reached. The effect of the small sample size on the power to detect a significant association should be considered. Wasting, by MAMC and FFM, was significantly associated with death, after adjusting for baseline serum albumin concentration and CD4 cell count.^ Conclusions. Wasting by MAMC and FFM were strongly associated with baseline CD4 cell counts in both the prevalence and incidence study and strong predictors of death. Of the two methods, MAMC is convenient, has available reference population data, may be the most appropriate for assessing the nutritional status of HIV-infected men. ^

AN ATTEMPT TO MEASURE FOOD SAFETY STATUS

The main objective of this study was to attempt to develop some indicators for measuring the food safety status of a country. A conceptual model was put forth by the investigator. The assumption was that food safety status was multifactorily influenced by medico-health levels, food-nutrition programs, and consumer protection activities. However, all these in turn depended upon socio-economic status of the country.^ Twenty-six indicators were reviewed and examined. Seventeen were first screened and three were finally selected, by the stepwise multiple regression analysis, to reflect the food safety status. Sixty-one countries/areas were included in this study.^ The three indicators were life expectancy at birth with multiple correlation coefficient (R2 = 34.62%), adult literacy rate (R2 = 29.66%), and child mortality rate for ages 1-4 (R2 = 9.99%). They showed a cumulative R2 of 57.79%. ^

THE RECOVERY OF ENTEROPATHOGENS FROM CONTAMINATED COOKED FOODS AT HOLDING TEMPERATURES

Hot foods served in foodservice establishments, institutions and homes, have always been regarded as safe, since cooking temperatures are more likely to kill the bacterial agents that may cause foodborne diseases. However, foods that are otherwise served hot have been epidemiologically incriminated for causing foodborne diseases. This situation arises due to the possible post-cooking food contamination. Post-cooking contamination of hot-held food is most threatening for it gives the contaminating agents the possibility of proliferation. On one hand, post-cooking contamination is least understood and on the other, hot-holding of food gives the consumer a false sense of freedom from foodborne diseases. In this study, the dynamics of food contamination before or after cooking and during hot-holding are discussed and a food contamination dynamics model is presented.^ The literature on foodborne cholera, cholera-like diarrhea, shigellosis and E. coli gastroenteritis together with the literature on the occurrence and growth of the causative enteropathogens; 01 V. cholerae, non-01 V. cholerae, S. sonnei, S. flexneri and E. coli were reviewed. The literature on the infective doses of these organisms were also cited.^ In the study, four cooked food types held hot at 40-60(DEGREES)C were deliberately contaminated with 01 V. cholerae, non-01 V. cholerae, S. sonnei, S. flexneri and E. coli, one at a time at each of the hot-holding temperatures. Tested food samples for the recovery of these enteropathogens were withdrawn at various time intervals of hot holding.^ The results showed bacterial recovery to decline with increasing temperature and with increasing hot-holding time within each holding temperature. All the bacterial types except V. cholerae were recovered even after holding the food at 60(DEGREES)C for one hour. V. cholerae was not recovered after hot-holding the food at 50-60(DEGREES)C at certain holding periods. After 48 hrs incubation, V. cholerae was recovered on TCBS agar plates that read negative after the initial 24 hrs of incubation. Effective hot-holding temperatures were determined for each of the food types contaminated by each of the bacterial types.^ Statistical analysis of the collected data showed temperature, bacterial type and their interaction to be significant in enteropathogen recovery. Food type and its interactions with temperature and bacterial type were found not significant. ^