An Indirect Estimate of the Incidence of Non-Insulin-Dependent Diabetes Mellitus
Barendregt, Jan J.; Baan, Caroline A.; Bonneux, Luk
From the Department of Public Health, Erasmus University Rotterdam, the Netherlands.
Submitted July 21, 1999; final version accepted October 25, 1999.
Address correspondence to: Jan J. Barendregt, Department of Public Health, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands.
Our goal was to estimate non-insulin-dependent diabetes mellitus incidence in the Netherlands in the absence of equivocal empirical data. Incidence can be expressed as a function of age, sex, prevalence, and mortality. We obtained prevalence data from a study that pooled existing prevalence estimates. We calculated diabetes-related mortality using relative risks on all-cause mortality. Sensitivity for the rate of excess mortality was determined using the 95% confidence intervals (95% CI) of the relative risks. The estimated incidence increases exponentially with age, with a doubling time of 10 years for men and 9 years for women. The rate increases from 8.1 per 10,000 (95% CI = 7.7–8.8) for men ages 40–44 years and 7.0 (95% CI = 6.8–8.0) for women to 79.7 per 10,000 (95% CI = 69.5–90.9) for men ages 75–79 years and 85.8 (95% CI = 80.6–91.0) for women. When empirical estimates of incidence are largely lacking, the methodology described offers a useful alternative, in particular for the assessment of potential intervention effects.
Non-insulin-dependent diabetes mellitus (NIDDM) is a common condition among the elderly and, with the aging of populations, is bound to increase. Describing the burden of disease caused by diabetes mellitus (henceforth, diabetes) can help to assess the potential gains in population health status that could be made by a better control of risk factors for diabetes, and of diabetes itself. Assessing such gains requires a consistent means of measuring incidence, prevalence, and mortality rates, which can be used as input in a causal epidemiologic model that describes the natural history of the disease and its complications. 1,2 The impact of changes in incidence, for example, through weight control, on diabetes prevalence and diabetes-related mortality can be estimated with such a model.
Describing the epidemiology of NIDDM is surprisingly difficult. The onset of NIDDM is a gradual process. Initially, the patient experiences few if any symptoms, and therefore a large proportion of all NIDDM patients is presumed to be undiagnosed; some estimates are as high as 50%. 3
In such a situation, of difficult case definition and a high prevalence of occult disease, the observed incidence and prevalence become highly dependent on factors other than the true occurrence of disease, such as patient and doctor awareness and level of case finding, resulting in highly variable estimates of incidence and prevalence. Estimates of prevalence and incidence in the Netherlands vary by a factor of about 3. 4–8
In addition, mortality, for most diseases the best recorded epidemiologic measure, in the case of diabetes cannot reliably be obtained from cause-of-death registration. Cause-of-death statistics are based on the concept of a single cause, termed the underlying cause of death. Diabetes is associated at the time of death with other conditions, such as cardiovascular diseases. It is often difficult to determine the role played by diabetes mellitus in the death process. But the coding may also promote difficulties in interpretation. 9,10
A previous study presented an estimate of diabetes prevalence in the Netherlands, based on a pooled analysis of existing studies. 4 Mortality of diabetes was estimated by combining data from epidemiologic studies on the prevalence of diabetes and the relative risks for mortality of diabetes with mortality data from Statistics Netherlands. 11
The purpose of the present study is to obtain an age- and sex-specific estimate of NIDDM incidence that is consistent with the previously estimated prevalence and mortality. By combining both the prevalence estimate and the mortality estimate in an incidence-prevalence-mortality (IPM) model, an estimate of the incidence of diabetes can be obtained. We compare the estimates with the few observations and a similar method available, and discuss results and the method used.
Subjects and Methods
IPM models of disease processes are not new to epidemiologic research. 12–14 The main advantage of IPM models is that incidence, prevalence, and mortality figures are linked through the causal chain of a disease process, and this chain limits the possible combinations of incidence, prevalence, and mortality rates. Limits are imposed because any prevalent case must have become incident at some younger age, and any person dead with a disease must have been an accident case previously and have been prevalent, however briefly. Jointly estimated incidence, prevalence, and mortality rates, using a causal model, are therefore internally consistent. 12
We constructed a diabetes-related mortality rate (m), independent from the cause-of-death statistics. The method is described in a previous study. 11 This diabetes-related mortality rate equals all excess mortality caused by diabetes, however coded in death statistics. Total mortality for people with and without diabetes is estimated from the average population total mortality, the relative risk of mortality for diabetics, and diabetes prevalence using the following equations:MATH 1 and MATH 2 Substituting Eq 2 in Eq 1, we can write the mortality of the nondiabetics as follows 11 :MATH 3 The diabetes-related mortality rate (m) in a population with a diabetes prevalence of p then becomes:MATH 4 Where p = prevalence of diabetes;R = relative risk on total mortality, given exposure to diabetes;m = average total mortality rate;m0 = total mortality rate of nondiabetics;m1 = total mortality rate of diabetics;md = diabetes-related mortality rate of the mixed population. Age and sex indexes are suppressed. Note that Eq 4 is the same as the population attributable risk times total mortality.
Given this mortality rate in the population and the prevalence of diabetes, we can now write incidence at age a as a function of prevalence at a and a + 1, and mortality at a, as follows:
Eq 5 is based on the description of the disease process as a continuous time Markov process and is derived elsewhere. 15 A moving average is applied to the resulting age-specific incidences to smooth the discontinuities that are caused by the age group subdivision of the relative risks used (see Table 1).
The relative risks for the calculations in this analysis are based on the Verona study (Table 1). 16 This decision was based on an earlier study, in which we compared several studies reporting relative risks on all-cause mortality for diabetes. 11 Although the various studies that reported age-specific relative mortality risks for diabetes differed in design, population, and time, the relative risks were similar, taking into account the different ages. 11 We chose the Verona study, as it is a recent population-based study, which used the nondiabetic population as the reference population.
We obtained prevalence of diabetes from a previous study in which a pooled estimate was made on the basis of 15 studies performed since 1970. 4 The studies largely fall into two groups, one based on registrations by general practitioners and one based on self-report in a survey. The 15 studies with their main characteristics are given in Table 2. We fitted an exponential curve on age-specific prevalence using logistic regression, with age and study design as independent variables. We used the coefficients from the logistic regression analysis to estimate the prevalence of diabetes in the Netherlands. This result gave us two age-specific prevalence estimates, one based on the survey group and one based on the general practice studies. As the relative risks used were obtained from a survey, we used the fitted curve of the survey studies to form the basis of the current analysis. Because of data limitations, the pooled prevalence estimate is restricted to the age range of 30–80 years, and therefore the prevalence estimate concerns mainly NIDDM patients. Figure 1 shows the resulting prevalence rates by age of men and women. More details on the pooled estimate have been published elsewhere. 4 We are aware of four studies in the Netherlands that have reported incidence of diabetes mellitus 5–8 (Table 3), and these will be compared with our estimation of diabetes incidence.
Figures 2 (men) and 3 (women) present a central incidence estimate by age and a lower and upper bound, based on the estimates of relative risks and their 95% confidence intervals from the Verona study. The central estimates are very similar for men and women, increasing over the whole age range and reaching an incidence of about 1% per year at age 80 years (see also Table 4). The lower bound relative risks result in an incidence estimate below the central estimate, the higher bound in one above; with lower mortality selection, a lower incidence will be needed to reproduce the prevalence and vice-versa. The difference between the lower and upper estimates is greater for men than for women. This difference is due to a relatively wider confidence interval of the relative risk (see also Table 1) and a higher absolute mortality risk for men.
In Figures 2 and 3, the observations from four Dutch incidence studies (Table 3) are presented as well. The data points are plotted in the middle of the (wide) age intervals; for the open-ended highest age groups, we used the average age of these groups as calculated with a life table. The four incidence studies give rather similar results for younger ages, but diverge at more advanced ages, with the Continuous Morbidity Registration (CMR)Nijmegen 1982–1993 estimate tending to be the highest, and the National Study the lowest. Comparing our results with the four studies, our estimates seem to be more or less in the middle of the observations for all age groups, except for the (usually open-ended) oldest, in which only the CMR observation is within the estimated range, whereas the other studies report (sometimes much) lower rates.
In Table 4, we compare our results with the results from those of a recent study in which NIDDM incidence from data on prevalence of known diabetes and disease duration is estimated, using data from the Cremona study. 17 In the Cremona study in Italy, performed in 1988, data on prevalence of diabetes, year of diagnosis, and duration of the disease were collected. 18 These data were used to estimate the incidence of diabetes using regression analysis. 17 Their results are rather different; for ages 40–70 years, their estimates are much higher, and they reach a peak of 70 (men) and 78 (women) per 10,000 for the 60–69-year age group (our estimate is about 40 per 10,000) and subsequently decrease to about 30 (men) and 50 (women) per 10,000 for the 80–89-year age group.
To estimate incidence and prevalence of NIDDM, sufficiently large empirical studies with adequate follow-up are preferred. To conduct such a study is difficult and expensive, and consequently most studies are too small to yield reliable estimates. This limitation is true in particular for incidence estimates, of which there are only a few, and they are of limited use because of small numbers when age-specific rates are required. As a result, the estimates vary widely.
As an alternative to direct observation, this paper describes an indirect method to estimate the incidence of NIDDM. It is based on the prevalence estimate from a previous study. Added to that is information about the excess mortality of diabetics as compared with nondiabetics, 16 and theoretical knowledge about the relation between incidence, prevalence, and mortality.
The relation between epidemiologic variables is not simple. The oft-cited relation that prevalence equals incidence times duration is an oversimplification. 19 With rising age, true duration is lower because of increasing general mortality and thus declining life expectancy, whereas duration estimated by age-specific prevalence divided by incidence is increasing because of the accumulation of prevalence cases.
The most convenient way to model a disease process is to assume independence from all other causes of death. Under that assumption, the mortality rate of the disease can be obtained from the disease-specific mortality as reported by the national statistics bureau, and an “all-other-causes” mortality rate can easily be calculated. 20 An independence assumption, although convenient, is not appropriate in the case of diabetes mellitus; in addition to being coded as a cause of death itself [International Classification of Diseases, 9th revision (ICD-9) 250], diabetes also acts as a risk factor for a range of causes of death, such as cardiovascular diseases. We therefore constructed a diabetes-related mortality rate with relative risks for mortality of diabetics, as well as the prevalence of diabetes. Because the diabetes-related mortality rate includes all excess mortality for diabetics, it is independent from all other mortality. Therefore, it can be used, unlike the specific mortality restricted to diabetes mellitus (ICD-9 250), in an IPM model that assumes independence from the non-diabetes-related mortality.
The incidence is jointly determined by the shape of the prevalence curve and the rate of mortality selection. From Figures 2 and 3, it can be deduced that the former is by far the more important influence; the 95% confi-dence intervals of the relative risk for total mortality, which determine the rate of mortality selection, result in a very narrow range. The rate of mortality selection is determined by the excess absolute risk, which, for most of the age range involved, remains small. Only for the higher ages among men does this absolute risk become big enough to have a sizable impact. Therefore, the incidence estimate is most sensitive to the prevalence used.
The incidence estimates comply well with the available empirical incidence estimates from four Dutch incidence studies, but have upper and lower bounds that are considerably more narrow than the observed range of values. Three of the four empirical studies reported a (much) lower incidence for the open-ended (oldest) age groups as compared with our estimates. This difference may be due in part to the calculation of the average age for the oldest age groups using a life table. Institutionalized people, who, on average, will be older than the noninstitutionalized, were not included in the empirical studies, but are in the life table. The calculated average age will therefore tend to be higher than the actual one in the studies, causing the data points to be plotted too far to the right.
The result of the Cremona Study (Table 4), also based on backcalculation, strikes us as implausible: the declining incidence suggests a pool of susceptible subjects that is being drained. But NIDDM is a senescent disease; glucose tolerance keeps declining with age for most people, not just for a limited group. 21,22 When among middle-aged groups the proportion of known cases is higher than among the elderly, the prevalence of known diabetes will be relatively higher at those middle ages. An IPM-based incidence estimate will then initially show a steeper increase in incidence at the younger and middle ages as the prevalence buildup is faster, and subsequently flatten out or even decline as the prevalence buildup slows at higher ages. Thus, it is possible to obtain such a peaked incidence curve of known diabetes, but its usefulness as a description of diabetes epidemiology seems limited.
An assumption implicit in using cross-sectional data is that there is no time trend in incidence and survival. With strong recent time trends in incidence or survival, currently observed cross-sectional prevalence will not be at their equilibrium values. For example, if incidence has recently increased, it will take several years for prevalence to reach the new, higher-equilibrium value. Because the incidence estimate is based on prevalence, it will reflect conditions prevailing in the past, so our estimates may diverge from current incidence.
The IPM model used in this study ignores remission; an extra parameter would be required, of which the value is uncertain. One study evaluated the diabetic status of patients after 8 years of follow-up and reported a remission of 14%. 23 There are reasons to suspect misclassification at baseline to be responsible for at least some of these cases. We assumed remission to be mostly temporary and too small to affect the incidence estimates substantially.
Our resulting incidence estimates are internally consistent with the prevalence and mortality estimates, which is not necessarily a property of empirical estimates, even when done in the same population. For example, the huge increases in prevalence (+40%) simultaneous with large decreases in incidence (–20%), as reported for Manitoba between 1986 and 1991, are difficult to explain. 24,25
The estimate is the incidence necessary to explain observed prevalence and estimated diabetes-related mortality. This calculation allows us to assess the impact on diabetes prevalence and excess mortality of interventions or trends that influence diabetes incidence, even if diabetes incidence itself is difficult to observe. The method is general enough to be used for other diseases for which incidence assessment is a problem, such as dementia. It can also be applied for specific ethnic groups with high prevalences of NIDDM, for example, to assess the potential effectiveness of interventions in such groups. It is in this field, of intervention impact assessment, where the method may prove most useful.
We thank Paul J. van der Maas (Department of Public Health, Erasmus University Rotterdam) and Edith J. Feskens (National Institute for Public Health and the Environment, Bilthoven) for their helpful comments on an earlier draft. This research was funded by The Netherlands Heart Foundation and The Netherlands Institute of Health Sciences.
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