Improving power with repeated measures

In their study, Marshall et al (1) found a significant relation between serum LDL cholesterol and saturated fat intake when random-effects models for longitudinal data were used. The model parameters were estimated by using data on 928 participants from the San Luis Valley of southern Colorado. Nutritional intakes were measured by the 24-h recall method; 2 observations were available for LDL cholesterol and nutrient intakes for most subjects. The models controlled for sex, age, body mass index, and energy intakes. The authors emphasized that significant associations were observed only in the 2 cases (models C and D) in which the statistical procedures took into account individual specific random effects. The earliest studies by Keys et al (2, 3) emphasized the importance of the role of cholesterol intakes on serum cholesterol concentrations. Because of the poor fit of the model, intakes of saturated and polyunsaturated fats were also introduced; functional forms were empirically selected. In a subsequent study of 46 adults in the Boston area, Kushi et al (4) reported significant partial correlations between serum cholesterol and intakes of dietary cholesterol and saturated fat. Thus, a natural starting point for the statistical models estimated by Marshall et al would have been to also include intakes of dietary cholesterol and polyunsaturated fat in their regression models. Furthermore, because cholesterol intakes exhibit high within-subject variation (5), and because the authors relied on 24-h dietary recalls for measuring nutrient intakes, it is plausible that the reported coefficients of saturated fat intakes were not robust to changes in model specification. The authors should have reported results for a model that included saturated and polyunsaturated fat and cholesterol intakes as regressors. It would be interesting to see whether the results with such a model would support results obtained with the Keys equation, which is often used for approximating serum cholesterol concentrations in groups of individuals. From an estimation standpoint, it seems preferable to treat fat intakes as continuously measured variables. The estimated coefficients from the expanded model would show the relative importance of saturated fat and cholesterol intakes for serum LDL. Second, because approximately half of cholesterol is endogenously produced, an individual’s current serum cholesterol concentration is likely to depend heavily on the measurement in the previous period. Dynamic models, which allow the dependent variable (serum cholesterol) to depend on its previous value, can be estimated by the principle of maximum likelihood in the presence of time-varying covariates (6–8). These models also take into account individual specific random effects that are assumed to be multivariate and normally distributed; equation 2 in Marshall et al’s article is a special case of the general formulation. Dynamic models and the “static” formulations used by Marshall et al are potentially useful for modeling serum cholesterol. However, because of the endogenous production of cholesterol, the underlying biological relations are perhaps better suited to dynamic modeling. With only 2 time observations available in the data used by Marshall et al, the empirical results from dynamic and static models are likely to be close. However, the model parameters have been interpreted differently. For example, it seems somewhat unlikely that serum LDL will decline immediately by 0.14 mmol/L after a 20-g decrease in saturated fat intakes on the day of a 24-h recall survey. Rather, there are complex delays underlying the relation between dietary intakes and serum LDL. One might be able to analyze these relations more systematically by using data from studies such as the Women’s Health Trial Vanguard Study (9) and the Women’s Health Trial Feasibility Study in Minority Populations (10), from which multiple observations on serum cholesterol and 4-d food records are available for relatively shorter time intervals. Last, Marshall et al state that “parameter estimates for age were so different in models A and B than in models C and D” (models A and B did not allow for individual specific random effects). The authors attributed these differences to the underlying differences in LDL-cholesterol concentrations in different age cohorts. However, an alternative explanation would be that the subject-specific random effects partially reflected the age distribution of the sample. Because the authors apparently used discrete groups to represent age, the random effects are likely to further detect age differences in serum LDL cholesterol. This in turn would decrease the magnitude of the coefficient of age in models that include random effects. Evidently, this is the case when one compares the estimated coefficients of age in models A and B with those in models C and D in Table 3 (1).