Semiparametric regression is concerned with the flexible incorporation of non-linear functional relationships in regression analyses. Any application area that benefits from regression analysis can also benefit from semiparametric regression. Assuming only a basic familiarity with ordinary parametric regression, this user-friendly book explains the techniques and benefits of semiparametric regression in a concise and modular fashion. The authors make liberal use of graphics and examples plus case studies taken from environmental, financial, and other applications. They include practical advice on implementation and pointers to relevant software. The 2003 book is suitable as a textbook for students with little background in regression as well as a reference book for statistically oriented scientists such as biostatisticians, econometricians, quantitative social scientists, epidemiologists, with a good working knowledge of regression and the desire to begin using more flexible semiparametric models. Even experts on semiparametric regression should find something new here.

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Multiple-day food records or 24-hour dietary recalls (24HRs) are commonly used as "reference" instruments to calibrate food frequency questionnaires (FFQs) and to adjust findings from nutritional epidemiologic studies for measurement error. Correct adjustment requires that the errors in the adopted reference instrument be independent of those in the FFQ and of true intake. The authors report data from the Observing Protein and Energy Nutrition (OPEN) Study, conducted from September 1999 to March 2000, in which valid reference biomarkers for energy (doubly labeled water) and protein (urinary nitrogen), together with a FFQ and 24HR, were observed in 484 healthy volunteers from Montgomery County, Maryland. Accounting for the reference biomarkers, the data suggest that the FFQ leads to severe attenuation in estimated disease relative risks for absolute protein or energy intake (a true relative risk of 2 would appear as 1.1 or smaller). For protein adjusted for energy intake by using either nutrient density or nutrient residuals, the attenuation is less severe (a relative risk of 2 would appear as approximately 1.3), lending weight to the use of energy adjustment. Using the 24HR as a reference instrument can seriously underestimate true attenuation (up to 60% for energy-adjusted protein). Results suggest that the interpretation of findings from FFQ-based epidemiologic studies of diet-disease associations needs to be reevaluated.

The sandwich estimator, also known as robust covariance matrix estimator, heteroscedasticity-consistent covariance matrix estimate, or empirical covariance matrix estimator, has achieved increasing use in the econometric literature as well as with the growing popularity of generalized estimating equations. Its virtue is that it provides consistent estimates of the covariance matrix for parameter estimates even when the tted parametric model fails to hold or is not even speci ed. Surprisingly though, there has been little discussion of properties of the sandwich method other than consistency. We investigate the sandwich estimator in quasi-likelihood models asymptotically, and in the linear case analytically. We show that under certain circumstances when the quasi-likelihood model is correct, the sandwich estimate is often far more variable than the usual parametric variance estimate. The increased variance is a xed feature of the method and the price that one pays to obtain consistency even when the parametric model fails or when there is heteroscedasticity. We show that the additional variability directly affects the coverage probability of con dence intervals constructed from sandwich variance estimates. In fact, the use of sandwich variance estimates combined with t-distribution quantiles gives con dence intervals with coverage probability falling below the nominal value. We propose an adjustment to compensate for this fact.

The Healthy Eating Index (HEI), a measure of diet quality, was updated to reflect the 2010 Dietary Guidelines for Americans and the accompanying USDA Food Patterns. To assess the validity and reliability of the HEI-2010, exemplary menus were scored and 2 24-h dietary recalls from individuals aged ≥2 y from the 2003-2004 NHANES were used to estimate multivariate usual intake distributions and assess whether the HEI-2010 1) has a distribution wide enough to detect meaningful differences in diet quality among individuals, 2) distinguishes between groups with known differences in diet quality by using t tests, 3) measures diet quality independently of energy intake by using Pearson correlation coefficients, 4) has >1 underlying dimension by using principal components analysis (PCA), and 5) is internally consistent by calculating Cronbach's coefficient α. HEI-2010 scores were at or near the maximum levels for the exemplary menus. The distribution of scores among the population was wide (5th percentile = 31.7; 95th percentile = 70.4). As predicted, men's diet quality (mean HEI-2010 total score = 49.8) was poorer than women's (52.7), younger adults' diet quality (45.4) was poorer than older adults' (56.1), and smokers' diet quality (45.7) was poorer than nonsmokers' (53.3) (P < 0.01). Low correlations with energy were observed for HEI-2010 total and component scores (|r| ≤ 0.21). Cronbach's coefficient α was 0.68, supporting the reliability of the HEI-2010 total score as an indicator of overall diet quality. Nonetheless, PCA indicated multiple underlying dimensions, highlighting the fact that the component scores are equally as important as the total. A comparable reevaluation of the HEI-2005 yielded similar results. This study supports the validity and the reliability of both versions of the HEI.