Estimating cardiovascular disease incidence from prevalence: a spreadsheet based model

Among PI models with different complexities, the one proposed by Hallett et al. has been widely cited and used [9]. Detail of model derivation and validation has been published elsewhere [9]. Briefly, the difference between observed prevalence in the second survey and the expected prevalence (estimated from prevalence in the first survey and survival fraction based on mortality) provides the incident cases; the proportion of disease-negative people, the mortality rate for these people and the time interval between the two cross-sectional surveys together generate the number of person-years. Age- and gender- specific prevalence and mortality should be used to obtain more accurate estimates. Mortality of people with/without the health outcome of interest can be based on population vital statistics or the literature. The model assumes prevalence and mortality are constant during the interval of two successive surveys to keep the model simple and easy to use.

Hallett’s method should work for other diseases and settings as long as the disease is not reversible. We made two major modifications to Hallett’s method to better fit cardiovascular diseases. First, the survival fraction of disease positive patients is estimated as a function of 30-day case fatality, 1-year, 5-year and 10-year survival/mortality rate whenever possible, instead of assuming a constant mortality rate between the time intervals of two surveys. Second, we calculated the age-standardized incidence rate to make the estimate more comparable to other health statistics in its target population.

We tested the performance of our modified Hallett’s method in two steps. First, we applied our model to estimate myocardial infarction (MI) incidence in the US population and compared estimated values to reported incidence rates from the national environmental public health tracking network (Tracking Network) of U.S. Centers for Disease Control and Prevention (CDC), existing epidemiological studies and population statistics. We chose MI in the US population as this condition was one of the most well studied cardiovascular outcomes. The mortality, prevalence, and survival data were relatively accurate and robust. Second, we expanded the outcome to the broader category of any heart disease (HD), which also includes heart failure and other forms of heart diseases, and compared incidence estimates with observed incidences from a national representative cohort study, in Canada. The cross-sectional surveys and the longitudinal survey we used share the same sampling framework and chronic disease module in their questionnaires. In the text hereafter, heart disease refers to combined MI, angina and heart failure in the Canadian population without further specification.

For the United States, we chose the National Health and Nutrition Examination Survey (NHANES), which provides MI prevalence estimates in the US population at two-year intervals from 1999 to 2012 [12]. NHANES is a repeated cross-sectional survey of a nationally representative sample of the US population, with a multistage, stratified sampling design. Our study population included all participants aged 35 years and older in the 7 consecutive waves of the survey. Participants who answered “Yes” to questionnaire item MCQ160e (“Has a doctor or other health professional ever told you that you had heart attack (also called myocardial infarction)”) will be classified as prevalent MI cases in this study. Sex-specific mortality data for MI patients were calculated from hospitalized mortality and 2-year mortality after hospital discharge [13, 14]. Mortality data for the MI-negative population were calculated as the difference between all-cause mortality rate and the mortality rate of MI, from “Underlying Cause of Death 1999-2011” on the CDC WONDER Online Database [15]. Hospitalized MI incidence data were based on 26 States which participated in the CDC environmental public health tracking program [16].

For Canada, we selected the Canadian Community Health Survey (CCHS), which provides prevalence of self-reported heart diseases in the Canadian population, also at two-year intervals from 2001 to 2011 [17]. The CCHS is a series of cross-sectional surveys conducted biannually before 2007 and yearly since then. It uses a stratified, multistage probability sampling design. It collects information on health status, health care utilization and health determinants for the Canadian population. In this study, we identified participants aged 12 years and older in 6 consecutive waves of the survey. Participants who answered “Yes” to questionnaire item CCQ121 (“Have you had heart diseases which lasted 6 months or more and have been diagnosed by a health professional?”) were classified as prevalent heart disease cases. The mortality rate of heart disease was calculated as the total of mortality from MI, angina and heart failure. Mortality rates for MI patients were assumed to be the same as the US population because studies suggest that 2-year mortality rates after MI are comparable between the two populations [13, 14, 18]. Mortality rates for angina and heart failure patients were based on Ontario data [19]. Mortality rates for heart disease free patients were calculated as the difference between all-cause mortality and mortality from heart disease, basing on data from Statistics Canada’s Canadian Mortality Database, as available online from the CANSIM Table “Cause of Death 2000-2011” [20]. Heart disease incidence rates were calculated from the NPHS, which is a longitudinal health survey [21]. It started in 1994/1995 with an initial sample size of 17276 and ended in 2012 after another 8 follow-ups, which was conducted every two years.

The incidence rate of the outcome of interest in each age- and sex- group is estimated by equation (1), where I _i is the incidence, F _i approximates the proportional cohort size change over the time interval between two surveys (which was given by equation (2)), SP _i is the proportion of disease-positive patients at the beginning of the first survey who survive to the next survey, SN _i is the corresponding proportion for the disease-negative people, p _i,0 is the prevalence of outcome of interest at the first survey, p _i,T is the prevalence at the second survey respectively. In this paper, the time intervals for both the NHANES and the CCHS were 2 years. Equation (1) calculates the point estimates of incidence. Poisson-based confidence intervals for incidence can be estimated, treating the survey as a simple random design, without considering the survey design and sampling procedure. After obtaining the crude incidence rate for each age- and sex- group, a standardized incidence for the population is calculated using the direct method. For the United States cohort, we used the total US population in 2000 as the standard population; for the Canadian cohort, we used the total Canadian population from the 2001 Census. As each wave of the NHANES and the CCHS covers two years (e.g. 1999–2000, 2001–2002), the incidence estimated from such two waves was presented as between January 1st of the second year of each wave, i.e.,between Jan 1, 2000, and Jan 1, 2002.

Sex-specific five-year age group was used as the smallest analytic unit. Prevalence estimates for each age- and sex- group were calculated with proper sample weights and survey design effect used by the NHANES and the CCHS. It was substituted with the value from next age group if the prevalence was zero in the very young age groups. Baseline 2-year mortality after MI was calculated with equation (3), for both the US population and the Canadian population, where M _MIin denotes MI mortality in hospital, and M _MIout denotes MI mortality after hospital discharge. A 3% decrease in mortality rate for MI positive patients each year was assigned according to the literature [22]. The 2-year survival fraction for MI patients (SP _MI ) was given by equation (4). Baseline 2-year survival fraction after heart disease (SP _HD ) for the Canadian population was calculated with equation (5), where w _MI , w _AG , w _HF denotes the weighted proportion of MI/angina/heart failure to the sum of the three (in the CCHS cycle 2001). The mortality rate for MI or heart disease negative people were calculated with equation (6) and (7), as the difference between all-cause mortality (MV _{All − cause} ) and MI/heart disease mortality (MV _MI , MV _HD ) from population vital statistics. The observed incidences of hospitalized MI in the US population were retrieved from CDC report, epidemiological studies and population statistics [2, 16, 23]. The observed incidences of heart disease in the Canadian population were calculated with corresponding weights from NPHS. In this paper, we will use the term “estimated” to refer to model calculated incidence, and the term “observed” to refer to incidence estimated from a cohort study, or reported in the literature or population statistics.

To validate the model performance, we compared the estimated incidence with observed values. We checked whether our estimated incidence fall into the high-low range (or 95% CIs) of observed incidence. When the definition of best available reported outcome is different from what we modeled, we adjusted our estimated values to make a fair comparison. For example, the most reliable statistics in the US population was hospitalized MI incidence. Thus we adjusted downward our estimated values, considering about 30% of MI would be silent cases, and another 20% would be fatal cases, to be more comparable [4, 24, 25]. The time trend of estimated incidence was investigated by fitting a linear regression, with estimated incidence as the y outcome and survey year minus 2000 as the single x predictor.

Estimated MI incidence in the US population (aged 35 years and older) from 2000 are provided in Table 1. The estimated MI incidence was 843 (1/100,000) between 2000 and 2001, and 678 (1/100,000) from 2010 to 2011, with a decreasing trend. The highest estimated MI incidence from the model was observed in 2002–2003. We also estimated hospitalized MI incidence to be 56% of MI incidence. Linear regression showed that the MI incidence decreased by approximately 32 (1/100,000) each year since 2000. The corresponding decrease in hospitalized MI was approximately 18 (1/100,000) respectively, which translated to a 3.8% decrease annually. We projected a 38% reduction in hospitalized MI incidence from 2000 to 2010, based on the prevalence from NHANES. Our hospitalized MI incidence estimates were compared against the reported values from those States which participated in the CDC environmental public health tracking program from 2000 to 2011 (Fig. 1). All of our estimated incidences fell into the high-low range of the reported values.

The model estimated heart disease incidence from CCHS, and observed heart disease incidence (with 95% CIs) from NPHS, for the Canadian population aged 12 years and older are shown in Table 2. We modelled two sets of heart disease incidence, with one set standardized to the NPHS age structure, and another set standardized to 2001 Canadian Census population. Our estimated heart disease incidence (first set) were very close to the NPHS values, with the smallest relative difference observed in 2009–2011 (0.7%), and the largest observed in 2003–2005 (12.9%). All of our first set estimated heart disease incidence fell into the 95% CIs of NPHS heart disease incidence. Figure 2 visually depicts how close between the NPHS incidence and our estimated incidence. The second set of heart disease incidence showed a decreasing trend among the Canadian population from 2001 to 2011. On average, heart disease incidence decreased by 13 (1/100,000) each year from 2001. The difference between the two sets of estimated heart disease incidence was due to the different age structures of the NPHS and the 2000 Canadian Census we used during direct standardization.

We provide the model input, which is also part of the results, in the Appendix. The mortality rate of acute MI during hospitalization, the 2-year mortality rate of acute MI after hospital discharge, and the survival fraction 2 years after acute MI for the U.S. population in 1999 are presented in Table 3 in Appendix. The prevalence of MI in the U.S. population from 1999 to 2009 (in a 2-year time interval) estimated from NHANES are shown in Table 4 in Appendix. Table 5 in Appendix shows the 2-year mortality rate after MI, angina, heart failure, and the constructed 2-year survival fraction after heart disease. Table 6 in Appendix presents the prevalence of heart disease in the Canadian population, calculated from CCHS 2001 to 2011. Hospitalized MI incidence data from 26 States which participated in the CDC environmental public health tracking program (from 2000 to 2012) are provided in Table 7 in Appendix. Table 8 and 9 in Appendix provide the population age structure of the U.S. population and the Canadian population used for standardization, respectively.