Joint mapping of cardiovascular diseases: comparing the geographic patterns in incident acute myocardial infarction, stroke and atrial fibrillation, a Danish register-based cohort study 2014–15

Study design and population

The study was based on prospectively collected data from nationwide, population-based Danish registers. Registers were linked using the unique personal identification number assigned to each Danish resident at birth or immigration [13].

Three separate study populations were established: one for each of the three considered diseases AMI, stroke and AF. For example, the AMI study population included adults aged ≥ 30 years living in Denmark 1 January 2014 with no previous AMI. In this population, follow-up ended at incident AMI, emigration, death or 31 December 2015, whatever came first. The stroke study population and the AF study population were established in similar ways. The three study populations were restricted to adults aged ≥ 30 years since the diseases are rare in young people. Moreover, at age 30 years, most people will have completed their education and income may serve as an indicator of lifestyle and health behaviour.

For each individual in the study populations, information on date of birth, sex, and residential municipality were available from population registers at Statistics Denmark. Residential municipality was assigned 1 January each year. Based on date of birth, age was calculated as a time-varying variable and grouped into age groups (30–59, 60–69, 70–79, 80 +) based on the distribution of the outcome (Table 1). Annual information on equivalized disposable household income was available from income registers at Statistics Denmark (assigned 31 December each year) and grouped into Low (lowest 20%), Medium (middle 60%) and High (highest 20%) based on age-specific quintiles.

Table 1 Characteristics of the acute myocardial infarction (AMI), stroke and atrial fibrillation (AF) cohortsStudy area

Denmark covers an area of approximately 43,000 km2 and the population counted 5.7 million people on January 1st, 2015. The country is divided into 98 municipalities, which serve as the geographical units in this study. The geographical relationship between municipalities was modelled by a symmetric, binary adjacency matrix (98 × 98) based on municipality borders (i.e. a non-diagonal matrix entry was 1 if two municipalities share a common border and 0 otherwise. Diagonal entries were 0). Seven municipalities were islands with no adjacent municipalities. In the matrix, they were linked to the municipality to which they were connected by ferry or bridge (shown on map in Additional file 1: Figure S1).

Outcome

Incident AMI, stroke, and AF cases were identified in the Danish National Patient Register (NPR) [14] and in the Danish Register of Causes of Death (RCD) [15]. The International Classification of Disease, 8th revision (ICD-8) was used in 1977 (start of NPR)-1993 and 10th revision (ICD-10) was used in 1994–2015 (AMI: ICD-8 code 410, ICD-10 code I21; stroke: ICD-8 codes 430, 431, 433, 434, 436, ICD-10 codes I60, I61, I63, I649; AF: ICD-8 codes 42,793, 42,794, ICD-10 code I48). Both primary and secondary diagnoses as well as underlying and contributing causes of death were considered. To identify incident cases of AMI, stroke and AF, individuals with a diagnosis before 2014 were excluded from the corresponding study population. For example, AMI cases before 2014 were excluded from the AMI study population.

Previous validation studies on diagnoses in NPR have found positive predictive values (PPV) ≥ 92% for incident AMI and AF [16], whereas PPV = 69.3% has been reported for stroke [17].

Statistical analysis

A multivariate Poisson model including a disease-specific random effect of municipality was used to simultaneously model the three diseases AMI, stroke and AF.

Let Yij denote the number of cases of disease j in municipality i, i = 1,…, 98, j = 1,2,3. In each study population, person-years at risk were calculated within sex, age and income groups in each municipality. Let \(_^\), i = 1,…, 98, j = 1,2,3, k = 1,…, 24, denote the person-years at risk in study population j in municipality i within combination k of sex, age and income groups. Then the expected number of cases of disease j in municipality i is

$$_=\sum_^_^_^, i=1,\dots , 98, j=\mathrm,3,$$

where \(_^\) is the calculated national incidence rate (IR) of disease j within combination k of sex, age and income groups.

Now, the multivariate Poisson model is given by

$$_\sim \mathrm(_\mathrm\left(_+ _\right)), i=1, \dots , 98, j=\mathrm,3,$$

where \(_\) is a disease-specific intercept and \(_\) is a disease-specific random effect of municipality. The Y’s are assumed to be independent given the random effects. The random component \(\boldsymbol=(}_,}_,}_)}\), \(j=\mathrm,3\), where \(}_=(_, \dots , _)}\), \(j=\mathrm,3\), was modelled by a multivariate conditionally autoregressive (MCAR) structure, [10] and included to account for residual spatial correlation within disease as well as residual correlation between diseases. The spatial correlation structure was based on the adjacency matrix described in the study area section.

The MCAR structure was modelled using linear models of co-regionalization [11]. The approach is based on writing the random component \(\boldsymbol\) as a linear combination of latent spatial processes \(}}_=(_,_)}\), \(j=\mathrm,3\). Thus, let

$$\boldsymbol=\left(} \otimes }}_\right)},$$

where \(}=(}}_,}}_, }}_)}\) and \(}\) is the 3 × 3 lower triangular matrix uniquely determined as the Cholesky decomposition of a matrix \(\boldsymbol=}}\boldsymbol}\). Now, the covariance structure within \(\boldsymbol\), i.e. within and between diseases, depends on the modelling of \(}\).

Each process \(}}_\), \(j=\mathrm,3\), was modelled by a conditional autoregressive (CAR) model. In the most complex model considered, the processes \(}}_,}}_,}}_\) were assumed independent with \(}}_\) modelled by a Leroux CAR model [18] with spatial correlation parameter \(_\), \(j=\mathrm,3\) (Model 1). This allows for different spatial structures within each of the three diseases and correlation between diseases is municipality specific (details elsewhere [11, 19]). This was simplified by assuming a common correlation parameter \(\rho\) for all \(}}_\), \(j=\mathrm,3\) (Model 2). In that case, the same spatial structure is assumed within all diseases and correlation between diseases is not municipality specific (equivalent to the separable model suggested by Gelfand and Vounatsou [10]). A simple model assuming no correlation between diseases were also considered (Model 3). This corresponds to standard, univariate modelling of each disease. In this model, disease-specific spatial correlation parameters were assumed.

Bayesian inference was based on Markov chain Monte Carlo (MCMC) methods using WinBUGS [20] and the approach described in detail by MacNab [19]. Instead of assigning a prior to \(}\), priors were assigned to the elements of \(\boldsymbol\), and \(}\) was determined by the one-to-one relationship between \(\boldsymbol\) and \(}\). The matrix \(\boldsymbol\) could be considered a covariance matrix, and uniform (0,1) priors were assigned to the correlation parameters, whereas uniform (0,10) priors were assigned to the standard deviation parameters. The spatial correlation parameter of the Leroux model was assigned a uniform (0,1) prior. The intercept term was assigned a weakly informative Gaussian prior with mean zero and precision 0.1 to improve convergence. In a sensitivity analysis, the prior on the standard deviation parameters was changed to uniform (0,100).

Posterior inference was based on a total of 10,000 samples generated from two chains with different initial values. The first 10,000 samples were discharged as burn-in, and the chains were thinned to every 100th sample to reduce autocorrelation. Convergence was evaluated by visual inspection of trace and density plots, autocorrelation plots, and Geweke diagnostics [21]. Effective sample size was also considered.

Point estimates are reported as the median of the posterior distribution together with 95% credible intervals (CI). Models were compared using the deviance information criterion (DIC) [22].

Based on the multivariate model, estimated municipality-specific standardized incidence rates (SIR) of AMI, stroke and AF, respectively, where calculated as \(}_/_\), i = 1, …, 98, j = 1,2,3, where \(}_\) is the estimated number of cases of disease j in municipality i. The estimated SIRs were mapped to display a smoothed map of municipality-specific SIRs for each disease.

Conditional correlation between diseases at collocation were derived from the 3 × 3 covariance matrix \(\boldsymbol\) [19].

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