The present study demonstrated how information inherent in the shape of OGTT glucose curves can be extracted. The FDA approach yielded quantifiable shape entities with physiologically interpretable information that was not contained in the traditional simple summary measures. The extracted shape information differed significantly between women who did and did not develop GDM, and between subgroups of women diagnosed with GDM later in pregnancy, while various simple summary measures did not.
The challenge of extracting shape information from glucose curves has been addressed by others [11–14], but these studies have focused on either simple shape indices or advanced parametric modelling. The present study is the first to use statistical tools and corresponding available software developed specifically for curves, to analyse OGTT data.
Our results were based on a large and relatively homogenous sample of healthy, pregnant women, but on a small number of glucose measurements per woman, as compared to those of an intravenous glucose tolerance test. One might expect to find even more physiologically interesting details and discriminating features of OGTT glucose curves, e.g. a larger number of FPCs with a substantial percentage of explained variability and more temporal details in the FPCs, in a more heterogeneous population with a more frequent OGTT sampling. For instance, our fitted curves could not reveal more than two peaks, but curves based on more densely sampled measurements over a longer time period than 2 h would likely show decreasingly oscillating curves rather than purely biphasic trajectories . We therefore proposed the term “oscillating” as a qualitative description of OGTT glucose curves with more than one peak rather than using the term “biphasic”, which has been used by others [12, 14]. Furthermore, the classification of OGTT glucose curves as “biphasic”, “monophasic” or “unclassified”, involves several ad hoc conditions . In the present study, we used FPC scores as continuous variables, as per general statistical recommendations, as this is the first choice of analysis in order to retain information and statistical power .
The mean of the fitted curves obtained from FDA (Figures 1, 2, 3) corresponded well with the familiar general shape of OGTT glucose curves [6, 34, 35]. In the literature in general, figures and analyses are usually based on the means at selected time points, with variability quantified by the SD or SE at the same time points, e.g. when comparing glucose responses . In general, as seen in Figures 1, 2 and 3, the temporal mean under-communicates the temporal variability. Although individual glucose curves have been presented in several publications [14, 35, 36], the variability in curve trajectories is highly under-reported, and thus largely unknown. As a result, the information indicated by the shape of OGTT glucose curves is rarely used in clinical practice, and only occasionally in research, although the standard practice of taking repeated blood samples during OGTT suggests a focus on the curve. We have presented the individual, fitted curves in order to emphasise the heterogeneity between our study women and to provide a reference for OGTT glucose curves in healthy, pregnant women.
While a FPCA will decompose the variation between individual curves into a set of uncorrelated, temporal features, the clinical usefulness of this analysis depends on how the FPCs are interpreted. In this study, current insight into metabolism supported the interpretations of the FPCs as plausible and important physiological features. FPC1, which represented the general level and was the most important temporal feature of the curves, was almost perfectly correlated with AUC, and was significantly higher in women with high BMI. The fasting value and the 2-h value were also correlated with FPC1, but not as strongly as AUC. This is to be expected as a single measurement from a temporal phenomenon rarely describes the most essential temporal feature of the corresponding curve satisfactorily. Moreover, AUC is much better than the widely used fasting, or 2-h value in capturing the essential temporal information of OGTT glucose curves, which is consistent with results from previous studies [37–39]. The strongest association between the shape index and the FPC scores was found for FPC3 scores, which explained the smallest proportion of the total variance. This proportion was so small that FPC3 could have been left out of the analyses. We chose to include FPC3 for the comparison of FDA with the shape index. The shape index is based on an a priori classification of curves, involving an ad hoc set threshold for change. Many curves (27%) failed to meet the classification criteria and were left out of the analyses, resulting in a severe reduction of power and a biased representation of metabolic profiles in the study sample. Another, recently suggested shape index  is based on a rough approximation of the mean of the second order derivatives in the intervals between the measurements during the OGTT, giving a rough approximation of the total curvature. In the present study, FPC3 scores, representing the smallest proportion of the variance, quantified the amount of curvature. The shape feature of FPC3 was however less clear than for the first two components, and although it is possible that the third component might explain a larger part of the total variation if the sampling was more frequent and over a longer time period, this component should be used and interpreted with caution.
Glucose tolerance early in pregnancy has been found to predict glucose tolerance later in pregnancy . The FPC1 scores, 2-h values and AUC differed significantly between groups of women without a GDM diagnosis at gestational weeks 30–32. However, only FPC2 scores were significantly different between women with and without GDM and only FPC2 and FPC3 scores differed significantly between diabetic women with the highest and second highest 2-h values in the third trimester. Thus, FPC1 or AUC alone did not capture all of the essential information about the differences in glucose metabolism. To distinguish curve trajectories reflecting deviating glucose tolerance from those considered normal, the information from FPC2 and FPC3 was necessary. A study of type 1 diabetes mellitus patients with islet transplantations showed that increased glucose AUC and time to peak C-peptide after metabolic testing were metabolic markers of islet allograft dysfunction , supporting the physiological importance of both FPC1 and FPC2 scores. The timing of the peak C-peptide was also found to be predictive of progression to type 1 diabetes mellitus in the Diabetes Prevention Trial .
The alternative to data-driven approaches such as FPCA for analysing full glucose curves is parametric modelling based on differential equation models of physiological mechanisms. Current concepts of blood glucose dynamics have been summarised in such models [14, 43–45]. For instance, blood glucose levels and, hence, the shapes of glucose curves are affected by a number of key organs and physiologic processes that regulate the entry and removal of glucose from the blood [12, 46]. A major disadvantage of parametric models is that estimating each person’s individual parameters requires many measurements, often based on intravenous test procedures . Although the use of OGTTs is debated , it is the simplest and most frequently used test procedure in larger studies because “gold-standard” intravenous procedures such as the euglycaemic clamp  are time-consuming, invasive and labour intensive.
Another important issue with parametric models of blood glucose regulation is the “closed loop” assumption, which can be hard to justify when modelling biological processes in the body because such processes are usually also susceptible to external influences. Diet, physical activity, obesity, changes in weight or visceral fat deposits, smoking and stress have all been shown to affect blood glucose levels  and external factors can have long-term effects on metabolism . The genetic disposition of each individual adds to this complexity . Finally, pregnancy causes alterations in a wide range of variables, including hormonal changes, insulin resistance and alterations in daily life habits. Nevertheless, parametric models seldom adjust for confounding by external variables [14, 44, 45]. Hence, even when parametric models seem to fit the data well, the error term for fit can include structural information not addressed in the pre-defined model, including information on the long-term effects of diet and the endocrine changes caused by pregnancy itself. This can make it difficult to validate the physiological theories underlying parametric models.
Although FDA or parametric modelling are the most natural approaches to glucose data for the study of glucose curves as single entities, there are alternatives to these analyses for the data presented in this article. For instance, the relation between BMI and glucose values could have been examined with a classical longitudinal data analysis with five repeated measurements per woman, with random effect of woman and modelling of the covariance structure. Also, instead of scores from FPCA, ordinary PCA scores based on the five glucose variables could be used as input to the regression analysis of glucose tolerance later in pregnancy. With only five measurements per curve, and measurements taken at the same time points for each woman, such traditional multivariate methods would be expected to extract similar information as the FDA. However, FDA is easier to apply in situations with more frequent sampling, sampling at unequal time points and missing data. In addition, FDA emphasizes the basic assumption about continuity of the underlying process and its derivatives, and opens for analysis of the derivatives of the curves.
Contrary to general statistical advice , we have categorised two continuous variables in the analyses. An important aim of the present work was to introduce FDA and its benefits to a clinical audience. To ease the presentation of FDA, we chose to categorise BMI and the 2-h glucose at gestational weeks 30–32, based on the use of these variables in clinical practice. Different BMI categories are assumed to represent different risk groups , and BMI categories are frequently reported in clinical literature. The categorised BMI variable was therefore used in the analyses, although functional regression with BMI as a continuous variable would be preferable from a statistical point of view , especially as there were no obvious signs of nonlinearity (Figure 4a). The categorisation of the 2-h glucose value at gestational weeks 30–32, in contrast, revealed important non-linear relations (Figure 6). As an alternative to the multinomial logistic regression model, a regression model with the 2-h value as a continuous response variable could have been used.
The women in the cohort underwent two OGTTs, but only one was considered functional in the present work. We chose the 2-h value in third trimester as the main outcome instead of the entire curve in third trimester, due to the clinical relevance of this value in pregnancy care. As glucose curves are not commonly used, inference about the 2-h value would better illustrate the usefulness of information from FDA for a maternal pregnancy outcome in clinical practice.
Continuous glucose monitoring devices allow for more frequent glucose sampling over longer periods and might increasingly be used in future studies and in individual patient care to obtain OGTT measurements and measurements of glucose profiles in daily life. An increasing use of continuous glucose monitoring advocates the use of statistical tools that can properly analyse the continuous stream of data by providing curves that may be subjected to FDA as illustrated in the current work.
Furthermore, comparison of curve shape information from individuals with insulin resistance or beta cell failure might reveal whether curve features can distinguish between these two main processes that lead to the development of diabetes. Also, the curve shape information as obtained by FPCA in early pregnancy has the potential to predict complications in later pregnancy better than simple summary measures.
Our work shows that the FDA approach worked well, despite the very limited number of measurements for each participant. Dynamic, physiological processes will often be represented by scarcely sampled measurements, especially when repeated blood samples are required. In addition to glucose regulation, other examples where an FDA approach can be valuable include diurnal measurements of hormone regulation, metabolic changes during or after meals, or after physical exercise. The presented techniques should therefore also be explored in studies of metabolic disorders in non-pregnant populations.