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.^

Food availability in the home and dietary intake of the Harris County Department of Education Head Start population

Background. The prevalence of obesity and overweight children has been an ongoing health epidemic in the US for the last several decades. The problem has consistently worsened and has disproportionately been the most prevalent among low socioeconomic status (SES) populations. Food availability in the home has been suggested to be a potential factor related to overweight and obesity, as availability is likely associated with intake. Food availability of low SES preschool aged children has not been well examined. The purpose of this study was to explore the food environment of the Harris County Department of Education (HCDE) Head Start population, and describe reported frequency of intake of particular food groups. The effect of food availability on reported intake was also examined.^ Methods. This was a cross-sectional study of secondary data analysis. Data obtained from 17 HCDE Head Start Centers was analyzed using PASW 18 Statistical Software. Demographic analyses included population, age, gender, race, parent occupation, type of home, and language spoken in the home. Descriptive statistics included reported availability of foods in the home as well as frequency of intake.^ Regression analysis examined the relationship of availability of foods on intake. The food categories included were: dark leafy green and orange vegetables, other vegetables, fruits, soda, salty snacks, and sweet snacks. For both vegetable categories reported intake of fresh, frozen, and canned vegetables were included. For the fruit category, intake of fresh, frozen, canned, and dried fruits were reported.^ Results. Results showed that 90-95% of parents reported having vegetables and fruits available in the home. However, the only significant relationship between availability and intake was for fresh fruit and dried fruit. No associations were seen among the vegetable groups. Other vegetables (bell peppers, eggplant, tomatoes, onions, iceberg lettuce, asparagus) that were frozen, approached significance for availability on intake, however once adjusted for confounders the relationship was no longer present. Among soda, salty snacks, and sweet snacks the only significant relationship was seen for soda availability and intake. Salty snacks and sweet snacks presence in the home was not a predictor of increased frequency of intake.^ Conclusions. This research supported the hypothesis that availability of foods has an impact on intake for fresh fruits, dried fruits and soda. No associations were seen for vegetables, salty snacks and sweet snacks. Additionally, most of the parents reported having fruits and vegetables in the home, but reported intakes were not meeting the Dietary Guidelines for Americans recommendations. Strengths of the study included the large sample size taken from numerous HCDE Head Start Centers. Limitations included questionable reliability of participant’s responses, ability to generalize to other populations, and the use of secondary data rather than prospectively collected data.^