Shape information from glucose curves: Functional data analysis compared with traditional summary measures

Abstract

Background Plasma glucose levels are important measures in medical care and research, and are often obtained from oral glucose tolerance tests (OGTT) with repeated measurements over 2–3 hours. It is common practice to use simple summary measures of OGTT curves. However, different OGTT curves can yield similar summary measures, and information of physiological or clinical interest may be lost. Our mean aim was to extract information inherent in the shape of OGTT glucose curves, compare it with the information from simple summary measures, and explore the clinical usefulness of such information.

Methods OGTTs with five glucose measurements over two hours were recorded for 974 healthy pregnant women in their first trimester. For each woman, the five measurements were transformed into smooth OGTT glucose curves by functional data analysis (FDA), a collection of statistical methods developed specifically to analyse curve data. The essential modes of temporal variation between OGTT glucose curves were extracted by functional principal component analysis. The resultant functional principal component (FPC) scores were compared with commonly used simple summary measures: fasting and two-hour (2-h) values, area under the curve (AUC) and simple shape index (2-h minus 90-min values, or 90-min minus 60-min values). Clinical usefulness of FDA was explored by regression analyses of glucose tolerance later in pregnancy.

Results Over 99% of the variation between individually fitted curves was expressed in the first three FPCs, interpreted physiologically as “general level” (FPC1), “time to peak” (FPC2) and “oscillations” (FPC3). FPC1 scores correlated strongly with AUC (r=0.999), but less with the other simple summary measures (−0.42≤r≤0.79). FPC2 scores gave shape information not captured by simple summary measures (−0.12≤r≤0.40). FPC2 scores, but not FPC1 nor the simple summary measures, discriminated between women who did and did not develop gestational diabetes later in pregnancy.

Conclusions FDA of OGTT glucose curves in early pregnancy extracted shape information that was not identified by commonly used simple summary measures. This information discriminated between women with and without gestational diabetes later in pregnancy.