Participation rates and geo-referencing
The statistical districts were used as the geographical reference system in which the MSP participation rates were assessed. The residence addresses of all MSP participants for the years 2005 to 2013 were stored at KV.it Dortmund, the institution which administrates the MSP documentation software MaSc [
12]. KV.it assigned MSP participants to one of the 62 statistical districts by linking their home addresses to a comprehensive list of street addresses for each district. A list of individual, anonymized participants who were geo-referenced to one of the statistical districts was then transferred to the Institute of Epidemiology and Social Medicine at the University Münster [
13] where all subsequent analyses were carried out.
The years 2005 and 2006 were excluded from the present analyses to avoid contamination with the various organizational aspects of the stepped-up implementation of the MSP. All eligible women receive a biennial invitation to the screening program, hence, we chose to analyze three 2-year periods: 2007/2008, 2009/2010, and 2011/2012. The participation rates were calculated using the aggregated numbers of participants and the averaged female background population (age group 50–69) for each two year-period.
Spatio-temporal mapping and regression
The spatio-temporal distribution of participation rates was analyzed within a hierarchical Bayesian framework using a multivariate binomial regression model (spatio-temporal odds model): Let n
it denote the number of eligible women resident in district i and period t and Y
it the number of participants in breast cancer screening, with I = 1, …, 62 and t = 1, 2, 3. We assumed that the observed number of participants (Y
it) had a binomial distribution with parameters n
it and θ
it (probability of participation). At a second level, the probability of participation θ
it was then decomposed on the logit scale into an overall participation rate (α), main spatial effects (u
i and v
i) (constant in time), main temporal effects (unstructured (Φ
t) and structured (γ
t)), and a space-time interaction term (ψ
it).
$$ {\mathrm{Y}}_{\mathrm{it}} \sim \mathrm{Binomial}\left({\mathrm{n}}_{\mathrm{it}},{\uptheta}_{\mathrm{it}}\right) $$
(1)
$$ \mathrm{logit}\ {\theta}_{it}=\alpha +{u}_i+{v}_i+{\varPhi}_t+{\gamma}_t+{\psi}_{it} $$
(2)
The proposed space-time models, assuming a nonparametric time trend and a spatio-temporal interaction term, were introduced by Knorr-Held [
14] and are an extension of the spatial model introduced by Besag et al. [
15]. All model terms were treated as random variables: The spatially unstructured random effect (u
i) was considered independent and identically distributed (iid) with zero mean and unknown precision (τ
u). To account for the assumption of correlated participation rates in nearby statistical districts, the spatially structured effect (v
i) is modelled for each 62 districts as an intrinsic Gaussian Markov random field with unknown precision (τ
v). This specification is also called a conditionally autoregressive (CAR) prior and was introduced by Besag et al.[
15]. In order to insure the identifiability of the intercept α (overall participation rate), a sum-to-zero constraint was imposed on the v
i’s [
16]. The unstructured temporal effect (Φ
t) was also modelled iid with zero mean and unknown precision. For the structured time effect (γ
t) random walks of first order were considered [
17,
18]. The interaction term (ψ
it) can be specified in several ways [
14], here it is assumed that the two unstructured effects (v
i and γ
t) interact [
17,
18]. Therefore, the interaction effect was also specified as zero mean normal with unknown precision (iid., i.e. ψ
it ~ N(0, τ
ψ). The distribution of the hyperpriors was specified as follows: Minimally informative priors were specified on the log of the unstructured effect precision (log τ
v ~ logGamma (1, 0.001)) and on the log of the structured effect precision (log τ
u ~ logGamma (1,0.001)). For the unstructured time effect, a log τ
φ ~ logGamma (1, 0.01) hyperprior was chosen. For the structured temporal effect and the interaction term, minimally informative priors (the default priors): log τ
ϒ, log τ
ψ ~ logGamma (1, 0.00005) have been used. Altogether, the distribution of the hyperpriors resembles the ones used by Ugarte et. al [
18].
$$ \mathrm{logit}\ {\theta}_{it}=\alpha +{u}_i+{v}_i+{\varPhi}_t+{\gamma}_t+{\psi}_{it}+\beta {x}_i^T $$
(3)
The specified model (Equation 3) was extended to βx
Ti, where x
Ti contains the covariates with a space-time index in order to investigate potential risk factors associated with spatio-temporal variations in the participation rates. The covariates were taken from the atlas of social structure (
Sozialstrukturatlas) of Dortmund which is a collection of administratively collected data reflecting social inequalities and differences in the population [
19]. These are grouped into the dimensions employment status, demography, income, welfare, and housing. A full description of the explanatory variables is given in Table
1. In order to account for multicollinearity, an initial correlation matrix was examined for high correlations among the variables. Variables with a high correlation (>0.8) were excluded from further regression analyses. For the three 2-year time periods, the data of 2008, 2010 and 2012, respectively, were included in the model, and all variables were dichotomized according to their median value. Following the suggestions of Rothman et al. [
20-
21] each covariate was fitted separately and model fit was assessed using the changes in deviance information criterion (DIC) (smaller values of DIC indicating more explained variance and better fit). A multivariable model was fit by selectively including variables, starting with those that showed the lowest DIC in univariable analyses, until the DIC could be no further reduced. For the Bayesian inference, the integrated nested Laplace approximation (INLA) approach was used as introduced b
y Rue et al. [
22] and implemented in the R package R-INLA [
21,
23,
24]. The Bayesian inference was also used to report the resulting odd ratios (OR) as point estimate (posterior mean) and 95 % credibility intervals (CI) as a quantification of parameter uncertainty. All computations and visualizations were done in R v. 3.0.2 [
25].
Table 1
Summary statistics of included variables in the 62 statistical districts and the three time periods
Employment/Unemployment |
Employment rate [%]
| 48.2; 48.4; 50.1 | Proportions of regular employees of the employable population (>15 to <65 years) with primary residence in Dortmund. |
|
Employment trend [%]
| 3.5; 5.9; 7 | Number of regular employees with primary residence in Dortmund in a five-year trend/comparison in percent. |
|
Unemployment rate (foreigner) [%]
| 12.6; 12.5; 12.7 | Proportion of unemployed, foreign persons of the employable, foreign population (>15 to <65 years) in percent. |
|
Unemployment rate (<25 aged) [%]
| 4.2; 4.5; 4.3 | Proportion of unemployed young persons (15 to < 25 years) of the population in the same age group. |
|
Unemployment rate (long-term) [%]
| 44.8; 41.3; 44.7 | Proportion of long-term unemployed persons (>12 months) to all unemployed persons in percent. |
Demography |
Female population [%]
| 51.7; 51.5; 51.5 | Proportion of women to all inhabitants with primary residence in Dortmund. |
|
Foreign residents [%]
| 7.5; 7.1; 7.7 | Proportion of persons without German nationality to all inhabitants with primary residence in Dortmund. |
|
Youth quotient
| 20.5; 20; 19 | Number of persons aged < 15 years per 100 persons aged 15 to < 65 years. |
|
Quotient of elderly
| 32.7; 32.7; 31.6 | Number of persons aged > 65 years per 100 persons aged 15 to < 65 years. |
|
Birth rate
| 8; 7.4; 7.5 | Number of births per 1000 inhabitants with primary residence in Dortmund by December 31. of each year. |
|
Mortality rate
| 10.4; 10.5; 10.5 | Number of deaths per 1000 inhabitants with primary residence in Dortmund by December 31. of each year. |
Social affairs |
Long-term social welfare (“Hartz IV”) rate [%]
| 10.3; 11.9; 11.6 | Proportions of unemployed (>12 months) persons (<65 years) with demand for basic financial benefits (Arbeitslosengeld II) of the residential population. |
Living/habitation |
Social housing rate [%]
| 8; 5.4; 6.2 | Proportion of council-sponsored apartments on all rental appartements in percent. |
|
Living space per person
| 39.6; 40.2; 40.4 | The total living space in [m2] divided by the number of inhabitants with primary and secondary residence in Dortmund. |