Projected growth of the adult congenital heart disease population in the United States to 2050: an integrative systems modeling approach

Background Mortality for children with congenital heart disease (CHD) has declined with improved surgical techniques and neonatal screening; however, as these patients live longer, accurate estimates of the prevalence of adults with CHD are lacking. Methods To determine the prevalence and mortality trends of adults with CHD, we combined National Vital Statistics System data and National Health Interview Survey data using an integrative systems model to determine the prevalence of recalled CHD as a function of age, sex, and year (by recalled CHD, we mean positive response to the question “has a doctor told you that (name) has congenital heart disease?”, which is a conservative lower-bound estimate of CHD prevalence). We used Human Mortality Database estimates and US Census Department projections of the US population to calculate the CHD-prevalent population by age, sex, and year. The primary outcome was prevalence of recalled CHD in adults from 1970 to 2050; the secondary outcomes were birth prevalence and mortality rates by sex and women of childbearing age (15–49 years). Results The birth prevalence of recalled CHD in 2010 for males was 3.29 per 1,000 (95 % uncertainty interval (UI) 2.8–3.6), and for females was 3.23 per 1,000 (95 % UI 2.3–3.6). From 1968 to 2010, mortality among zero to 51-week-olds declined from 170 to 53 per 100,000 person years. The estimated number of adults (age 20–64 years) with recalled CHD in 1968 was 118,000 (95 % UI 72,000–150,000). By 2010, there was an increase by a factor of 2.3 (95 % UI 2.2–2.6), to 273,000 (95 % UI 190,000–330,000). There will be an estimated 510,000 (95 % UI: 400,000–580,000) in 2050. The prevalence of adults with recalled CHD will begin to plateau around the year 2050. In 2010, there were 134,000 (95 % UI 69,000–160,000) reproductive-age females (age 15–49 years) with recalled CHD in the United States. Conclusion Mortality rates have decreased in infants and the prevalence of adults with CHD has increased but will slow down around 2050. This population requires adult medical systems with providers experienced in the care of adult CHD patients, including those familiar with reproduction in women with CHD. Electronic supplementary material The online version of this article (doi:10.1186/s12963-015-0063-z) contains supplementary material, which is available to authorized users.

1 The DisMod-PDE model As described in [1], the DisMod-PDE model employs a two-compartment systems dynamics model of the progression of disease through a population, where the stocks and flows are all dependent on both time and age. Let a denote age and t denote time, and let S(a, t) and C(a, t) denote the fraction of a cohort susceptible and with-condition for a specific disease. Furthermore, let ι(a, t) be the incidence hazard, ρ(a, t) be the remission hazard, χ(a, t) be the excess-mortality hazard, and ω(a, t) be the background-mortality hazard.
In this notation, the system of differential equations for the the two compartment model is To make computation tractable, the age/time-specific stocks and flows are parameterized by knots for user-specified cohorts and ages in a computational grid, and values for a and t between grid points are calculated via bilinear interpolation. Although it is possible to make the differential equations stochastic in this formulation, for our purposes here, we will always enforce equality of the S and C values with the approximation solution to the differential equations for the linearly interpolates ι, ρ, χ, and ω values.
Descriptive epidemiological data is often noisier than one would expect from sampling error alone, while age/time-specific disease parameters are expected to vary smoothly. We incorporate these observations into the model by smoothing across cohorts and ages.
Smoothing across cohorts is implemented as a penalty on second-order differences of points in the computational grid. For example, for with-condition stock C, for age grid point a, for cohorts c k , c k+1 , c k+2 , the log-prior is equal to where σ is the prior on second-order smoothing of C with respect to cohort.
Smoothing across ages is implemented analogously, but only for flows such as χ. For example, for excess-mortality hazard χ, for cohort grid point c, for age grid points a j , a j+1 , a j+2 , the log-prior is equal to where σ is the prior on second-order smoothing of χ with respect to age.
Smoothing across age and cohort is also implemented with an analogous approximation of the cross derivative. For an example again with excess-mortality hazard χ, for cohort grid points c k , c k+1 and age grid points a j , a j+1 , the logprior is equal to where σ is the prior on smoothing of χ with respect to age and cohort. The model and smoothing priors are combined with a data likelihood to produce a posterior distribution on model parameters. The data likelihood is an offset lognormal model, where each observation i is coded as a triple (v i , s i , z i ), and using I i to denote the integrand of the model parameters corresponding to this observation, observation i contributes the following to the log-likelihood: The model is fit by finding the maximum a posteriori value for the parameters, using the Ipopt system for constrained nonlinear optimization.

Specialized/Simplified for CHD
Since CHD is a congenital condition, in all of the modeling in the present paper the DisMod-PDE model can be simplified to a one-compartment ODE. The first step in this simplification is to constrain the incidence and remission rates to be zero for all ages and times (i.e. ι(a, t) = ρ(a, t) = 0). This removes all flow between compartments, and simplifies the differential equations to the following Since the data we have available is either a measurement of CHD prevalence or of CHD cause-specific mortality rate, the integrands that appear as I i in the model likelihood are C/(S + C) and χ · C/(S + C). We may further simplify the model for a rare condition like recalled CHD (with prevalence less than 0.5%) by constraining ω = 0 and S = 1, which introduces an inaccuracy of less than 1% in the integrand C/(S + C). This further simplified the differential equations to a single ODE dC(a + τ, t + τ ) dτ = −χ(a, t)C(a, t).
Since we assumed that birth prevalence was constant over time, there is a single parameter C 0 which defines the initial conditions C(0, t) = C 0 . For χ(a, t) we used knots in age at ages (0, 1, 2, 3, 4, 5, 10, 15, . . . , 65) and knots in cohorts at 5 year age intervals from 1900 to 2020, as well as knots at 2050 and 2100 for extrapolation. The stock C was smoothed across cohorts with σ = 1, and the excess mortality χ was smoothed across ages, cohorts, and age/cohort with σ = 1 as well. For knots outside the time period where data was available (i.e. before 1968 and after 2010), we constrained χ to be constant in cohort, meaning χ(a, t − 1) = χ(a, t).
For each age-/time-specific prevalence measurement, we calculated the value v i as the survey-weighted mean from National Health Interview Survey, and for the standard deviation s i , we used 0.003/n i , where n i is the number of respondents in the survey for the given age and time and 0.003 is a rough estimate of the prevalence of CHD (per one). We took the offset z i = 1 to make the error distribution roughly Gaussian.
For each age-/time-specific excess-mortality measurement, we calculated the value v i as the number of cause-specific deaths in Multiple-Cause Mortality Files divided by the population from the Human Mortality Database. We set standard deviation s i = 0.05 and offset z i = 10 −6 , which makes the error distribution roughly log-normal, with around 5% relative deviations from the observed data allowed.
To generate uncertainty intervals for our estimates, we used a parametric bootstrap procedure to resample each prevalence measurements from a binomial distribution Bi(n i , v i ) with parameter n i equal to the number of respondents in the survey for this measurement and parameter v i equal to the survey-weighted mean of responses. We repeated this procedure 1, 000 times and reported the 2.5-and 97.5-th percentile values as our 95% uncertainty intervals. We fit the model separately for males and females.