Bimodal Distribution of Glucose Is Not Universally Useful for Diagnosing Diabetes

This study is based on the Evaluation of Screening and Early Detection Strategies for Type 2 Diabetes and Impaired Glucose Tolerance (DETECT-2) database, a worldwide collaborative study based on original data from population-based surveys of ≥500 participants (14). The individual studies have been described precisely (supplemental data, available in an online appendix at http://dx.doi.org/10.2337/dc08-0867). In this analysis, only studies in which plasma glucose was measured during a 75-g oral glucose tolerance test were included.

Participants who had been told by a doctor they had diabetes or who were receiving antidiabetes treatment (diet or medication) were defined as having known diabetes. All others were classified according to the WHO 1999 diagnostic criteria (15). Participants with one glucose value in the nondiabetic range and missing data for the other glucose value could not be classified according to the WHO criteria and were excluded. All analyses were performed first excluding and then including participants with known diabetes. In all surveys, participants gave their consent for participation in accordance with the Declaration of Helsinki.

Analyses were performed using R version 2.8.0. All analyses were stratified by country.

The distributions of both fasting plasma glucose (FPG) and 2-h plasma glucose are skewed to the right. To reduce skewness, glucose values were log transformed before model fitting. A normal distribution and a mixture of two normal distributions were fitted to the log-transformed glucose data. The probability density function for the normal distribution is as follows:

Here, μ and σ are the mean and SD of x. We fitted the normal distribution to data using the maximum likelihood method. The probability density function for the mixture model of two normal components is as follows:

Here, α and 1 − α are the mixture proportions with α between zero and unity. The mixture model was fitted using a combination of a Newton-type method and the expectation-maximization (EM) algorithm (16) (the normalmixEM2comp function from the Mixtools package in R).

To assess the presence of bimodality, the mixture model was compared with the unimodal distribution. The variance of the two components in the mixture model may differ. In that case, simulation results have shown that the limiting function for the likelihood ratio test is bounded by χ² distributions with 4 and 6 degrees of freedom (d.f.) (17). In this study, P values for significance of the mixture model were based on a χ² distribution with 4 d.f. A significance level of 5% was used.

A cut point for normal glycemia was calculated as the crossing point of the two normal distributions in the mixture model. Approximate CIs for the cut points were estimated by bootstrapping (1,000 bootstraps) (18).

The aim of this study was to detect whether distributions of FPG and 2-h plasma glucose give two distinct entities that may be used to separate individuals into two groups: those having normal or abnormal glycemia. For this separation to be biologically meaningful, the cut point separating these two entities should be between their modes (μ₁, μ₂). If not, the estimated cut point would not be useful because more than half of the individuals in the upper entity would have a glucose level below the cut point, which, consequently, would identify them as having normal glycemia.

Mixture models were fitted to the glucose values in each country to derive cut points for normal glycemia. In countries in which this cut point was biologically meaningful, the presence of bimodality was tested. As described in an earlier study on bimodality (10), the ability of a fitted mixture model to be statistically superior to a unimodal model depends on the sample size, the prevalence of diabetes, and the difference between the means of the two underlying distributions in units of SDs. In small samples, a lack of power may prohibit significance of the mixture model even when bimodality is truly present. To not be limited by lack of power, all biologically meaningful cut points for normal glycemia are reported in this article irrespective of the statistical significance of the mixture model.

This study included 135,383 participants with measurements of FPG and/or 2-h plasma glucose from 43 studies in 27 different countries covering 12 different geographic regions. Table 1 lists the characteristics of the study populations.

The prevalence of screen-detected diabetes (SDM) ranged from 0.7% in Cameroon to 14.7% in Nauru. Analysis was done by country, pooling the individual studies within a country. Because the individual studies varied in both sex and age distribution, the pooled data for a country do not necessarily reflect the age and sex distribution in that country. Individual records have not been weighted in the analyses.

The proportion of men and the age range varied among the countries. In studies including both sexes, men seemed slightly underrepresented. The Dutch and German studies were the oldest (49–89 and 55–74 years, respectively), whereas the French study was restricted to the middle-aged (44–55 years) population. In the remaining countries, age range was well represented. In all countries, prevalence of diabetes increased with age, with the only exception being Samoa, where a small decrease was observed.

For FPG, the mixture model resulted in a biologically meaningful cut point for normal glycemia in 5 of 27 countries (19%). Except for Singapore, the mixture model was also statistically superior to the unimodal model; i.e., bimodality was present (Table 2). The estimated cut points ranged from 6.1 mmol/l (95% CI 6.0–6.3) in Korea to 7.2 mmol/l (6.8–7.6) in Nauru (Fig. 1). Pooling the five meaningful cut points, the overall cut point for normal glycemia was estimated to be 6.7 mmol/l (6.5–6.9) (Fig. 2). This result is somewhat lower than the WHO diabetes diagnostic cut point for fasting plasma glucose of 7.0 mmol/l. Removing Singapore (where bimodality was not significant) from the pooled analysis decreased the overall estimated cut point by 0.2 mmol/l.

For 2-h plasma glucose, 8 of 26 countries (30%) produced a meaningful cut point. Except for Sweden, Spain, and Tonga, the mixture model was statistically superior (Table 2). The estimated cut points ranged from 8.5 mmol/l (95% CI 7.6–9.5) in Egypt to 12.7 mmol/l (7.6–14.9) in Taiwan (Fig. 1). The overall cut point was 11.0 mmol/l (10.6–11.4) (Fig. 2). This result corresponds to the WHO diabetes diagnostic cut point for 2-h plasma glucose of 11.1 mmol/l. Removing Sweden, Spain, and Tonga from the pooled analysis decreased the overall estimated cut point by 0.2 mmol/l.

All countries except two had measurements of FPG in participants with known diabetes (n = 103,410). Repeating the analyses for FPG including patients with known diabetes, 11 of 25 countries (44%) now produced a meaningful cut point. In only one of these 11 countries (Singapore) was the mixture model not statistically superior to the unimodal model (Table 2). The pooled cut point was 6.8 mmol/l (95% CI 6.7–6.8) both with and without Singapore, which is consistent with the result found when patients with known diabetes were excluded. In addition, the range in cut points was comparable: from 6.4 mmol/l (5.9–6.7) in India to 7.4 mmol/l (6.9–7.7) in Nauru.

Ten studies from eight different countries had measurements of 2-h plasma glucose in participants with known diabetes (n = 18,872). Of these, five (63%) produced a meaningful cut point for normal glycemia, and, in addition, the mixture model was significantly superior in Egypt, India, and the U.S. (Table 2). The corresponding pooled cut point was 10.9 mmol/l (95% CI 8.3–11.3), which was reduced by 0.6 mmol/l when Sweden and Japan, which had nonsignificant mixture models, were removed from the analysis. This result is also consistent with the result found when patients with known diabetes were excluded but with a greater range in the individual cut points from 8.2 mmol/l (7.8–8.7) in India to 13.6 mmol/l (12.8–14.7) in Sweden.

When known diabetes was excluded from the analysis, results from less than one-third of the countries were useful for deriving a cut point for normal glycemia in FPG and 2-h plasma glucose. Consequently, when known diabetes is removed, distributions of plasma glucose do not commonly give rise to a bimodal structure that is useful for deriving a cut point for diabetes. Inclusion of participants with known diabetes, although not universally present, more than doubled this proportion to 44% for FPG and 63% for 2-h plasma glucose. In most countries with a meaningful cut point, the mixture model was significantly superior to the unimodal normal model. This test was, however, based on a χ² distribution with 4 d.f. to err on the side of rejecting unimodality in favor of bimodality. These results indicate that the presence of a biologically meaningful bimodal structure in glucose seems to be driven by patients with known diabetes.

The overall pooled cut points for normal glycemia were almost invariant to whether or not participants with known diabetes were included. However, the estimated cut points were inconsistent between countries, especially for 2-h plasma glucose when participants with known diabetes were included. Comparing these results with those of earlier studies, we found that the overall cut point for FPG was somewhat lower (2,3,8,9), whereas the cut point for 2-h plasma glucose was well in line (1–3,5,8,10,11,13), except for the studies of South African Indians (9) and Western Samoans (12), which produced lower cut points for 2-h plasma glucose.

Earlier studies reported that bimodal structure in glucose distribution is more pronounced in the older age-groups, in whom the prevalence of diabetes is higher (1,2,5,8,9,11,12). We addressed the possible effect of age by considering the subpopulation aged ≥60 years (data not shown). In general, our main results were reproduced in this age-group. Only very few additional countries produced a biologically meaningful cut point, but again, including patients with known diabetes increased the proportion of meaningful bimodal structures. This finding is in line with an earlier study showing the mean of the upper normal component to be similar in different age-groups (4).

To increase sample size, we also pooled populations that were geographically in the same ethnic area: Caucasians, Africans, Asians, and Pacific Islanders (data not shown). A meaningful bimodal structure of data was only detected in half of the ethnic areas.

Excluding participants with known diabetes from the analyses reduces the prevalence of diabetes in the population by ∼50%, which may prohibit a significant fit of the mixture model. In addition, the mean of the second component is likely to be lower when patients with known diabetes that is more advanced are excluded. This exclusion potentially makes the two components less distinct and thereby decreases the probability of a meaningful cut point separating them. However, as acknowledged in previous studies (3,10,13), including patients with known diabetes in the analyses will induce a treatment bias for the following reasons. In accordance with existing treatment guidelines, patients with diabetes are treated with the aim of lowering their glucose to a near-normal range. This implies that diabetic patients with higher glucose values are treated relatively more aggressively than patients with only slightly raised glucose values. It seems reasonable to assume that aggressively treated patients have a larger absolute decrease in glucose values than patients who are treated less aggressively (19). Therefore, the effect of treatment is not an equal shift to the left in the glucose distribution of the entire diagnosed population but, rather, a shift that increases with glucose values at diagnosis (20). Hence, the glucose values of the subgroup with the highest values is shifted toward the glucose values of the rest of the diagnosed population. This means that patients with diagnosed diabetes are bunched together, thereby potentially creating an artificial bimodal structure in the glucose data.

How do we overcome this problem? The ideal setting for studying bimodality in glucose distribution is a treatment-naive population (including diabetes treatment) in whom diabetes is undiagnosed. This is not the case in any of the studies in this analysis. A theoretical solution to the problem is to adjust the measured glucose value of a treated patient to its untreated level. This would require knowledge of the exact effect of treatment for each patient. However, different doctors may prescribe different treatments to patients with the same glucose levels. In addition, even if the same treatment is administered, its effect will vary among patients because of differences in phenotype as well as in adherence to treatment. Hence, adjusted glucose values are highly uncertain. A study from Malaysia (10) suggested imputing glucose values for the patients with known diabetes using the measured glucose values of the participants with SDM in the same population and taking into account age, sex, ethnicity, and medical history of diabetes status. The model does not account for diabetes duration. However, glucose is known to increase with diabetes duration despite increasing treatment (21). Participants with SDM have, by definition, newly diagnosed diabetes, whereas patients with known diabetes may have had the diagnosis several years previously, which questions the validity of imputing their glucose values based on those of participants with SDM.

In summary, this study has shown that distributions of FPG and 2-h plasma glucose, in general, do not give rise to a bimodal structure that is useful for deriving a cut point for diabetes in populations of different origin. Including patients with known diabetes increases the possibility of deriving a meaningful cut point, but the bimodal structure in data may be a treatment artifact. In addition, cut points produced for normal glycemia were inconsistent over geographical regions. Thus, bimodality is not a suitable method for defining diagnostic cut points for diabetes. Instead, it seems more relevant to base the diagnostic criteria on thresholds for diabetes-specific micro- and macrovascular complications. However, further analyses are needed in this area.

DETECT-2 Writing Committee for this article. Dorte Vistisen, MSc, PhD, Steno Diabetes Center, Gentofte, Denmark; Prof. Stephen Colagiuri, MD, Department of Medicine, University of Sydney, Sydney, Australia; and Prof. Knut Borch-Johnsen, DMSc, Steno Diabetes Center, Gentofte, Denmark.

DETECT-2 Steering Committee. S. Colagiuri (Australia), K. Borch-Johnsen (Denmark), G. Alberti (U.K.), R. Williams (U.K.), G. Roglic (Switzerland), B. Balkau (France), A. Ramachandran (India), and J. Tuomilehto (Finland).

Principal investigators of the studies. P. Zimmet and J. Shaw (Australia); L. Fezeu (Cameroon); T. Jørgensen and K. Borch-Johnsen (Denmark); B.P. Tabai (Egypt); J. Tuomilehto and R. Tilvis (Finland); E. Eschwege and B. Balkau (France); W. Rathmann (Germany); P. Bjerregaard (Greenland); V. Mohan, S.R. Iyer, and A. Ramachandran (India); G. Semiardji (Indonesia); R. Dankner (Israel); M. Tominaga (Japan); N.H. Cho and H.L. Kim (Korea); P. Zimmet and J. Shaw (Mauritius, Nauru); B. Wang and Y. Dong (China); Z. Szybinski (Poland); S. Viali (Samoa); J. Cutter (Singapore); P.L. de Pablos-Velasco (Spain); M. Eliasson and B. Zethelius (Sweden); P. Chou (Taiwan); J.M. Dekker, G. Nijpels, and E.J.M. Feskens (the Netherlands); T. Palu and S. Colagiuri (Tonga); N. Wareham, Sir K.G.M.M. Alberti, and M. Marmot (U.K.); Y.J. Cheng, M. Engelgau, and M.I. Schmidt (U.S.); and T.V. Binh (Vietnam). See online appendix for details.

The DETECT-2 project was undertaken on the initiative of the World Health Organization and the International Diabetes Federation.

No potential conflicts of interest relevant to this article were reported.