Changes in serum lipids with change and fluctuation in body mass index and body fat distribution in Mexican Americans with type 2 diabetes

This dissertation was written in the format of three journal articles. Paper 1 examined the influence of change and fluctuation in body mass index (BMI) over an eleven-year period, on changes in serum lipid levels (total, HDL, and LDL cholesterol, triglyceride) in a population of Mexican Americans with type 2 diabetes. Linear regression models containing initial lipid value, BMI and age, BMI change (slope of BMI), and BMI fluctuation (root mean square error) were used to investigate associations of these variables with change in lipids over time. Increasing BMI over time was associated with gains in total and LDL cholesterol and triglyceride levels in women. Fluctuation of BMI was not associated with detrimental lipid profiles. These effects were independent of age and were not statistically significant in men. In Mexican-American women with type 2 diabetes, weight reduction is likely to result in more favorable levels of total and LDL cholesterol and triglyceride, without concern for possible detrimental effects of weight fluctuation. Weight reduction may not be as effective in men, but does not appear to be harmful either. ^ Paper 2 examined the associations of upper and total body fat with total cholesterol, HDL and LDL cholesterol, and triglyceride levels in the same population. Multilevel analysis was used to predict serum lipid levels from total body fat (BMI and triceps skinfold) and upper body fat (subscapular skinfold), while controlling for the effects of sex, age and self-correlations across time. Body fat was not strikingly associated with trends in serum lipid levels. However, upper body fat was strongly associated with triglyceride levels. This suggests that loss of upper body fat may be more important than weight loss in management of the hypertriglyceridemia commonly seen in type 2 diabetes. ^ Paper 3 was a review of the literature reporting associations between weight fluctuation and lipid levels. Few studies have reported associations between weight fluctuation and total, LDL, and HDL cholesterol and triglyceride levels. The body of evidence to date suggests that weight fluctuation does not strongly influence levels of total, LDL and HDL cholesterol and triglyceride. ^

Selection bias and the cross-validation of regression models for prediction

Strategies are compared for the development of a linear regression model with stochastic (multivariate normal) regressor variables and the subsequent assessment of its predictive ability. Bias and mean squared error of four estimators of predictive performance are evaluated in simulated samples of 32 population correlation matrices. Models including all of the available predictors are compared with those obtained using selected subsets. The subset selection procedures investigated include two stopping rules, C$\sb{\rm p}$ and S$\sb{\rm p}$, each combined with an 'all possible subsets' or 'forward selection' of variables. The estimators of performance utilized include parametric (MSEP$\sb{\rm m}$) and non-parametric (PRESS) assessments in the entire sample, and two data splitting estimates restricted to a random or balanced (Snee's DUPLEX) 'validation' half sample. The simulations were performed as a designed experiment, with population correlation matrices representing a broad range of data structures.^ The techniques examined for subset selection do not generally result in improved predictions relative to the full model. Approaches using 'forward selection' result in slightly smaller prediction errors and less biased estimators of predictive accuracy than 'all possible subsets' approaches but no differences are detected between the performances of C$\sb{\rm p}$ and S$\sb{\rm p}$. In every case, prediction errors of models obtained by subset selection in either of the half splits exceed those obtained using all predictors and the entire sample.^ Only the random split estimator is conditionally (on $\\beta$) unbiased, however MSEP$\sb{\rm m}$ is unbiased on average and PRESS is nearly so in unselected (fixed form) models. When subset selection techniques are used, MSEP$\sb{\rm m}$ and PRESS always underestimate prediction errors, by as much as 27 percent (on average) in small samples. Despite their bias, the mean squared errors (MSE) of these estimators are at least 30 percent less than that of the unbiased random split estimator. The DUPLEX split estimator suffers from large MSE as well as bias, and seems of little value within the context of stochastic regressor variables.^ To maximize predictive accuracy while retaining a reliable estimate of that accuracy, it is recommended that the entire sample be used for model development, and a leave-one-out statistic (e.g. PRESS) be used for assessment. ^

DISTRIBUTION FUNCTIONS, MEAN SQUARED ERRORS, AND CONFIDENCE LIMITS FOR RIDGE REGRESSION ESTIMATORS

A large number of ridge regression estimators have been proposed and used with little knowledge of their true distributions. Because of this lack of knowledge, these estimators cannot be used to test hypotheses or to form confidence intervals.^ This paper presents a basic technique for deriving the exact distribution functions for a class of generalized ridge estimators. The technique is applied to five prominent generalized ridge estimators. Graphs of the resulting distribution functions are presented. The actual behavior of these estimators is found to be considerably different than the behavior which is generally assumed for ridge estimators.^ This paper also uses the derived distributions to examine the mean squared error properties of the estimators. A technique for developing confidence intervals based on the generalized ridge estimators is also presented. ^