Clinical Application

In this section, we illustrate one of our method’s applications to clinical data arising from a clinical study of youth with type 1 diabetes (T1D). We first (Section 3.5.1) introduce the clinical study and explain the data we use. We then (Section 3.5.2) apply our method to these data and discuss the results.

3.5.1 CCAT study and data

T1D is the cell-mediated autoimmune destruction of the beta-cells of the pancreas, resulting in an absolute insulin deficiency and hyperglycemia. As a result, patients with type 1 diabetes are tasked with the daily management of blood glucose levels using exogenous insulin replace- ment in the form of multiple daily injections or continuous infusions (Mayer-Davis et al., 2018a; Association et al., 2018). Levels of blood glucose outside the normal range can lead to adverse consequences: sustained hyperglycemia, or high serum glucose, is associated with increased risk of complications such as cardiovascular disease and stroke (Nathan et al., 2014; Maahs et al., 2014), while acute hypoglycemia, or low serum glucose, invites the risk of coma or even death (Cryer et al., 2003). A growing body of research, however, suggests that due to its effect on ox- idative stress, the volatility of serum glucose may be as important as the raw levels, if not more, when it comes to predicting complications of T1D (Monnier et al., 2008; Saisho, 2014).

hemoglobin A1c does not capture transient glucose excursions or glycemic variability. With the recent emergence of continuous glucose monitoring (CGM) systems, which provide a reading of blood glucose levels on a minute-to-minute scale, attention has turned to this data to better characterize dysglycemia in the setting of type 1 diabetes. While the physiologic effect of in- sulin on blood glucose levels is causal and clear, the exact effect of physical activity and dietary intake can be more heterogenous and is less well-characterized, although these factors play im- portant parts in the overall management of diabetes (Wright and Hirsch, 2017; Beck et al., 2017; Monnier et al., 2008; Kilpatrick et al., 2008). Additionally, the exact nature of the dependence between blood glucose volatility and these factors is not well-studied, especially at the resolution that CGM data provide. Due to the density of blood glucose readings that CGM data provide as well as the physiologic and patient-oriented implications of blood glucose variabilty, we chose to apply our method to data arising from CGM. We note that best practices for linking measures of blood glucose process volatility to clinically meaningful thresholds of blood glucose variability remain to be established; however, our approach is at least as likely as existing methods to offer a sufficient resolution for system volatility to do so.

The Carbohydrate Counting in Adolescents with T1D (CCAT) study followed 30 adolescent outpatients with T1D over 5 days with the goal of measuring acute changes to their blood glu- cose levels as well as key factors known to affect blood glucose levels: insulin, dietary intake, and physical activity (Maahs et al., 2012). Participants wore a CGM and an accelerometer-based tracker of physical activity (PA) for these 5 days. During the entire course of the study, patients’ insulin doses were tracked, either by an insulin pump (20 participants) or an insulin pen record- ing multiple daily injections (10 participants). During day 1 and 3 of observation, participants logged their dietary intake, which was confirmed using time-stamped cell phone photographs. Di- etary intake was then divided into a number of macronutrient categories, including carbohydrates, fats, and protein.

3.5.2 Application to CCAT study

We illustrate a proof-of-concept of our method by applying it to data from one CCAT pa- tient. As the primary process of inferential and predictive interest in the CCAT study was blood glucose, we letX(·)represent blood glucose (mg/dL), whileH(·)contained PA (counts/min), bolus insulin dose (U), carbohydrates consumed (g), fat consumed (g), and protein consumed (g). As the effects of dietary data were of scientific interest, we limited ourselves to the two days containing dietary data. We averaged the data from this patient over ten-minute intervals, giving usn = 288evenly spaced measurements through the 2-day period.

The results of our CCAT analysis revealed a few interesting trends. First, all explanatory factors inZ(t)were found to have a significant effect on both the patient’s drift and volatility of blood glucose—that is,Sˆµ = ˆSσ = {1, . . . , p}. Given the posited causal links between blood glucose and the explanatory factors considered in this study, this should perhaps come as little shock for the glycemic drift; the fact that all factors appear to play a significant role in the volatility of blood glucose may represent an interesting finding worth exploring at a larger scale, though. The saturation of the regulator set has large potential implications on future interventions aimed at controlling blood glucose in a patient population similar to the patient analyzed here: namely, it suggests that physical activity, bolus dose, and the macronutrient breakdown are all important factors to consider intervening upon. We note, however, that this statement carries a hefty caveat: this is merely a proof-of-concept analysis. Substantial work must be done to study the properties of this method in already-collected data of this nature before we can make any practical suggestions for the collection of future research data. On the more technical side of things, we found thatM1 = 3andM2 = 6this patient. This mirrors the trend discussed in

Section 3.4.1: σ(·)appears to be a more complicated function thanµ(·), as using further basis depth to characterize its shape appears to be justified by cross-validation error.