Transitions from Ideal to Intermediate Cholesterol Levels may vary by Cholesterol Metric

To examine the ability of total cholesterol (TC), a low-density lipoprotein cholesterol (LDL-C) proxy widely used in public health initiatives, to capture important population-level shifts away from ideal and intermediate LDL-C throughout adulthood. We estimated age (≥20 years)-, race/ethnic (Caucasian, African American, and Hispanic/Latino)-, and sex- specific net transition probabilities between ideal, intermediate, and poor TC and LDL-C using National Health and Nutrition Examination Survey (2007–2014; N = 13,584) and Hispanic Community Health Study/Study of Latinos (2008–2011; N = 15,612) data in 2016 and validated and calibrated novel Markov-type models designed for cross-sectional data. At age 20, >80% of participants had ideal TC, whereas the race/ethnic- and sex-specific prevalence of ideal LDL-C ranged from 39.2%-59.6%. Net transition estimates suggested that the largest one-year net shifts away from ideal and intermediate LDL-C occurred approximately two decades earlier than peak net population shifts away from ideal and intermediate TC. Public health and clinical initiatives focused on monitoring TC in middle-adulthood may miss important shifts away from ideal and intermediate LDL-C, potentially increasing the duration, perhaps by decades, that large segments of the population are exposed to suboptimal LDL-C.

The supporting information has the following sections in order:

I. Estimation of net transition probabilities
Our approach to estimating net transition probabilities was built upon a foundation established by operations research, allowing us to view the estimation of age-specific net transition probabilities between cholesterol levels as a transportation problem. Briefly, the transportation problem was conceptualized by specifying supplies, demands, shipping costs, decision variables, and an objective function. The supplies were interpreted as smoothed prevalence proportions , where a represented age and i indexed the cholesterol level at age a-1, the demands were the prevalence proportions one year later , j indexed the cholesterol level at age a, the cost constants were specified beforehand (cij, see below), the decision variables were the net transitions ( , to be calculated) and the objective function J kept track of the total transportation costs between cholesterol levels at age a-1 to cholesterol levels at age a. The objective function J was then minimized: , subject to the conditions and . The conditions ensured that the total flow from cholesterol level i represented the supply of that level, that the total flow into cholesterol level j was equal to the demand of that level, the overall supply always equalled the overall demand, and that no transitions were negative. The net transition probabilities were then estimated as .

II. Calibration of net transition probabilities
Overview. Estimation of net transition probabilities requires the specification of a cost constant, cij, yet no study has attempted to calibrated cost constraints that describe movement within and between cholesterol levels using longitudinal data.
The prevalence for cholesterol category j at age ( 1) a  is The net transition probability is then obtained for each of the four race-sex groups and then averaged over the four groups.
We then used a numerical integration approach to calculate the integrals described in the above formulas. 3  The net transition probability obtained from the cross sectional model were based on the baseline value only. The cost parameters were searched in [0,20] with an increment of one, ensuring that the cost of remaining in the same group were less than that of transitioning to a different group and the cost of transitioning from category 0 to category 2 or category 2 to category 0 were larger than the sum of the other two cost parameters. The optimal cost parameters were then chosen as the parameters for which the calibration error was minimum.

Results.
Our results showed that net transitions estimated using optimized cost constraints of 2, 8, and 15 calculated using longitudinal CARDIA data produced net transitions and standard errors that differed on average less than 0.01% from net transitions estimated using initial cost constraints (0, 1, and 3), suggesting little influence of cost constraint definition on the estimation of net transitions or associated standard errors.

Validation of net transition probabilities
Overview. To evaluate the assumption that cholesterol levels transitions remained approximately III. Finally, we used locally weighted scatterplot smoothing (LOESS) to smooth the prevalence proportions across age.
Results. The results of the simulation are summarized in the following plot comparing expected and observed prevalence proportions in the population. From the plot we can see that the curve of the smoothed expected and observed proportion behave very similarly and are very close to each other which suggests that the cross sectional method performs well.

IV. Supplemental Tables
Supplementary Table 1